The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal (...) algebraic study of their corresponding algebraic semantics. Firstly, we present a Hilbert-style axiomatization of a new logic called "Dually hemimorphic semi-Heyting logic" (\(\mathcal{DHMSH}\), for short), as an expansion of semi-intuitionistic logic \(\mathcal{SI}\) (also called \(\mathcal{SH}\)) introduced by the first author by adding a weak negation (to be interpreted as a dual hemimorphism). We then prove that it is implicative in the sense of Rasiowa and that it is complete with respect to the variety \(\mathbb{DHMSH}\). It is deduced that the logic \(\mathcal{DHMSH}\) is algebraizable in the sense of Blok and Pigozzi, with the variety \(\mathbb{DHMSH}\) as its equivalent algebraic semantics and that the lattice of axiomatic extensions of \(\mathcal{DHMSH}\) is dually isomorphic to the lattice of subvarieties of \(\mathbb{DHMSH}\). A new axiomatization for Moisil's logic is also obtained. Secondly, we characterize the axiomatic extensions of \(\mathcal{DHMSH}\) in which the "Deduction Theorem" holds. Thirdly, we present several new logics, extending the logic \(\mathcal{DHMSH}\), corresponding to several important subvarieties of the variety \(\mathbb{DHMSH}\). These include logics corresponding to the varieties generated by two-element, three-element and some four-element dually quasi-De Morgan semi-Heyting algebras, as well as a new axiomatization for the 3-valued Łukasiewicz logic. Surprisingly, many of these logics turn out to be connexive logics, only a few of which are presented in this paper. Fourthly, we present axiomatizations for two infinite sequences of logics namely, De Morgan Gödel logics and dually pseudocomplemented Gödel logics. Fifthly, axiomatizations are also provided for logics corresponding to many subvarieties of regular dually quasi-De Morgan Stone semi-Heyting algebras, of regular De Morgan semi-Heyting algebras of level 1, and of JI-distributive semi-Heyting algebras of level 1. We conclude the paper with some open problems. Most of the logics considered in this paper are discriminator logics in the sense that they correspond to discriminator varieties. Some of them, just like the classical logic, are even primal in the sense that their corresponding varieties are generated by primal algebras. (shrink)

This paper is a contribution toward developing a theory of expansions of semi-Heyting algebras. It grew out of an attempt to settle a conjecture we had made in 1987. Firstly, we unify and extend strikingly similar results of [ 48 ] and [ 50 ] to the (new) equational class DHMSH of dually hemimorphic semi-Heyting algebras, or to its subvariety BDQDSH of blended dual quasi-De Morgan semi-Heyting algebras, thus (...) settling the conjecture. Secondly, we give a criterion for a unary expansion of semi-Heyting algebras to be a discriminator variety and give an algorithm to produce discriminator varieties. We then apply the criterion to exhibit an increasing sequence of discriminator subvarieties of BDQDSH . We also use it to prove that the variety DQSSH of dually quasi-Stone semi- Heyting algebras is a discriminator variety. Thirdly, we investigate a binary expansion of semi-Heyting algebras, namely the variety DblSH of double semi-Heyting algebras by characterizing its simples, and use the characterization to present an increasing sequence of discriminator subvarieties of DblSH . Finally, we apply these results to give bases for “small” subvarieties of BDQDSH , DQSSH , and DblSH. (shrink)

We investigate the class of those algebras in which is a de Morgan algebra, is a quasi-Stone algebra, and the operations \ and \ are linked by the identity x**º = x*º*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.

In this note we introduce the variety $${{\mathcal C}{\mathcal D}{\mathcal M}_\square}$$ of classical modal De Morgan algebras as a generalization of the variety $${{{\mathcal T}{\mathcal M}{\mathcal A}}}$$ of Tetravalent Modal algebras studied in [ 11 ]. We show that the variety $${{\mathcal V}_0}$$ defined by H. P. Sankappanavar in [ 13 ], and the variety S of Involutive Stone algebras introduced by R. Cignoli and M. S de Gallego in [ 5 ], are examples of (...) classical modal De Morgan algebras. We give a representation theory, and we study the regular filters, i.e., lattice filters closed under an implication operation. Finally we prove that the variety $${{{\mathcal T}{\mathcal M}{\mathcal A}}}$$ has the Amalgamation Property and the Superamalgamation Property. (shrink)

An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ ≈ x ∧ y, x ∧ ≈ x ∧ [ → ], and x → x ≈ 1.

In this paper we prove that the free algebras in a subvariety equation image of the variety equation image of semi-Heyting algebras are directly decomposable if and only if equation image satisfies the Stone identity.

In this paper we pursue the study of the variety of m -generalized Łukasiewicz algebras of order n which was initiated in [1]. This variety contains the variety of Łukasiewicz algebras of order n . Given , we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain Łukasiewicz algebra of order n and for each congruence on A we find a description via the corresponding Stone filter. We characterize the (...) principal congruences on A via Stone filters. In doing so, we obtain a polynomial equation which defines the principal congruences on the algebras of . After showing that for m > 1 and n > 2, the variety of Łukasiewicz algebras of order n is a proper subvariety of , we prove that is a finitely generated discriminator variety and point out some consequences of this strong property, one of which is congruence permutability. (shrink)

In this note we introduce and study algebras of type such that is a bounded distributive lattice and ⌝ is an operator that satisfies the condition ⌝ = a ⌝ b and ⌝ 0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi-Stone algebras.

In this paper we obtain characterizations of subalgebras of Heyting algebras and De Morgan Heyting algebras. In both cases we obtain these characterizations by defining certain equivalence relations on the Priestley-type topological representations of the corresponding algebras. As a particular case we derive the characterization of maximal subalgebras of Heyting algebras given by M. Adams for the finite case.

In this paper we use Hobby's duality for semi-De Morgan algebras, to characterize those algebras having only principal congruences in the classes of semi-De Morgan algebras, demi-pseudocomplemented lattices and almost pseudocomplemented lattices. This work extends some of the results reached by Beazer in [3] and [4].

We determine the number of non‐isomorphic semi‐Heyting algebras on an n‐element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non‐isomorphic semi‐Heyting chains of a given size in some important subvarieties of the variety of semi‐Heyting algebras that were introduced in [5]. We further exploit this recursive method to (...) calculate the numbers of non‐isomorphic semi‐Heyting chains with n elements such that removing the mth element () we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi‐Heyting chain with elements can be extended to a n element semi‐Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers that provides some extra information. (shrink)

Extending the relation between semi-Heyting algebras and semi-Nelson algebras to dually hemimorphic semi-Heyting algebras, we introduce and study the variety of dually hemimorphic semi-Nelson algebras and some of its subvarieties. In particular, we prove that the category of dually hemimorphic semi-Heyting algebras is equivalent to the category of dually hemimorphic centered semi-Nelson algebras. We also study the lattice of congruences of a (...) dually hemimorphic semi-Nelson algebra through some of its deductive systems. (shrink)

In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes’ representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas–Dunn duality and introduce the categories of 2spaces and 2spaces\. The categories of 2spaces and 2spaces\ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category (...) of Stone spaces with respect to the category of Boolean algebras. Actually, the aim of this work is to show that these categories are, in fact, dually equivalent. (shrink)

De Morgan's Formal Logic, which was published on virtually the same day in 1847 as Boole's The Mathematical Analysis of Logic, contains a logic of complex terms (LCT) which has been sadly neglected. It is surprising to find that LCT contains almost a full theory of Boolean algebra. This paper will: (1) provide some background to LCT; (2) outline its main features; (3) point out some gaps in it; (4) compare it with Boole's algebra; (5) show that it is (...) a lattice-theoretical formulation of Boolean algebra; (6) discuss some issues of historical priority; and (7) conclude with the puzzle of LCT's lack of influence. (shrink)

In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.

In this paper we exhibit a non-finitely based, finitely generated quasi-variety of De Morgan algebras and determine the bottom of the lattices of sub-quasi-varieties of Kleene and De Morgan algebras.

