Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie “non-computational” proofs from the mainstream literature. To this end, we (...) establish logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On the one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches. (shrink)

This thesis is concerned with extending the underlying logical approach as well as the breadth of applications of the proof mining program to various (mostly previously untreated) areas of nonlinear analysis and optimization, with a particular focus being placed on topics which involve set-valued operators.For this, we extend the current logical methodology of proof mining by new systems and corresponding so-called logical metatheorems that cover these more involved areas of nonlinear analysis. Most of these systems crucially rely on the (...) use of intensional methods, treating sets with potentially high quantifier complexity in the defining matrix via characteristic functions and axioms that describe only their properties and do not completely characterize the elements of the sets.The applicability of all of these metatheorems is then substantiated by a range of case studies for the respective areas which in particular also highlight the naturalness of the use of intensional methods in the design of the corresponding systems.The first new area covered thereby is the theory of nonlinear semigroups induced by corresponding evolution equations for accretive operators. In that context, we present (besides an initial foray into the area from 2015) essentially the first applications of proof mining to the theory of partial differential equations. Concretely, we provide quantitative versions of four central results on the asymptotic behavior of solutions to such equations.The second new area unlocked in this thesis is that of the continuous dual of a Banach space and its norm (which are also approached via intensional methods). This in particular relies on a proof-theoretically tame treatment of suprema over (certain) bounded sets in this intensional context which is further exploited later on. These systems, which give access to this until now untreated fundamental notion from functional analysis, are then used to provide further substantial extensions to treat various notions from convex analysis like the Fréchet derivative of a convex function, Fenchel conjugates, Bregman distances, and monotone operators on Banach spaces in the sense of Browder.These systems are then utilized to provide applications in the context of Picard- and Halpern-style iterations of so-called Bregman strongly nonexpansive mappings where we provide both new quantitative and qualitative results.Lastly, we discuss the key notion of extensionality of a set-valued operator and its relation to set-theoretic maximality principles in more depth (which was already singled out—to some degree—in previous work). We thereby exhibit an issue arising with treating full extensionality in the context of these intensional approaches to set-valued operators and present useful fragments of the full extensionality statement where these issues are avoided.Corresponding to these fragments, we discuss a range of uniform continuity statements for set-valued operators beyond the usual notion involving the Hausdorff-metric. In particular, in that context, we utilize the previous tame treatment of suprema over bounded sets to also provide the first proof-theoretic treatment of that Hausdorff-metric in the context of systems for proof mining.The applicability of this treatment of the Hausdorff-metric is then in particular substantiated by a last case study where we provide quantitative information for a Mann-type iteration of set-valued mappings which are nonexpansive w.r.t. the Hausdorff-metric.The abstract was taken directly from the thesis.Abstract prepared by Nicholas Pischke, Technische Universität Darmstadt, Darmstadt, GermanyE-mail: [email protected]: https://doi.org/10.26083/tuprints-00026584. (shrink)

Classical medicine operates in a climate of rational discourse, scientific knowledge accretion and the acceptance of ethical standards that regulate its activities. Criticism has centred on the excessive technological emphasis of modern medicine and on its social strategy aimed at defending exclusiveness and the privileges of professional status. Alternative therapeutic approaches have taken advantage of the eroded public image of medicine, offering treatments based on holistic philosophies that stress the non-rational, non-technical and non-scientific approach to the unwell, disregarding traditional diagnostic (...) categories and concentrating on enhancing subjective comfort and well-being, but remaining oblivious to the organic substrate of disease. This leads to questionable ethics in terms of false hopes and lost opportunities for effective therapy. (shrink)

Of course, words aren’t magic. Neither are sextants, compasses, maps, slide rules and all the other paraphenelia which have accreted around the basic biological brains of homo sapiens. In the case of these other tools and props, however, it is transparently clear that they function so as to either carry out or to facilitate computational operations important to various human projects. The slide rule transforms complex mathematical problems (ones that would baffle or tax the unaided subject) into simple tasks of (...) perceptual recognition. The map provides geographical information in a format well-suited to aid complex planning and strategic military operations. The compass gathers and displays a kind of information that (most) unaided human subjects do not seem to command. These various tools and props thus act to generate information, or to store it, or to transform it, or some combination of the three. In so doing, they impact our individual and collective problem- solving capacities in much the same dramatic ways as various software packages impact the performance of a simple pc. (shrink)