Varieties like groups, rings, or Boolean algebras have the property that, in any of their members, the lattice of congruences is isomorphic to a lattice of more manageable objects, for example normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras.algebraic logic can explain these phenomena at a rather satisfactory level of generality: in every member A of a τ-regular variety ������ the lattice of congruences of A is isomorphic to the lattice (...) of deductive filters on A of the τ-assertional logic of ������. Moreover, if ������ has a constant 1 in its type and is 1-subtractive, the deductive filters on A ∈ ������ of the 1-assertional logic of ������ coincide with the ������-ideals of A in the sense of Gumm and Ursini, for which we have a manageable concept of ideal generation. However, there are isomorphism theorems, for example, in the theories of residuated lattices, pseudointerior algebras and quasi-MV algebras that cannot be subsumed by these general results. The aim of the present paper is to appropriately generalise the concepts of subtractivity and τ-regularity in such a way as to shed some light on the deep reason behind such theorems. The tools and concepts we develop hereby provide a common umbrella for the algebraic investigation of several families of logics, including substructural logics, modal logics, quantum logics, and logics of constructive mathematics. (shrink)

Modal pseudocomplemented De Morgan algebras were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 53, 1, pp. 65–79, and they constitute a proper subvariety of the variety of pseudocomplemented De Morgan algebras satisfying xΛ* = *))* studied by H. Sankappanavar in 1987. In this paper the study of these algebras is continued. More precisely, new characterizations of mpM-congruences are shown. (...) In particular, one of them is determined by taking into account an implication operation which is defined on these algebras as weak implication. In addition, the finite mpM-algebras were considered and a factorization theorem of them is given. Finally, the structure of the free finitely generated mpM-algebras is obtained and a formula to compute its cardinal number in terms of the number of the free generators is established. For characterization of the finitely-generated free De Morgan algebras, free Boole-De Morgan algebras and free De Morgan quasilattices see: [16, 17, 18]. (shrink)

The study of the theory of operators over modal pseudocomplemented De Morgan algebras was begun in papers [20] and [21]. In this paper, we introduce and study the class of modal pseudocomplemented De Morgan algebras enriched by a k-periodic automorphism -algebras). We denote by \ the automorphism where k is a positive integer. For \, the class coincides with the one studied in [20] where the automorphism works as a new unary operator which can be (...) considered as a negation. In the first place, we develop an algebraic study of the class of \-algebras; as consequence, we prove the class \-algebras is a semisimple variety and determine the generating algebras. After doing the algebraic study and using these properties, we built two families of sentential logics that we denote with \ and \ for every k. \ is a 1-assertional logic and \ is the degree-preserving logic both associated with the class of \-algebras. Working over these logics, we prove that \ is paraconsistent with respect to the de Morgan negation \, which is protoalgebraic and finitely equivalential but not algebraizable. In contrast, we prove that \ is algebraizable, sharing the same theorems with \, but not paraconsistent with respect to \. Furthermore, we show that \ and \ are paracomplete logics with respect to \ and \ and paraconsistent logics with respecto to \, for every k. (shrink)

SummaryThe germs of future development, contained in Aristotle's logical works, are indicated, and their influence on the later evolution of logic is explained.The history of symbolic logic since Boole's Mathematical analysis and De Morgan's Formal logic, both of which were published in 1847, is divided into four approximately subsequent phases, viz.:1. algebra of logic; this phase is characterized by Boole's work;2. logical foundation of mathematics; this phase is characterized by Frege's, Peano's and Russell's work, by the discovery of the (...) antonomies of logic and set theory, by the Couturat‐Poincaré debate and by the rise of Brouwer's intuitionism;3. intuitive metamathematics, concentrating in Hilbert's attempts towards a consistency proof for classical analysis; the discovery of Gödel's theorem necessitated a change of policy;4. axiomatic methodology, deriving from Hilbert's metamathematics and culminating so far in Tarski's semantics. — E. W. B. (shrink)

. Relational semantics for nonclassical logics lead straightforwardly to topological representation theorems of their algebras. Ortholattices and De Morgan lattices are reducts of the algebras of various nonclassical logics. We define three new classes of topological spaces so that the lattice categories and the corresponding categories of topological spaces turn out to be dually isomorphic. A key feature of all these topological spaces is that they are ordered relational or ordered product topologies.

We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of l-algebras (...) and filtering unification. We consider examples of frontal Heyting algebras, in particular Heyting algebras with the successor, γ and G operations as well as expansions of some commutative integral residuated lattices with successor operations. (shrink)

Given a variety we study the existence of a class such that S1 every A can be represented as a global subdirect product with factors in and S2 every non-trivial A is globally indecomposable. We show that the following varieties (and its subvarieties) have a class satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan (...) algebras, etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean. (shrink)

In this paper we shall introduce the variety WQS of weak-quasi-Stone algebras as a generalization of the variety QS of quasi-Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬-lattices to give a duality for WQS. We prove that a weak-quasi-Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice (...) congruences. We will also determine the simple and subdirectly irreducible algebras. (shrink)

A sequent calculus S for the variety tqBa of all topological quasi-Boolean algebras is established. Using a construction of syntactic finite algebraic model, the finite model property of S is shown, and thus the decidability of S is obtained. We also introduce two non-distributive variants of topological quasi-Boolean algebras. For the variety TDM5 of all topological De Morgan lattices with the axiom 5, we establish a sequent calculus S5 and prove that the cut elimination holds (...) for it. Consequently the decidability of S5 is established. Furthermore, this proof-theoretic method is applied to some subvarieties of TDM5. (shrink)

Poor people predominate as a subgroup of those who take part in healthy volunteer research. They are subjected to minimised but unknown risks and unpleasant burdens so that the safety of new medicines can be evaluated. This is prima facie unfair especially given that the poor are often unable to access expensive medicines. Although participants in this kind of research often do receive compensation for their time, these payments are usually capped at a very low level. This paper defends (...) a version of a reimbursement model for the payment of research subjects. This model is practical, would benefit those without an income who take part in research, and would make it possible for those in regular work to take part in phase 1 research. (shrink)

The aim of this paper is to give a certain algebraic account of truth: we want to define what we mean by De Morgan-valued truth models and show their existence even in the case of semantical closure: that is, languages may contain their own truth predicate if they are interpreted by De Morgan-valued models. Before we can prove this result, we have to repeat some basic facts concerning De Morgan-valued models in general, and we will introduce a (...) notion of truth both on the object- and on the metalanguage level appropriate for such models. The definitions and the existence theorem are extensions of Kripke's, Woodruff's, and Visser's concepts and results concerning three- and four-valued truth models. (shrink)

Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B〉 〈B|. An exact “correspondence” exists between the Born-Jordan-Dirac “wavelike” algebra of transition amplitudes and the 1774 Laplace algebra of conditional probabilities, where the intermediate summations |B) (...) (B| were over “real hidden states.” While the latter used conditional (or transition) probabilities (A|C) = (C|A), the former uses transition (or conditional) amplitudes 〈A|C〉 = 〈C|A〉*. The formal parrallelism breaks down at the level of interpretation because (A|C) = |〈A|C〉|2. CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is 〈Ψ| U |Φ〉 = 〈Ψ| UΦ〉 = 〈ΦU|Φ〉, with |Φ〉 denoting a preparation, |Ψ〉 a measurement, and U the evolution operator. The transformation |Ψ〉 = |UΦ〉 or |Φ〉 = |U−1Ψ〉 exchanges the “preparation representation” and the “measurement representation” of a system and is ancillary in the formalization of the quantum chance game by the “wavelike algebra” of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude 〈A|C〉 = Σ 〈A|B〉〈B|C〉 between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility 〈A|C〉 = 〈C|A〉* implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of “blind statistical retrodiction”—that is, of “final cause.”. (shrink)

continent. 2.1 (2012): 29–35. Translated by Vincent W.J. van Gerven Oei from Jeroen Mettes. "Politieke Poëzie: Enige aantekeningen, Poëtica bij N30 (versie 2006)." In Weerstandbeleid: Nieuwe kritiek . Amsterdam: De wereldbibliotheek, 2011. Published with permission of Uitgeverij Wereldbibliotheek, Amsterdam. L’égalité veut d’autres lois . —Eugène Pottier The modern poem does not have form but consistency (that is sensed), no content but a problem (that is developed). Consistency + problem = composition. The problem of modern poetry is capitalism. Capitalism—which has no (...) image: the unrepresentable Idea of “everything.” The problem is that a poem cannot be justified. There is no excuse for it. Political poetry— pure poetry—has to be problematic, though not in a mannerist way. Yes, its problem is first its own problem—poetry’s existence in the same world as the newspaper—but therefore also always everybody’s problem (the problem of any world at all). The cult of the sublime points at a suspect desire for transcendence, nostalgia for paradise lost (the womb?). Melancholia of the post-. But a problem neither sorrows nor mourns, it is alive, and the fact that it is alive is the problem—the problem for death (rigidity, the status quo). Our symbols and ideologies do not hide any god: symbolic = state; imaginary = human; real = money. Problem: the possibility of communal speech (poetry) in the absence of a “we.” Or: what is a “we” that is not a collective subject (or in any case is not a volonté générale )? What is a universal history that is not a History? This work was started in the shade of the anti-globalization protests at the end of November 1999. I considered N30 to be the closure of the nineties, of my adolescence, and of the a seemingly total extinction of social desire. From the beginning I was skeptical about the alterglobalization movement as the avant-garde of a new politics, but something was happening . Maybe this event did not show that, as the slogan would have it, “another world” is possible, but for me it indicated that such possibility was at least still possible. That naked possibility is carrying forward. And if the fundamental tone of this work sounds more desperate than utopian, this is not caused by the catastrophic sequence that since 1999 has plunged us ever deeper into the right-wing nightmare—a nightmare that this work also gives an account for—but because my hope as yet remains empty. Composition . Composition is no design, but the production of an autonomous block of affects (i.e. a POEM), rhythmically subtracted from the language of a community. A poem does something. Is something. New Sentence . Choosing the non sequitur as compositional unit has the advantage that an abstract composition is subjected to the stress of concrete, social references. Where there is a sentence, there is always a world. (This does not hold necessarily for words on their own.) And where sentences collide, something akin to a textual civil war takes place. It is not about “undermining” whatever, or de-scribing the raging global civil war, but about writing social (or even: ontological) antagonism -- including all its catastrophic and utopian possibilities. Minor resistance. Why would poetry be the no protest zone par excellence? It is nothing but protest, not simply qua “content,” but in its most fundamental essence: rhythm. Rhythm is resistance against language, time, and space, and the basis of (what we will continue to call) autonomy. Rhythm starts with the anti-rhythmic caesura as Hölderlin remarked about Sophocles, a disruption of the quotidian drone. The destruction of everything that is dead inside of us. The noise of the avant-garde has never been the representation of the noise of (post)modernity (from the television or shopping mall), but the sober noise of the systematic exchange of an unbearable worldview. The poet does not describe, but looks for a way out: There is a Grain of Sand in Lambeth that Satan cannot find Nor can his Watch Fiends find it, tis translucent & has many Angles But he who finds it will find Oothoons palace, for within Opening into Beulah every angle is a lovely heaven William Blake was not mad. And there has always been only one poetry: the poetry of paradise. The principle is that there is something in art (the essentially creative element) that is disgusted by that which, unlike art, does not aim for the supreme. Wonder is not supreme, tranquility is not supreme, beauty is not supreme. Even amusement is not supreme! The supreme is supremely open, “das Einfache,/ Das Schwer zu machen ist” 1 : paradise. That is abstract. Literally. For me it is not about a concrete imagination, an idyll or utopia. There is no doubt a need for that, but it is not so much the supposed lack of imagination or ideals (human rights are ideals), but a fundamental lack of desire (human rights are no desires) that we suffer from, and from which we do not need to remove Nietzsche’s label of “nihilism.” “We.” George Oppen: “ Of Being Numerous asks the question whether or not we can deal with humanity as something which actually exists.” What is less actual than humanity? Nowadays it appears as a lifeless ideology of cynical power politics. Or as what makes one think. It is a shame to be human. The event is the caesura that defines rhythm. Writing toward the event is not the description of the event, but marking an abstract and intense space in which the event may unfold and keep itself. It is a task. “Remember that thou blesseth the day on which I seized thee, because such is thy obligation.” The event is a contraction (or a series of contractions) with its own rhythm and unique qualities. It is more than an explosion or demonstration. But at the same time less. The endless repetition of images and stories in the media points to a fear for the indeterminate and indeterminable void of the event. In the end there is nothing to see. We do not live in disaster’s shade or miracle’s light, but rather in the rhythm, which is contracted time, having little to do with omnipresent representations. For this book I did not intend a rhythm of evental representations (a narrative rhythm), but a rhythm which would be an event itself , because it draws the border between artwork and history. My desire for a direct engagement with the “extra-textual reality” has nothing to do with the representation of “rumor in the streets.” (What has less street cred than representation?) Naturally, a poem is no historical event and does not change anything. But a poem is a part of history that wants to be repeated forever, constructed in such a way that it is worthy of repetition. It is a part of desire (composition) made consistent (durable). The “historical event” flares up and burns down, and has to burn down to be effective. The leftovers are images and stories (representations), History—no event. The artwork—that is the ambition— remains event (though monumental and inefficient/inoperable). (No wonder that a historical singularity, a revolution, reminds us of a work of art; the resurrection yearns for a judgment, an affirmation; everything depends on it.) Hence the title does not summarize the book, let alone contract its “content” into a quasi-transcendental signifier. The title is juxtaposed to the book, like everything else inside the book, and in that relation it precisely forms a part of it. The ideal work is an open whole, lacking nothing but to which everything may be added. I have been interested in this “everything,” the world, or as I said above: capitalism. “Everything” is not the space for “wonder”—a code word, a shibboleth for petty bourgeois imagination (I recognize myself in the strangest things, a speaking dog, a canal, a pond standing straight—oh my god). No. The world is a social world, not YOUR world, poet. Power is number one. I will call “Dutch,” or “shitty,” whatever denies this power. That hurts, but this pain is an expression of the desire in the world to write another world, or as Blanchot says, “the other of all worlds” 2 : the world. Not as what “is there,” but rather as that which urges for an escape from what “is.” This is a testament of how radical reality has become, for me—or rather, a writing body—in a having-been-written. I am not interested in the problem of “meaning” as misunderstood by literary scholarsi: “order” in “chaos,” “symbolization.” Bullshit. What is there, hop, hope, now: the meaning of the taste in my mouth. Bullshit. I am not interested in the frustration of interpretation; I am writing for readers who do not want to interpret. I do not know how many “professional readers” will hear the music of a paragraph like: Sun. Sushi. Volvo. I hope more than I would think. There is a suggestion (or rather, an actual production) of speed and infinitive owing to the absence of plosives, i.e. articulations such as /k/, /t/, or /p/. Can you hear the slick suaveness? Driving car dark, vocal chiaroscuro of the word “sushi.” The unstressed /i/ stands in the middle of dark vowels and thus acquires its own special out of focus , like a momentary flash or brilliance—an obscure light. It is not about recognizing a story, but about avoiding any story whatsoever: the car disappears in the glow, cars and raw fish have nothing in common except their articulation in a language that brings them together, blurring them. A world appears in its disappearance. For a moment, light is a metaphor for language, though it cannot be reduced to tenor. It is not necessary to be a linguist or philosopher to hear this—a “difficult” poem all too often becomes an allegory of its own impenetrable being-language. The only demand: leave your hermeneutical fetish at home. This was no interpretation. Most shit has been stolen etcetera. That is no longer interesting. You cannot shoot the body with information and let your lawyers reclaim the bullets. So every sentence has been stolen. Also the ones “out” “of” “my” “head.” Why would I be allowed to steal from myself and not from others? Man takes what he needs to move forward. Whatever he encounters, finds in front of him, “occurs” to him. The writer as text editor, or singing pirate. Nothing new here. Important difference with for example Sybren Polet’s 4 montage technique: anti-thematicism. Most of the time ferocious citation from whatever I was reading, listening to, ended up in, and so on. I wrote chapter 12 on my laptop while watching CNN. On the air instead of en plein air . I often employed search engines to generate material. Chapter 20 offers the purest example of this. Often I stop recognizing a particular citation after some time. It is not uncommon for a stolen sentence to conform itself to the paragraph in which it finds itself. Sometimes I nearly arbitrarily replace words. Arbitrariness as a guarantee for absolute democracy. It is a poetics of the non sequitur : a conclusion that does not follow from the premises, the strange element in the discourse. A discourse of strangers. No logical, narrative, thematic unity. There is unity in speed/flight. It has to be read linearly, but not necessarily (not preferably) from beginning to end. The shortest distance between two points is a straight line, but this line precedes every point. The middle, the acceleration, comes first. A point occurs where two lines cross. It has been written from up close, at the level of the tension between sentences. Nothing to be seen from a distance: no form except the exchange of form, no geometrical or mythical meaning. You have to get in, “groping toward a continuous present, a using everything a beginning again and again” (Stein). 5 In Dutch, experimental poetry has been mainly dense: a small rectangular form filled with a maximum amount of poetic possibility. But at the moment the poem starts to relax, the anecdotical content seems to increase. This is what is called “epic”: long, narrative. I believe that an epic is more than that, in fact something completely different. An epic is “a poem including history,” 6 a long poem tied up with the life of community, that as a whole does not need to be narrative. The American poets of the twentieth century (Pound, Williams, Zukofsky, Oppen, Olson, Silliman) have put the epic back on the map by interpreting the poem itself as a map, and writing it as navigation. They have invented the experimental epic, a genre that has generated little original following in “our” poetry. N30 is the middle part—“always start in the middle”—of a trilogy, the contours of which remain as of yet unclear, although each episode investigates one of the three “ecstasies of time”—past, present, future—concerning society X. N30 concerns itself with the PRESENT: not with the description of actual facts but of the rhythm and the intense depth in which facts appear to us. Where are we? We are camping in the desert. Sometimes we are looking at the stars. As opposed to maximum density and minimal tension (a characteristic of most (post-)experimental lyricism), I have sought a minimal density and maximum tension in this book, considered as a long non-narrative prose poem. On the one hand, the minimal density is obtained by the inherent formlessness of prose, on the other hand by the conscious refusal of any active (formal, non-rhythmic) synthesis: the poem tells nothing, shows nothing, has no theme. I did not seek maximum tension either by loading the quotidian with epiphanic radioactivity (“wonder,” confirmation from above), or by means of the intensity of the linguistic structure. I want an abstract tension, but social in its abstraction, in other words, not neutralized by and subjected to Form. Instead of form (transcendent): composition (immanent). The concept is series. Ideal: every unit is necessary for the efficacy of the others and the whole, their relation is purely linear, i.e. non-hierarchic, non-syllogistic, non-discursive, non-narrative. Sentence related to sentence like paragraph to paragraph and chapter to chapter; the whole means nothing and represents nothing. Inside the sentence: syntax (Chomsky’s tree, a type of parallel circuit), outside: parataxis (coordination, an asyntactic line through language and world). I consider duration—the energy of duration (rhythm)—to be the fundament of a poem, the temporal inclination to delimit a “space.” Being as consistency, its consistency. A spatial part of time is not merely a metaphor for an inevitable trajectory, an inescapable time, something like “our time.” Not merely—because rhythm comes from language and is not projected onto it; the poem derives from the world like a scent and a color and a life from a flower. A series, a sequence: nothing potential, but truly infinite—the movement of an infinitude. The infinite series = everything minus totality. That means that there is no container—no Form, no Self, no Image, no Structure, not even a Fragment—just “the prose of the world.” No representation, but also no staging of the impossibility of representation (the postmodern sublime). These are no fragments, no image of a fragmented world or personality, no cautious incantations around the Void. It does not exist. It is a movement. Buying bread, a flock of birds, a bomb falling—they do not depict or represent anything, not literally, not metaphorically. There is an Idea, which is however nothing more than a rhythm, in the same way that capitalism is nothing more than a pure function. Parataxis: the white space between two sentences stresses, which is nevertheless always there, also between words, even between letters: the out of focus of idle talk, the gutter, the irreducible Mallarméan mist which renders even the seemingly most transparent text legible. The white space suggests a neutral medium for free signification, a substance of language. A non sequitur is an element from a foreign discourse, which stresses the white space as space, and problematizes freedom for supra-sentential signification. I start by withdrawing material, leaving the initiative to the sentences. In general a word presupposes less often a discourse than a sentence. What discourse is presupposed by “dog”? We could think of several, but why would we? It is more probable that, when faced with the naked word, we think of its naked (dictionary) meaning, of its denotative signified. By means of two simple interventions we may also write the word as sentence: Dog. In no way this suggests the discourse from which this sentence originates, but in any case we’re presupposing one. This is shown by questions like: “Whose dog? Who’s a dog? What kind of dog?” Etc. (Sentences are question marks.) A sentence implies/is a microcosm—a subject, a verb, an object, and so on. Even an incomplete or ungrammatical sentence does so. My main fascination while writing this book is the worldly and social aspect of language, an aspect that often becomes invisible, or rather, transparent in narrativity—the stretching of sentences into stories. Narrativity organizes a new discourse and a new world, and places a sometimes all too dispersing relation of transparence in between. The conventional novel is the brothel of being. I do not intend to prohibit brothels, and I have certainly not intended to write an anti-novel (THIS IS A POEM), but I do consider narrativity (in general, in poetry, in the news, in daily life) to be ontologically secondary with regard to an immediate being in the world through sentences, also if the latter have been withdrawn from a narrative or otherwise externally structured discourse (which in that case would therefore be chronologically primary ). Naturally, two or more sentences are always in danger of telling stories or arguing, just like the world is always in danger of becoming an objective representation, facing us, strangers. That is why need to wage war—against representation and against the interface, against interaction. AGAINST THE “READER.” To the extent that a sentence is worldly, writing is a condensed global war, and in so far as there is ultimately only one world and one open continuum of languages, it is a global civil war. Nice subject for an epic. The elaboration of a singular problem—prose as the outside of poetry, the form of the novel as purely prosodic composition scheme—“expresses” the universal problem: capitalism as Idea of the world vs. poetry as language of an (im)possible community. The paragraphs are blocks of rhythmically contracted social material. By choosing the sentence as the basic compositional component, an abstract whole may contain social sounds, without telling a story or showing an image. Composition is subrepresentative —a rhythmic, passive synthesis, or rather: a synthesis of syntheses. I never write large blocks of prose in one sitting, because there is no obvious organizational vector —plot, theme, conscience—outside the inherent qualities of the material itself. Usually I write down one sentence, sometimes two, but rarely more than three. Those sentences are usually placed in the text which I am editing at the time. In fact, there is no original composition, new chapters split off from chapters which became too long during the editing process. (Revision mainly consists of adding and inserting, displacing and dividing; only during the last phase, when the text has gained enough consistency, there may be subtraction to tighten the composition; each chapter requires a season of daily revision). This constant revision, accompanied by a continuous influx of collective background noise (to speak with Van Bastelaere), 7 makes every chapter a block condensed (“historical” and “personal”) time. The block itself is a-personal and a-historic; it is ontologically autonomous. If there is such a thing as a spirit of the times, I do not try to offer an image of it, but rather to cancel something of it by erecting a monument of its own excrement within its own boundaries. Tuning and dis-tuning , “in de taal der neerslachtigen een eigen geluid doen klinken,” 8 in other words, desiring in an Elysian way. In this sense I have intended to be able to write a political poetry. The ultimate political poem is the epic, “the tale of the tribe.” I consider N30 to be a prolegomenon to a future epic (of which it in the end will form a part a structural moment, as introduction-in-the-middle), an extended pile on top of an epic as narrative, a question of the tribe and question of its history. I was burdened by too much satire, too much bullshit. But: satire willy-nilly = the only justifiable satire. Against the abstract universalism of the market (“globalism”): concrete disgust, a positive way of saying “No.” Moreover, disgust is a specifically total attitude, which ultimately concerns the world as a whole. I hate this or that, but I am disgusted by EVERYTHING (when I am disgusted), and so it appears that satire is in fact related to the epic, in so far as it concerns society, the cosmos, history. Maybe it is no coincidence that the Dutch literary canon knows no great poet of disgust; what could be more fearful to us than society, the cosmos, and history? The T-tendency (T from Tollens 9 ) clearly points into the direction of the small, friendly, ironic, melancholic, acquiescent, wondrous, and so on. The anti-political, anti-cosmic, anti-historical. (Why am I so philosophical? To scare away the Dutchies.) And most of all: the “poetical” (the pseudo-mysticism from the backyard). Yes, the N in N30 also stands for the Netherlands (just like 30 indicates the number of chapters). I was not in Seattle, I do not live in Iraq. But is not the whole world bleeding to death on Dutch paving stones? Let’s hope that we mowed away something with this total satire, also “in myself.” The arrogant stupidity that definitely thinks to know the essence of freedom (the free development of esthetic needs inside the void), that cannot take anything serious, only believes in the disciplined bestiality of the individual (“norms and values”) and the mere functioning of a social factory which finds no justification whatsoever outside its functioning (“get to work”)… Who knows. A certain aimed destruction leaves grooves and craters, mapping out a next adventure. Pound’s periplum : sailing while mapping the coasts. Immanent orientation. The terrain changes with the map, history changes with the poem. Maps never merely organize the chaos, transcendent schemes imposed on a formless Ding-an-sich . They organize from within, surfing. But they are most of all routes back into the chaos or forward to paradise (final identity of chaos and paradise; Schlegel: “ Nur diejenige Verworrenheit ist ein Chaos aus der eine Welt entspringen kann ”10). A poem is not only a piece of history, it is also a flight from history. Maps give chaos to the form of reality , open escape routes, break through representations, make us shivery and dazed. Paradise is immanent to a fleeting desire. History is the history of labor—this is Adam’s curse—and the poet works too: For to articulate sweet sounds together Is to work harder than all these, and yet Be thought an idler by the noisy set Of bankers, school masters, and clergymen The martyrs call the world 11 But: the poet works in paradise. The paradox of the artwork, the work that is no work, the piece of history that cannot be reduced to History—this is explained by The Space of Literature , a virtual space, an autonomous rhythm, not outside, but in the midst of the noise, a piece of paradise in hell, a postcard from the vale of tears addressed to paradise, to X. Political poetry means: a poetry that dares to think about itself, about its language and about its world and about the problematic relation between both, which is this relation as problem. A poetry that thinks at all, articulates its problem. It has nothing to do with journalism or morality or debate, let alone the law or the state. It has nothing to do with “criticism” if this means the replacement of incorrect representations by other, more correct representations. It has something to do with ethics in the sense of learning to live. It has something to do with the community and the language of the community (whichever that may be) and the role of the poet regarding the community. It concerns justice without judgement or measure. In the end the just word is just a word , to paraphrase Godard: it is from a future that is unimaginable. It Is no rational engagement, but an aversion against everything that obstructs life, and love for everything what is worthy of having been loved. The world is engaged with me, not the other way round. First Exodus, then Sinai. A desire does not start with an agenda. To answer the question whether I am really so naive as to want to change the world: “We only want the world.” Justice is the world appealing to us to liberate it from all possible chains, from each organization and inequality, to be it, smooth, equal, under a clear sky—a desert and a people in a desert. That moment between Egypt and the Law. It is not a revolution, but the sky above the revolution. Poetry = the science of escape. There is no art that we already know. The weakness of modernistic epic poetry seems to me to be the unwillingness to completely abandon narrative as a structural principle, in favor of a composition “around” or from an event. The China Cantos and Adams Cantos are the low point, and the Pisan Cantos the high point of Pound’s poetry. Two types of research: archival representation of the past vs. ontology of the present (which virtually presupposes the entire history). Presupposing an event means that it is impossible for the poet to stage his own absence, but in no way makes the work personal. An event is the unknown, the new invading into the business as usual, so also the personal. The question heading this research is not: “Who am I?” but “What is happening?” The book is as little illegible as Mondrian’s work is invisible. Form is of interest only to the extent that it empowers liberation. Ron Silliman So no formalism, but what it means to live in this world and to have a future in it. I want something that holds together that’s not smooth. Bruce Andrews The past above, the future below and the present pouring down: the roar, the roar of the present, a speech— William Carlos Williams If my confreres wanted to write a work with all history in its maw, I wished, from the beginning to start all over again, attempting to know nothing but a will to create, and matter at hand. Ronald Johnson NOTES 1) “The easy thing/ that is difficult to make.” Bertold Brecht, Lob des Kommunismus . (All footnotes are the translator’s) 2) Maurice Blanchot, The Space of Literature , trans. Ann Smock. Lincoln/London: University of Nebraska Press (1989), 75. 3) Mettes uses the word “Neerlandicus,” which refers to scholars of Dutch language and literature. 4) Dutch poet. 5) Gertrude Stein. “Composition as Explanation.” A Stein Reader . Ed. Ulla E. Dydo. Evanston, IL: Northwestern University Press (1993), 495-503. 6) Ezra Pound. 7) Flemish poet. 8) “Resounding an original sound in the language of the despondent.” A. Roland Holst, De afspraak . 9) Dutch poet. 10) “Only such a confusion is a chaos which can give rise to a world.” 11) W.B. Yeats, “Adam’s Curse.&rdquo. (shrink)

Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these ‘lattice spacing’ weights do not have to be independent of the direction of the arrow. We use this greater freedom to give a quantum geometric interpretation of discrete Markov processes with transition probabilities as arrow weights, namely taking the diffusion form ∂+f = f for the graph Laplacian Δθ, potential functions q, p built from the probabilities, and (...) finite difference ∂+ in the time direction. Motivated by this new point of view, we introduce a ‘discrete Schrödinger process’ as ∂+ψ = ıψ for the Laplacian associated to a bimodule connection such that the discrete evolution is unitary. We solve this explicitly for the 2-state graph, finding a 1-parameter family of such connections and an induced ‘generalised Markov process’ for f = |ψ|2 in which there is an additional source current built from ψ. We also mention our recent work on the quantum geometry of logic in ‘digital’ form over the field F2 = {0, 1}, including de Morgan duality and its possible generalisations. (shrink)

Some algebraic structures determined by the class σ(þ) of all effects of a Hilbert space þ and by some subclasses of σ(þ) are investigated, in particular de Morgan-Brouwer-Zadeh posets [it is proved that σ(þ n )(n<∞) has such a structure], Brouwer-Zadeh * posets (a quite trivial example consisting of suitable effects is given), and Brouwer-Zadeh 3 posets which are both de Morgan and *.It is shown that a nontrivial class of effects of a Hilbert space exists which is (...) a BZ 3 poset. An ɛ-preclusivity relation on the set of all vectors of þ is introduced, and it is shown that it satisfies the regularity condition also for ε∃ [1/2, 1]. (shrink)

This study evaluated the effects of an exergame program combined with traditional tennis training on autonomic regulation, tennis technique, gross motor skills, clinical reaction time, and cognitive inhibitory control in children. Sixty-three children were randomized into four groups and compared at baseline, 6-month immediately post intervention and at 1-year follow-up post intervention. At 6-month post intervention the combined exergame and regular training sessions revealed: higher breathing frequency, heart rate and lower skin conductance levels during exergaming; additional benefits in the (...) point of contact and kinetic chain elements of the tennis forehand and backhand technique ; negative impact on the shot preparation and the follow-through elements ; higher ball skills ; higher percentages of clinical reaction time improvement and cognitive inhibitory control improvement in both congruent and incongruent trials. The 1-year follow-up test showed no differences in the tennis technique, clinical reaction time and cognitive inhibitory control improvement between groups with the same number of trainings per week. The findings support exergaming as an additional training tool, aimed to improve important cognitive-motor tennis skills by adding dynamics to the standardized training process. Caution should be placed to planning this training, e.g., in a mesocycle, since exergaming might decrease the improvement of specific tennis technique parts of the trainees.. (shrink)