Ghost variables are variables in program languages that do not correspond to physical entities. This special issue, based on a panel on “Race as a Ghost Variable” at the 2017 Meeting of the Society for Social Studies of Science, traces ideas of “race” in particular niches of science, technology, and medicine where it is submerged and disavowed, yet wields power. Each paper is a case study exploring ghosts that emerge through the resonance among things as heterogeneous as hair patterns, hormone (...) levels, food tastes, drug use, clinic locations, proximity to disaster, job classifications, and social belonging and suspicion, all of which vibrate with meanings accumulated over long racial histories. Together, the papers further elaborate methods and analytic models for identifying the operations of race—the relations and processes that make it, the effects that it has. A chief appeal of the metaphor of the ghost is that it brings the importance of history to the fore. Ghosts are simultaneously history and the present, not just an accretion of earlier experiences, but the palimpsest left when one tries to erase them. Sometimes faint and hard to discern, sometimes rambunctious and disruptive, ghosts refuse our attempts to simply move on. (shrink)

continent. 2.1 (2012): 40–43. Lance Olsen is a professor of Writing and Literature at the University of Utah, Chair of the FC2 Board of directors, and, most importantly, author or editor of over twenty books of and about innovative literature. He is one of the true champions of prose as a viable contemporary art form. He has just published Architectures of Possibility (written with Trevor Dodge), a book that—as Olsen's works often do—exceeds the usual boundaries of its genre as it (...) explores his interests in narrative theory and pedagogy. The book is a kind of “anti-textbook;” a performative polemic against the stale, conservative and monolithic conception of the literary that so often dominates institutional discourse around creative writing. The following interview takes the occasion of AoP's publication as a chance to speak with Olsen about the book itself as well as to engage with larger, unanswerable, questions about the futures and intersections of literature and education. —Ben Segal INTERVIEW: 1) First, I want to start before the beginning, with the title. I’m really fascinated by the concept it conjures. Can you say something about innovative/experimental/(choose your adjective) literature in relation to both ideas around architecture and possibility? Innovative or experimental are tremendously fraught adjectives, needless to say. But for the purposes of my book, they modify a fiction concerned with the questions: What is fiction? What can it do, and how, and why? Now, of course, what looks “innovative” or “experimental” to one at 17 may not be what looks “innovative” or “experimental” to one at 27 or 57, and what looks “innovative” or “experimental” in 1812 may not be what looks “innovative” or “experimental” in 2012. A certain existential and historical perspectivism is always at work. But I think it’s fair to say that innovative and experimental usually refer to a narrativity that includes a self-reflective awareness of and engagement with theoretical inquiry, concerns, and obsessions, as well as a sense of being in conversation with fiction across space and time. One can't create challenging writing in a vacuum; it has to challenge in relation to something. So contemporary writers interested in the subject are not only in pursuit of the innovative, but are also always-already writing subsequent to it—writing, that is, in its long wake. Architectures of Possibility conceives of creativity as a possibility space, a locale just outside our comfort zones where we can and should take multiple chances in order to imagine in new ways, explore fresh strategies for finding and cultivating ideas, re-view what it is we’re doing and why, better understand what Samuel Beckett meant when he wrote: “Try again. Fail again. Fail better.” It reminds us that there are other ways of narrating our worlds and ourselves than those we have inherited from the entertainment industry, the government, academia, previous writing, and so on. 2) AoP seems to be directed at several audiences (and purposes) simultaneously. What I mean is that it seems at times a polemic in favor of innovative literature, at other times a creative writing textbook, and still other times a guide to the network of publishers, journals, and programs that make up the current world of non-mainstream literary art in the U.S. In my mind, Architectures is a theorized anti-textbook about writing. Most textbooks on the subject (think of Janet Burroway’s Writing Fiction: A Guide to Narrative Craft , taught in most creative-writing classroom across the country) orchestrate how to construct conventional stories. They instruct from a place of power how to generate familiar stories that are repeated so often that many of us begin to take them as the primary model for narrativity, if not unconsciously as a kind of truth. The result, as Brian Kiteley points out in 3 A.M. Epiphany (one of the only other alternative textbooks about innovative writing around, by the way, and a tremendous repository of exercises), is merely competent texts. Architectures problematizes that gesture by outlining what conventional narrativity looks like, urging writers to think about its ideology of form as well as content, and invites them to imagine writing, not as a set of relatively stable conventions, but, rather, as a possibility space where everything can and should be thought, tried, challenged. It thereby rhymes with Roland Barthes’s definition of literature: the question minus the answer—which is to say Architectures poses complications to the act of writing rather than solutions. 3) One of the most notable things about the book is the use of interviews. This is also one of the reasons that I think the book works so well for a variety of audiences—that anyone with even a passing interest in the state and future of literature will have an interest in your conversation with people like Ben Marcus, Samuel Delany, and Lydia Davis. I was hoping you could just talk a little about how you chose these subjects to interview, how you edited the interview material, and which answers you received struck you the most. Experimentalism , like realism , wants to appear in the plural. The idea of gathering more than forty interviews (with the help of my awesome collaborator, Trevor Dodge, himself a fine innovative author) represents an attempt to suggest that: the wide, rich, exciting opportunities inherent in the term. There are interviews with younger writers, elder statesmen in the field, publishers, editors, hypermedia artists, comic book makers, and so on: Joe Wenderoth, Carole Maso, Scott McCloud, Nick Montfort, Kathy Acker, et al. Trevor and I decided to do flash interviews: short, concentrated Q&As, each focusing on a particular troubling of writing. We only lightly edited the results to match the manuscript’s overall style, and every interview arrived as a surprise housing several unexpected insights. Three brief examples: Michael Mejia, when asked about what he dreads when setting about writing: “Dread is an interesting word here. I associate it less with loathing or aversion, I suppose, than with a kind of productive fear. Do I dread a project’s failure? Sure, who doesn’t? Who wants to waste time on something that comes to nothing, or is unreadable? But then, what do these terms mean, and who or what defines a work as a ‘failure,’ as ‘waste,’ as ‘unreadable’? Should a work actually try to interrogate and exceed these conceptual limitations? My tendency is to write into dread in order to reveal to myself, as much as to any reader that may come after, the varied complacencies that make other, mostly more conventional writings, readable. It’s at the frontier between readability (security) and unreadability (terror) that I want to live creatively.” Carole Maso, when asked what she’d like a sentence to accomplish: “I think a sentence can if allowed carry emotional and intellectual states as they flee, as they come and go, an escaping essence difficult to hold in other ways. In this way I think the sentence can work as a phrase of music does, sounding something large and elusive in us. Alternatively it can provide sometimes a stability, an essence, a moment of being. Unlike music the sentence also of course carries language with all its potential for meaning making and memory traces and association with it as well. I probably love the accretion of sentences most—those patterns, that shimmer, that resonance.” Shelley Jackson, when asked what is innovative about the innovative: “The purpose of the innovative is, I think, to wake us up. We are not quite alive, most of the time; we occupy a sort of cartoon version of our lives, its lines made smooth by repetition. Writing can open the seams in that world, reintroduce us to the real lives that we have forgotten. Maybe all good writing is innovative in some sense, in that it shows or tells or makes you feel something you never felt before—something for which you have no cartoon ready.” 4) You talk a little about N. Katherine Hayles’s concept of Media Specific Analysis and propose the supplemental notion of Medium Specific Generation—basically taking Hayles and applying her thought from the perspective of the writer. I’ve been trying to develop somewhat related theoretical frameworks, so I was really excited to come upon this section of the book. I’m wondering if you can talk a little more about this idea and, in general, about the potentials that you see as being opened up by writers engaging with and exploiting different media as literary platforms? “Lulled into somnolence by five hundred years of print,” Hayles urges in her (at least for me) transformative 2004 essay, “Print is Flat, Code is Deep,” “literary analysis should awaken to the importance of media-specific analysis, a mode of critical attention which recognizes that all texts are instantiated and that the nature of the medium in which they are instantiated matters.” She goes on to argue critics should learn to become more attuned to the materiality of the medium under investigation—which is to say a story isn’t a story isn’t a story. Rather, the “same” story remediated through film is intrinsically different from that story remediated through conventionally printed books is intrinsically different from that story remediated through hypermedia. “Materiality,” Hayles goes on, “is reconceptualized as the interplay between a text’s physical characteristics and its signifying strategies, a move that entwines instantiation and signification at the outset.” My point in Architectures is simply to emphasize Media Specific Generation: the idea that when writing you should be cognizant, not only of the thematics of the text you are working on, and, as it were, the internal components of its narrativity (character, language, plot, etc.), but also of the material embodiment those components take, and, perhaps more important, the material embodiment those components can take. The idea that the way texts matter matters isn’t something usually addressed in any significant way in creative-writing classrooms and textbooks. It may almost go without saying such experimentation with typography, layout, and white space has a long tradition—certainly one that tracks back at least as far as Guillaume Apollinaire’s early twentieth-century Calligrammes , Laurence Sterne’s textually ribald eighteenth-century Tristram Shandy , although one could arguably plot a hypothetical trajectory that reaches to ancient Greek romances like Achilles Tatius’ second-century Leucippe and Clitophon . Experiments into atomic materiality and digital immateriality bracket the definition of “book” at the same time they highlight Michael Martone’s prediction of its present future as increasingly viral, collaborative, and ephemeral. Or, as Matthew Battles points out: the future of the “book” has already arrived, and it is “ethereal and networked” rather than “an immutable brick.”While conventional writing and reading practices are conceptualized as private, individual, relatively fixed experiences, many of the new forms indicate that writing and reading—from production through dissemination—are rapidly becoming public, collective, incrementally unfixed experiences. That strikes me as an astonishing set of opportunities for a writer to investigate. 