Table of contentsI1 Proceedings of the 4th World Conference on Research IntegrityConcurrent Sessions:1. Countries' systems and policies to foster research integrityCS01.1 Second time around: Implementing and embedding a review of responsible conduct of research policy and practice in an Australian research-intensive universitySusan Patricia O'BrienCS01.2 Measures to promote research integrity in a university: the case of an Asian universityDanny Chan, Frederick Leung2. Examples of research integrity education programmes in different countriesCS02.1 Development of a state-run “cyber education program of research ethics” in (...) KoreaEun Jung Ko, Jin Sun Kwak, TaeHwan Gwon, Ji Min Lee, Min-Ho LeeCS02.3 Responsible conduct of research teachers’ training courses in Germany: keeping on drilling through hard boards for more RCR teachersHelga Nolte, Michael Gommel, Gerlinde Sponholz3. The research environment and policies to encourage research integrityCS03.1 Challenges and best practices in research integrity: bridging the gap between policy and practiceYordanka Krastev, Yamini Sandiran, Julia Connell, Nicky SolomonCS03.2 The Slovenian initiative for better research: from national activities to global reflectionsUrsa Opara Krasovec, Renata SribarCS03.3 Organizational climate assessments to support research integrity: background of the Survey of Organizational Research Climate and the experience with its use at Michigan State UniversityBrian C. Martinson, Carol R. Thrush, C.K. Gunsalus4. Expressions of concern and retractionsCS04.1 Proposed guidelines for retraction notices and their disseminationIvan Oransky, Adam MarcusCS04.2 Watching retractions: analysis of process and practice, with data from the Wiley retraction archivesChris Graf, Verity Warne, Edward Wates, Sue JoshuaCS04.3 An exploratory content analysis of Expressions of ConcernMiguel RoigCS04.4 An ethics researcher in the retraction processMichael Mumford5. Funders' role in fostering research integrityCS05.1 The Fonds de Recherche du Québec’s institutional rules on the responsible conduct of research: introspection in the funding agency activitiesMylène Deschênes, Catherine Olivier, Raphaëlle Dupras-LeducCS05.2 U.S. Public Health Service funds in an international setting: research integrity and complianceZoë Hammatt, Raju Tamot, Robin Parker, Cynthia Ricard, Loc Nguyen-Khoa, Sandra TitusCS05.3 Analyzing decision making of funders of public research as a case of information asymmetryKarsten Klint JensenCS05.4 Research integrity management: Empirical investigation of academia versus industrySimon Godecharle, Ben Nemery, Kris Dierickx5A: Education: For whom, how, and what?CS05A.1 Research integrity or responsible conduct of research? What do we aim for?Mickey Gjerris, Maud Marion Laird Eriksen, Jeppe Berggren HoejCS05A.2 Teaching and learning about RCR at the same time: a report on Epigeum’s RCR poll questions and other assessment activitiesNicholas H. SteneckCS05A.4 Minding the gap in research ethics education: strategies to assess and improve research competencies in community health workers/promoteresCamille Nebeker, Michael Kalichman, Elizabeth Mejia Booen, Blanca Azucena Pacheco, Rebeca Espinosa Giacinto, Sheila Castaneda6. Country examples of research reward systems and integrityCS06.1 Improving systems to promote responsible research in the Chinese Academy of SciencesDing Li, Qiong Chen, Guoli Zhu, Zhonghe SunCS06.4 Exploring the perception of research integrity amongst public health researchers in IndiaParthasarathi Ganguly, Barna Ganguly7. Education and guidance on research integrity: country differencesCS07.1 From integrity to unity: how research integrity guidance differs across universities in Europe.Noémie Aubert Bonn, Kris Dierickx, Simon GodecharleCS07.2 Can education and training develop research integrity? The spirit of the UNESCO 1974 recommendation and its updatingDaniele Bourcier, Jacques Bordé, Michèle LeducCS07.3 The education and implementation mechanisms of research ethics in Taiwan's higher education: an experience in Chinese web-based curriculum development for responsible conduct of researchChien Chou, Sophia Jui-An PanCS07.4 Educating principal investigators in Swiss research institutions: present and future perspectivesLouis Xaver Tiefenauer8. Measuring and rewarding research productivityCS08.1 Altimpact: how research integrity underpins research impactDaniel Barr, Paul TaylorCS08.2 Publication incentives: just reward or misdirection of funds?Lyn Margaret HornCS08.3 Why Socrates never charged a fee: factors contributing to challenges for research integrity and publication ethicsDeborah Poff9. Plagiarism and falsification: Behaviour and detectionCS09.1 Personality traits predict attitude towards plagiarism of self and others in biomedicine: plagiarism, yes we can?Martina Mavrinac, Gordana Brumini, Mladen PetrovečkiCS09.2 Investigating the concept of and attitudes toward plagiarism for science teachers in Brazil: any challenges for research integrity and policy?Christiane Coelho Santos, Sonia VasconcelosCS09.3 What have we learnt?: The CrossCheck Service from CrossRefRachael LammeyCS09.4 High p-values as a sign of data fabrication/falsificationChris Hartgerink, Marcel van Assen, Jelte Wicherts10. Codes for research integrity and collaborationsCS10.1 Research integrity in cross-border cooperation: a Nordic exampleHanne Silje HaugeCS10.3 Research integrity, research misconduct, and the National Science Foundation's requirement for the responsible conduct of researchAaron MankaCS10.4 A code of conduct for international scientific cooperation: human rights and research integrity in scientific collaborations with international academic and industry partnersRaffael Iturrizaga11. Countries' efforts to establish mentoring and networksCS11.1 ENRIO : a network facilitating common approaches on research integrity in EuropeNicole FoegerCS11.2 Helping junior investigators develop in a resource-limited country: a mentoring program in PeruA. Roxana Lescano, Claudio Lanata, Gissella Vasquez, Leguia Mariana, Marita Silva, Mathew Kasper, Claudia Montero, Daniel Bausch, Andres G LescanoCS11.3 Netherlands Research Integrity Network: the first six monthsFenneke Blom, Lex BouterCS11.4 A South African framework for research ethics and integrity for researchers, postgraduate students, research managers and administratorsLaetus OK Lategan12. Training and education in research integrity at an early career stageCS12.1 Research integrity in curricula for medical studentsGustavo Fitas ManaiaCS12.2 Team-based learning for training in the responsible conduct of research supports ethical decision-makingWayne T. McCormack, William L. Allen, Shane Connelly, Joshua Crites, Jeffrey Engler, Victoria Freedman, Cynthia W. Garvan, Paul Haidet, Joel Hockensmith, William McElroy, Erik Sander, Rebecca Volpe, Michael F. VerderameCS12.4 Research integrity and career prospects of junior researchersSnezana Krstic13. Systems and research environments in institutionsCS13.1 Implementing systems in research institutions to improve quality and reduce riskLouise HandyCS13.2 Creating an institutional environment that supports research integrityDebra Schaller-DemersCS13.3 Ethics and Integrity Development Grants: a mechanism to foster cultures of ethics and integrityPaul Taylor, Daniel BarrCS13.4 A culture of integrity at KU LeuvenInge Lerouge, Gerard Cielen, Liliane Schoofs14. Peer review and its role in research integrityCS14.1 Peer review research across disciplines: transdomain action in the European Cooperation in Science and Technology “New Frontiers of Peer Review ”Ana Marusic, Flaminio SquazzoniCS14.2 Using blinding to reduce bias in peer reviewDavid VauxCS14.3 How to intensify the role of reviewers to promote research integrityKhalid Al-Wazzan, Ibrahim AlorainyCS14.4 Credit where credit’s due: professionalizing and rewarding the role of peer reviewerChris Graf, Verity Warne15. Research ethics and oversight for research integrity: Does it work?CS15.1 The psychology of decision-making in research ethics governance structures: a theory of bounded rationalityNolan O'Brien, Suzanne Guerin, Philip DoddCS15.2 Investigator irregularities: iniquity, ignorance or incompetence?Frank Wells, Catherine BlewettCS15.3 Academic plagiarismFredric M. Litto16. Research integrity in EuropeCS16.1 Whose responsibility is it anyway?: A comparative analysis of core concepts and practice at European research-intensive universities to identify and develop good practices in research integrityItziar De Lecuona, Erika Löfstrom, Katrien MaesCS16.2 Research integrity guidance in European research universitiesKris Dierickx, Noémie Bonn, Simon GodecharleCS16.3 Research Integrity: processes and initiatives in Science Europe member organisationsTony Peatfield, Olivier Boehme, Science Europe Working Group on Research IntegrityCS16.4 Promoting research integrity in Italy: the experience of the Research Ethics and Bioethics Advisory Committee of the Consiglio Nazionale delle Ricerche Cinzia Caporale, Daniele Fanelli17. Training programs for research integrity at different levels of experience and seniorityCS17.1 Meaningful ways to incorporate research integrity and the responsible conduct of research into undergraduate, graduate, postdoctoral and faculty training programsJohn Carfora, Eric Strauss, William LynnCS17.2 "Recognize, respond, champion": Developing a one-day interactive workshop to increase confidence in research integrity issuesDieter De Bruyn, Bracke Nele, Katrien De Gelder, Stefanie Van der BurghtCS17.4 “Train the trainer” on cultural challenges imposed by international research integrity conversations: lessons from a projectJosé Roberto Lapa e Silva, Sonia M. R. Vasconcelos18. Research and societal responsibilityCS18.1 Promoting the societal responsibility of research as an integral part of research integrityHelene IngierdCS18.2 Social responsibility as an ethical imperative for scientists: research, education and service to societyMark FrankelCS18.3 The intertwined nature of social responsibility and hope in scienceDaniel Vasgird, Stephanie BirdCS18.4 Common barriers that impede our ability to create a culture of trustworthiness in the research communityMark Yarborough19. Publication ethicsCS19.1 The authors' forum: A proposed tool to improve practices of journal editors and promote a responsible research environmentIbrahim Alorainy, Khalid Al-WazzanCS19.2 Quantifying research integrity and its impact with text analyticsHarold GarnerCS19.3 A closer look at authorship and publication ethics of multi- and interdisciplinary teamsLisa Campo-Engelstein, Zubin Master, Elise Smith, David Resnik, Bryn Williams-JonesCS19.4 Invisibility of duplicate publications in biomedicineMario Malicki, Ana Utrobicic, Ana Marusic20. The causes of bad and wasteful research: What can we do?CS20.1 From countries to individuals: unravelling the causes of bias and misconduct with multilevel meta-meta-analysisDaniele Fanelli, John PA IoannidisCS20.2 Reducing research waste by integrating systems of oversight and regulationGerben ter Riet, Tom Walley, Lex Marius BouterCS20.3 What are the determinants of selective reporting?: The example of palliative care for non-cancer conditionsJenny van der Steen, Lex BouterCS20.4 Perceptions of plagiarism, self-plagiarism and redundancy in research: preliminary results from a national survey of Brazilian PhDsSonia Vasconcelos, Martha Sorenson, Francisco Prosdocimi, Hatisaburo Masuda, Edson Watanabe, José Carlos Pinto, Marisa Palácios, José Lapa e Silva, Jacqueline Leta, Adalberto Vieyra, André Pinto, Mauricio Sant’Ana, Rosemary Shinkai21. Are there country-specific elements of misconduct?CS21.1 The battle with plagiarism in Russian science: latest developmentsBoris YudinCS21.2 Researchers between ethics and misconduct: A French survey on social representations of misconduct and ethical standards within the scientific communityEtienne Vergès, Anne-Sophie Brun-Wauthier, Géraldine VialCS21.3 Experience from different ways of dealing with research misconduct and promoting research integrity in some Nordic countriesTorkild VintherCS21.4 Are there specifics in German research misconduct and the ways to cope with it?Volker Bähr, Charité22. Research integrity teaching programmes and their challengesCS22.1 Faculty mentors and research integrityMichael Kalichman, Dena PlemmonsCS22.2 Training the next generation of scientists to use principles