5) Another concept you elaborate in AoP is that of limit texts, basically texts that, once you read them, change what you imagine as the shape/horizon/potential of literature. You provide a fantastic reading list of limit texts at the end of AoP. I was hoping you could talk about a few of them in terms of how they specifically operate as limit texts for you—how they expand your understanding of what literature could be or do. Karl Jaspers coined the word Grenzsituationen (border/limit situations) to describe existential moments accompanied by anxiety in which the human mind is forced to confront the restrictions of its existing forms—moments that make us abandon, fleetingly, the securities of our limitedness and enter new realms of self-consciousness. Death, for example. Limit texts are a variety of disturbance that carries various elements of narrativity to their brink so the reader can never quite imagine them in the same terms again. Once you’ve taken one down from the shelf, you’ll never be able to put it back up again. They won’t leave you alone. They will continue to work on your imagination long after you’ve read them. Simply by being in the world, they ask us to embrace difficulty, freedom, radical skepticism. One of the most important for me is Samuel Beckett’s The Unnamable . Instead of establishing conventional setting and building traditional character, from its first words it unsettles both: “Where now? Who now? When now?” That first trio of question marks broadcasts the thematics of the writing (“novel” may be too strong a word) that will follow: it is all about a voice (or, perhaps, voices, about the grammatical mistake of the first-person pronoun), a consciousness (maybe, again, too strong a word), often genderless, removed from place and chronology and socioeconomic reality, hovering in a state of perpetual aporia. All it knows is what it doesn’t know, and its not-knowing is blackly, sardonically comic. The Unnamable is the embodiment of an unreliable narrator—a subject position that can’t trust itself, let alone be trusted by a reader. It contradicts, takes back, digresses, undoes what it just did, forgets, lies, hallucinates gloriously. The language is abstract, disembodied, devoid of sensory data, grayish rather than painterly in texture. Without knowing this passage is from a novel, a reader might well conclude s/he were reading a patch of (anti-)Cartesian philosophy. It might be helpful to conceive of what Beckett is doing as post-genre writing, then, or perhaps what Raymond Federman referred to as critifiction—a mode that blurs conventional distinctions between theory and narrative. In completely different register, and much more recently, Anne Carson’s Nox blew me away. It takes the form of an elegy for her older brother, whom she didn’t know well and who died unexpectedly while on the run from the law in Europe. The thing itself arrives in a box that simulates a thick book, as well as the brother’s textual coffin. Open it, and inside you discover, not a codex, but an accordioned series of “pages” that folds out into an arrangement that suggests an ancient scroll (Carson is, perhaps illuminatingly, a professor of classics) made up of shards of her brother’s letters, old photographs, tickets, Carson’s observations, Catullus’ poem 101 (the one addressed to the Roman poet’s dead brother, a doubling of Carson’s situation), and extensive dictionary entries on all the words that compose that poem. The aggregate produces a collage about the impossibilities of aggregates, the impossibilities of understanding fully, of capturing absences in language. At times Nox feels less an example of what most readers consider a book than something closer to a three-dimensional work of assemblage art. It’s a beautiful mechanism for contemplating Media Specific Analysis, for urging us all to be more extreme. 6) Finally, I want to talk a little about pedagogy and institutions. I’m less interested in questions like “Are MFA programs good for writers?” than in questions about how your role as teacher informs your understanding of literature and your writing practice. I’m also very curious about your take on how commercially marginal literary art is largely patronized by large state institutions and at the same time often imagines itself as a critical and even possibly revolutionary practice. How have your own positions within universities and university-affiliated organizations shaped your thinking about them and about innovative literature? I can imagine in many ways it might make you even more critical. And (I know, another ‘and’...) how does AoP (especially given its relation to Rebel Yell , your previous text on creative writing) reflect your personal history and experience as a teacher and member of communities that are largely defined by institutions? In the classroom, I try to generate the pedagogical field I would have liked to have inhabited as a student, but didn’t. Roland Barthes has a lovely line about this: “We need to substitute for the magisterial [classroom] space of the past (the word delivered by the master from the pulpit above with the audience below, the flock, the sheep, the herd)—a less upright, less Euclidean space where no one, neither teacher nor students, would ever be in his final place.” Easier said than done, of course, but an important life project for all who think of themselves as educators. My own classroom, my own writing, and Architectures of Possibility itself attempt to create the sort of possibility space where, as I mentioned at the outset of our interview, everything should be thought, tried, challenged; where everything rhymes with Roland Barthes’s definition of literature: the question minus the answer. I’m not sure I could write what I’m writing now without the conversations I have almost daily with my students, the conversations they have with each other, the conversations we all have with the texts we study. Especially in light of the paradigm shift over the last, say, quarter century from academia as intellectual exploration to academia as McDonaldized trade school, the irony isn’t lost on me concerning the discrepancy between the safe harbor innovative authors find there and the cultural critiques those authors launch through their writing and pedagogical work. In 2001, I quit my full professorship at one institution precisely because of my disappointment over what had happened to the learning environment there. I had no intentions of reentering the field. In 2007, however, the University of Utah approached me, and I found myself in an environment much more hospitable to the sort of work I want to do—teaching experimental narrative theory and practice. It isn’t by any means a simple irony. One could easily argue innovative writing and pedagogy represents the trace of the paradigm Barthes suggests, and that trace is tremendously productive in all kinds of ways. Innovative writing has never and will never change the world in any large, macrocosmic way. But we’ve all had our lives changed, one by one, by an encounter with a difficult, rich, resonant piece of prose, poetry, music, art, you name it. We’ve all had our lives changed at the ahistorical, microcosmic moment by a class we’ve taken, a teacher we’ve studied with, to such an extent that we became, quite literally, different people. I just came across a stunning set of sentences from Derrida on the topic: “What is education? The death of the parents.” That’s what we’re all up to in the innovative, be it in written texts or the texts we call our classrooms or the texts we call our politics: trying to disrupt what both can and can’t be disrupted, trying to undo what both can and can’t be undone, continuously. (shrink)