of research quality assurance to improve data integrity and reliabilityRebecca Lynn Davies, Katrina LaubeCS22.3 Fostering research integrity in a culturally-diverse environmentCynthia Scheopner, John GallandCS22.4 Towards a standard retraction formHervé Maisonneuve, Evelyne Decullier23. Commercial research and integrityCS23.1 The will to commercialize: matters of concern in the cultural economy of return-on-investment researchBrian NobleCS23.2 Quality in drug discovery data reporting: a mission impossible?Anja Gilis, David J. Gallacher, Tom Lavrijssen, Malwitz David, Malini Dasgupta, Hans MolsCS23.3 Instituting a research integrity policy in the context of semi-private-sector funding: an example in the field of occupational health and safetyPaul-Emile Boileau24. The interface of publication ethics and institutional policiesCS24.1 The open access ethical paradox in an open government effortTony SavardCS24.2 How journals and institutions can work together to promote responsible conductEric MahCS24.3 Improving cooperation between journals and research institutions in research integrity casesElizabeth Wager, Sabine Kleinert25. Reproducibility of research and retractionsCS25.1 Promoting transparency in publications to reduce irreproducibilityVeronique Kiermer, Andrew Hufton, Melanie ClyneCS25.2 Retraction notices issued for publications by Latin American authors: what lessons can we learn?Sonia Vasconcelos, Renan Moritz Almeida, Aldo Fontes-Pereira, Fernanda Catelani, Karina RochaCS25.3 A preliminary report of the findings from the Reproducibility Project: Cancer biologyElizabeth Iorns, William Gunn26. Research integrity and specific country initiativesCS26.1 Promoting research integrity at CNRS, FranceMichèle Leduc, Lucienne LetellierCS26.2 In pursuit of compliance: is the tail wagging the dog?Cornelia MalherbeCS26.3 Newly established research integrity policies and practices: oversight systems of Japanese research universitiesTakehito Kamata27. Responsible conduct of research and country guidelinesCS27.1 Incentives or guidelines? Promoting responsible research communication through economic incentives or ethical guidelines?Vidar EnebakkCS27.3 Responsible conduct of research: a view from CanadaLynn PenrodCS27.4 The Danish Code of Conduct for Research Integrity: a national initiative to promote research integrity in DenmarkThomas Nørgaard, Charlotte Elverdam28. Behaviour, trust and honestyCS28.1 The reasons behind non-ethical behaviour in academiaYves FassinCS28.2 The psychological profile of the dishonest scholarCynthia FekkenCS28.3 Considering the implications of Dan Ariely’s keynote speech at the 3rd World Conference on Research Integrity in MontréalJamal Adam, Melissa S. AndersonCS28.4 Two large surveys on psychologists’ views on peer review and replicationJelte WichertsBrett Buttliere29. Reporting and publication bias and how to overcome itCS29.1 Data sharing: Experience at two open-access general medical journalsTrish GrovesCS29.2 Overcoming publication bias and selective reporting: completing the published recordDaniel ShanahanCS29.3 The EQUATOR Network: promoting responsible reporting of health research studiesIveta Simera, Shona Kirtley, Eleana Villanueva, Caroline Struthers, Angela MacCarthy, Douglas Altman30. The research environment and its implications for integrityCS30.1 Ranking of scientists: the Russian experienceElena GrebenshchikovaCS30.4 From cradle to grave: research integrity, research misconduct and cultural shiftsBronwyn Greene, Ted RohrPARTNER SYMPOSIAPartner Symposium AOrganized by EQUATOR Network, Enhancing the Quality and Transparency of Health ResearchP1 Can we trust the medical research literature?: Poor reporting and its consequencesIveta SimeraP2 What can BioMed Central do to improve published research?Daniel Shanahan, Stephanie HarrimanP3 What can a "traditional" journal do to improve published research?Trish GrovesP4 Promoting good reporting practice for reliable and usable research papers: EQUATOR Network, reporting guidelines and other initiativesCaroline StruthersPartner Symposium COrganized by ENRIO, the European Network of Research Integrity OfficersP5 Transparency and independence in research integrity investigations in EuropeKrista Varantola, Helga Nolte, Ursa Opara, Torkild Vinther, Elizabeth Wager, Thomas NørgaardPartner Symposium DOrganized by IEEE, the Institute of Electrical and Electronics EngineersRe-educating our author community: IEEE's approach to bibliometric manipulation, plagiarism, and other inappropriate practicesP6 Dealing with plagiarism in the connected world: An Institute of Electrical and Electronics Engineers perspectiveJon RokneP7 Should evaluation of raises, promotion, and research proposals be tied to bibliometric indictors? What the Institute of Electrical and Electronics Engineers is doing to answer this questionGianluca SettiP8 Recommended practices to ensure conference content qualityGordon MacPhersonPartner Symposium EOrganized by the Committee on Freedom and Responsibility in the Conduct of Science of ICSU, the International Council for ScienceResearch assessment and quality in science: perspectives from international science and policy organisationsP9 Challenges for science and the problems of assessing researchEllen HazelkornP10 Research assessment and science policy developmentCarthage SmithP11 Research integrity in South Africa: the value of procedures and processes to global positioningRobert H. McLaughlinP12 Rewards, careers and integrity: perspectives of young scientists from around the worldTatiana Duque MartinsPartner Symposium FOrganized by the Online Resource Center for Ethics Education in Engineering and Science / Center for Engineering, Ethics, and Society of the National Academy of EngineeringP13 Research misconduct: conceptions and policy solutionsTetsuya Tanimoto, Nicholas Steneck, Daniele Fanelli, Ragnvald Kalleberg, Tajammul HusseinPartner Symposium HOrganized by ORI, the Office of Research Integrity; Universitas 21; and the Asia Pacific Research Integrity NetworkP14 International integrity networks: working together to ensure research integrityPing Sun, Ovid Tzeng, Krista Varantola, Susan ZimmermanPartner Symposium IOrganized by COPE, the Committee on Publication EthicsPublication without borders: Ethical challenges in a globalized worldP15 Authorship: credit and responsibility, including issues in large and interdisciplinary studiesRosemary ShinkaiPartner Symposium JOrganized by CITI, the Cooperative Institutional Training InitiativeExperiences on research integrity educational programs in Colombia, Costa Rica and PeruP16 Experiences in PeruRoxana LescanoP17 Experiences in Costa RicaElizabeth HeitmanP18 Experiences in ColumbiaMaria Andrea Rocio del Pilar Contreras NietoPoster Session B: Education, training, promotion and policyPT.01 The missing role of journal editors in promoting responsible researchIbrahim Alorainy, Khalid Al-WazzanPT.02 Honorary authorship in Taiwan: why and who should be in charge?Chien Chou, Sophia Jui-An PanPT.03 Authorship and citation manipulation in academic researchEric Fong, Al WilhitePT.04 Open peer review of research submission at medical journals: experience at BMJ Open and The BMJTrish GrovesPT.05 Exercising authorship: claiming rewards, practicing integrityDésirée Motta-RothPT.07 Medical scientists' views on publication culture: a focus group studyJoeri Tijdink, Yvo SmuldersPoster Session B: Education, training, promotion and policyPT.09 Ethical challenges in post-graduate supervisionLaetus OK LateganPT.10 The effects of viable ethics instruction on international studentsMichael Mumford, Logan Steele, Logan Watts, James Johnson, Shane Connelly, Lee WilliamsPT.11 Does language reflect the quality of research?Gerben ter Riet, Sufia Amini, Lotty Hooft, Halil KilicogluPT.12 Integrity complaints as a strategic tool in policy decision conflictsJanneke van Seters, Herman Eijsackers, Fons Voragen, Akke van der Zijpp and Frans BromPoster Session C: Ethics and integrity intersectionsPT.14 Regulations of informed consent: university-supported research processes and pitfalls in implementationBadaruddin Abbasi, Naif Nasser AlmasoudPT.15 A review of equipoise as a requirement in clinical trialsAdri LabuschagnePT.16 The Research Ethics Library: online resource for research ethics educationJohanne Severinsen, Espen EnghPT.17 Research integrity: the view from King Abdulaziz City for Science and TechnologyDaham Ismail AlaniPT. 18 Meeting global challenges in high-impact publications and research integrity: the case of the Malaysian Palm Oil BoardHJ. Kamaruzaman JusoffPT.19 University faculty perceptions of research practices and misconductAnita Gordon, Helen C. HartonPoster Session D: International perspectivesPT.21 The Commission for Scientific Integrity as a response to research fraudDieter De Bruyn, Stefanie Van der BurghtPT. 22 Are notions of the responsible conduct of research associated with compliance with requirements for research on humans in different disciplinary traditions in Brazil?Karina de Albuquerque Rocha, Sonia Maria Ramos de VasconcelosPT.23 Creating an environment that promotes research integrity: an institutional model of Malawi Liverpool Welcome TrustLimbanazo MatandikaPT.24 How do science policies in Brazil influence user-engaged ecological research?Aline Carolina de Oliveira Machado Prata, Mark William NeffPoster Session E: Perspectives on misconductPT.26 What “causes” scientific misconduct?: Testing major hypotheses by comparing corrected and retracted papersDaniele Fanelli, Rodrigo Costas, Vincent LarivièrePT.27 Perception of academic plagiarism among dentistry studentsDouglas Leonardo Gomes Filho, Diego Oliveira GuedesPT. 28 a few bad apples?: Prevalence, patterns and attitudes towards scientific misconduct among doctoral students at a German university hospitalVolker Bähr, Niklas Keller, Markus Feufel, Nikolas OffenhauserPT. 29 Analysis of retraction notices published by BioMed CentralMaria K. Kowalczuk, Elizabeth C. MoylanPT.31 "He did it" doesn't work: data security, incidents and partnersKatie SpeanburgPoster Session F: Views from the disciplinesPT.32 Robust procedures: a key to generating quality results in drug discoveryMalini Dasgupta, Mariusz Lubomirski, Tom Lavrijssen, David Malwitz, David Gallacher, Anja GillisPT.33 Health promotion: criteria for the design and the integrity of a research projectMaria Betânia de Freitas Marques, Laressa Lima Amâncio, Raphaela Dias Fernandes, Oliveira Patrocínio, and Cláudia Maria Correia Borges RechPT.34 Integrity of academic work from the perspective of students graduating in pharmacy: a brief research studyMaria Betânia de Freitas Marques, Cláudia Maria Correia Borges Rech, Adriana Nascimento SousaPT.35 Research integrity promotion in the Epidemiology and Health Services, the journal of the Brazilian Unified Health SystemLeila Posenato GarciaPT.36 When are clinical trials registered? An analysis of prospective versus retrospective registration of clinical trials published in the BioMed Central series, UKStephanie Harriman, Jigisha PatelPT.37 Maximizing welfare while promoting innovation in drug developmentFarida LadaOther posters that will be displayed but not presented orally:PT.38 Geoethics and the debate on research integrity in geosciencesGiuseppe Di Capua, Silvia PeppoloniPT.39 Introducing the Professionalism and Integrity in Research Program James M. DuBois, John Chibnall, Jillon Van der WallPT.40 Validation of the professional decision-making in research measureJames M. DuBois, John Chibnall, Jillon Van der Wall, Raymond TaitPT.41 General guidelines for research ethicsJacob HolenPT. 42 A national forum for research ethicsAdele Flakke Johannessen, Torunn EllefsenPT.43 Evaluation of integrity in coursework: an approach from the perspective of the higher education professorClaudia Rech, Adriana Sousa, Maria Betânia de Freitas MarquesPT.44 Principles of geoethics and research integrity applied to the European Multidisciplinary Seafloor and Water Column Observatory, a large-scale European environmental research infrastructureSilvia Peppoloni, Giuseppe Di Capua, Laura BeranzoliF1 Focus track on improving research systems: the role of fundersPaulo S.L. Beirão, Susan ZimmermanF2 Focus track on improving research systems: the role of countriesSabine Kleinert, Ana MarusicF3 Focus track on improving research systems: the role of institutionsMelissa S. Anderson, Lex Bouter. (shrink)

This thesis is divided into three parts, the first and second ones focused on combinatorics and classification problems on discrete and geometrical objects in the context of descriptive set theory, and the third one on generalized descriptive set theory at singular cardinals of countable cofinality.Descriptive Set Theory (briefly: DST) is the study of definable subsets of Polish spaces, i.e., separable completely metrizable spaces. One of the major branches of DST is Borel reducibility, successfully used in the last 30 years to (...) solve and compare many classification problems. One of our goals is the classification of knots, very familiar and tangible objects in everyday life, which also play an important role in modern mathematics. The study of knots and their properties is known as knot theory. Our plan is to gain insight into knots using discrete objects, such as linear and circular orders. This approach was already exploited in [6]. The first part of this work is therefore devoted to countable linear orders and the study of the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results. We also expand our research to the case of circular orders.Another objective of this first part is to extend the notion of convex embeddability on countable linear orders. We provide a family of quasi-orders of which embeddability is a particular case as well. We study these quasi-orders from a combinatorial point of view and analyse their complexity with respect to Borel reducibility. Furthermore, we extend the analysis of these quasi-orders to the set of uncountable linear orders.The second part of the project deals with classification problems on knots and $3$ -manifolds. The goal here is to apply the results obtained in the first part to the study of proper arcs and knots, establishing lower bounds for the complexity of some natural relations between these geometrical objects. We also obtain some combinatorial results which are particularly interesting when we restrict to the set of wild proper arcs and wild knots, classes which haven’t received much attention so far. These parts are included in the two preprints [4, 5] in collaboration with my supervisor Alberto Marcone, Luca Motto Ros (University of Torino), and Vadim Weinstein (University of Oulu).The second part of this work also includes the classification of non-compact $3$ -manifolds up to homeomorphism (the case of compact $3$ -manifolds has already been solved: indeed, there are only countably many $3$ -manifolds up to homeomorphism; see [7]), and that of Cantor sets of $\mathbb {R}^3$ up to conjugation (answering to Question 5.5 of [3]). Here we resort to algebraic tools. Stone duality gives a neat way to go back-and-forth between totally disconnected Polish spaces and countable Boolean algebras (see [1]). The main ingredient is the Stone space of all ultrafilters on a Boolean algebra. In this work we introduce a weaker concept which we call “blurry filter”. Using blurry filters instead of ultrafilters enables one to extend the class of spaces under consideration beyond totally disconnected. As an application of this method, we show that both homeomorphism on non-compact $3$ -manifolds and conjugation of Cantor sets in $\mathbb {R}^3$ are completely classifiable by countable structures. These results are part of an upcoming paper in collaboration with Vadim Weinstein.The last part of this thesis concerns the natural generalization of descriptive set theory that occurs when countable is replaced by uncountable, called Generalized Descriptive Set Theory (briefly: GDST). In particular, we focus on the case of GDST for a singular cardinal $\kappa $ of countable cofinality. The goal here is to study the generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set $\mathcal {P}(\kappa )$. We consider the question under which large cardinal hypotheses classes of definable subsets of these spaces possess such regularity properties, focusing on rank-into-rank axioms, like I2, and classes of sets definable by $\Sigma _1$ -formulas with parameters from various collections of sets. The obtained results are included in [2], a joint work with my co-supervisor Vincenzo Dimonte and Philipp Lücke (University of Hamburg).Abstract prepared by Martina IannellaE-mail: [email protected]: https://air.uniud.it/handle/11390/1262824. (shrink)

Formally, a description of weak BCK-algebras can be obtained by replacing the first BCK axiom \ - \le z - y}\) by its weakening \. It is known that every weak BCK-algebra is completely determined by the structure of its initial segments. We consider weak BCK-algebras with De Morgan complemented, orthocomplemented and orthomodular sections, as well as those where sections satisfy a certain compatibility condition, and characterize each of these classes of algebras by an equation or (...) quasi-equation. For instance, those weak BCK-algebras in which all initial segments are De Morgan complemented are just commutative weak BCK-algebras. (shrink)

The fundamental purpose of this research work was to explain how the management of agile methodologies for the development of competencies of university students in the Peruvian context. Based on this question, it has been hypothesized that agile methodologies significantly help the development of students' competencies. This is complemented by a quantitative approach study, with a quasi-experimental design of the "Design with pre-test - post-test with experimental groups and control groups" model. The students of the one Peruvian University were (...) considered as the study population, of which the students of the Faculty of Initial Education were taken as a study sample, within which 100 students participated as an experimental group. 100 from V, VII, X cycle and as a control group 100 students from II, III, and IV cycle respectively. Therefore, as the main result, it is evident that, with a bilateral significance of.000 less than the predetermined significance of 0.05 and a result of F = 1.013, they confirm that the first condition of equality of variances is met and thus establish the Test of the General Hypothesis or HG according to the normal "Z" equal to 8.965, in the case of two independent samples and a difference of 3.81 plus Gl = 51 degrees of freedom and assuming a 95% confidence level, the hypothesis is rejected null and the alternative Hypothesis is accepted, concluding that agile methodologies significantly help the development of students' competencies with a significance of pv,000.. (shrink)

Let p be prime number, K be a p‐adically closed field, a semi‐algebraic set defined over K and the lattice of semi‐algebraic subsets of X which are closed in X. We prove that the complete theory of eliminates quantifiers in a certain language, the ‐structure on being an extension by definition of the lattice structure. Moreover it is decidable, contrary to what happens over a real closed field for. We classify these ‐structures up to elementary equivalence, and get (...) in particular that the complete theory of only depends on m, not on K nor even on p. As an application we obtain a classification of semi‐algebraic sets over countable p‐adically closed fields up to so‐called “pre‐algebraic” homeomorphisms. (shrink)

We investigate expansions of Heyting algebras in possession of a unary term describing the filters that correspond to congruences. Hasimoto proved that Heyting algebras equipped with finitely many normal operators have such a term, generalising a standard construction on finite-type boolean algebras with operators. We utilise Hasimoto’s technique, extending the existence condition to a larger class of EHAs and some classes of double-Heyting algebras. Such a term allows us to characterise varieties with equationally (...) definable principal congruences using a single equation. Moreover, in the presence of a dual pseudocomplement operation, discriminator varieties are characterised by a pair of equations. We also prove that a variety of dually pseudocomplemented EHAs with a normal filter term is semisimple if and only if it is a discriminator variety. This generalises two known results, one by Kowalski and Kracht for finite-type varieties of BAOs, and the other by the present author for dually pseudocomplemented Heyting algebras without additional operations. (shrink)

Abstract. The aim of this paper is to show that the topological interpretation of knowledge as an interior kernel operator K of a topological space (X, OX) comes along with a partially ordered family of belief modalities B that fit K in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB logic of knowledge and belief with the exception of the contentious axiom of negative introspection (NI). The new belief modalities B introduced in this paper are (...) defined with the help of the (dense) nuclei of the Heyting algebra OX of open subsets on the topological space (X, OX). In this way, the natural context for the belief operators B related to topological knowledge operator K is shown to be the Heyting algebra NUC(OX) of the nuclei of the Heyting algebra OX.1 More precisely, the dense nuclei of NUC(OX) can be used to define a variety of bimodal logics of knowledge operators K and belief operators B. The operators K and B are compatible with each other in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB system with the exception of the axiom (NI). Therefore, for (X, OX), one obtains a bounded, partially ordered family of belief operators B defined by the elements of NUC(OX). (shrink)

Let R be a real closed field, and X⊆Rm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq R^m}$$\end{document} semi-algebraic and 1-dimensional. We consider complete first-order theories of modules over the ring of continuous semi-algebraic functions X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\to R}$$\end{document} definable with parameters in R. As a tool we introduce -piecewise vector bundles on X and show that the category of piecewise vector bundles on X is equivalent to the category of (...) syzygies of finitely generated submodules of free modules. We give an explicit method to determine the Baur–Monk invariants of free modules in terms of pre-piecewise vector bundles. When R is a recursive real closed field this yields the decidability of the theory of free modules. Where it makes sense, we address the same questions for continuous definable functions in o-minimal expansions of a real closed field. From the free module case we are able to deduce generalisations of some results to arbitrary modules over the ring. We present a geometrically motivated quantifier elimination result down to the level of positive primitive formulae with a certain block decomposition of the matrix of coefficients. (shrink)

In this paper we introduce a logic that we name semi Heyting–Brouwer logic, \, in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, the Heyting–Brouwer logic \ is an axiomatic extension of \ and that the propositional calculi of intuitionistic logic \ and semi-intuitionistic logic \ turn out to be fragments of \.

A contraction-free and cut-free sequent calculus \ for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus \ for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: \ is embedded into \ via Gödel–Gentzen translation. \ is embedded into a sequent calculus for classical propositional logic. \ is embedded into the (...) sequent calculus \ for intuitionistic propositional logic. (shrink)

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics. In a logic N has been investigated in the language with (...) negation; implication; conjunction and disjunction by axioms of positive intuitionistic logic; the right-to-left part of the second de Morgan law; and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation. In the present paper we consider an extension of N denoted by N+. We will prove that every extension of N+ that is closed under the same rules as N+; corresponds to a regular logic being an extension of the regular deontic logic D21. The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N+. (shrink)