We briefly overview some of the historical landmarks on the path leading to the reduction of the number of logical connectives in classical logic. Relying on the duality inherent in Boolean algebras, we introduce a new operator ( Nallor ) that is the dual of Schönfinkel’s operator. We outline the proof that this operator by itself is sufficient to define all the connectives and operators of classical first-order logic ( Fol ). Having scrutinized the proof, we pinpoint the theorems (...) of Fol that are needed in the proof. Using the insights gained from the proof, we show that there are four binary operators that each can serve as the only undefined logical constant for Fol . Finally, we show that from every n -ary connective that yields a functionally complete singleton set of connectives two Schönfinkel-type operators are definable, and all the latter are so definable. (shrink)

In this paper, we study the introduction of modal past temporal operators in Temporal Equilibrium Logic, an hybrid formalism that mixes linear-time modalities and logic programs interpreted under stable models and their characterisation in terms of Equilibrium Logic. We show that Kamp’s translation can also be used to translate the new extension of TEL with past operators into Quantified Equilibrium Logic. Additionally, we provide a method for removing past operators that consists in replacing past-time subformulas by fresh (...) auxiliary atoms, obtaining an equivalent formula, modulo the original alphabet. (shrink)

Montague, Prior, von Wright and others drew attention to resemblances between modal operators and quantifiers. In this paper we show that classical quantifiers can, in fact, be regarded as S5-like operators in a purely propositional modal logic. This logic is axiomatized and some interesting fragments of it are investigated.

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often (...) justified only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

This essay argues that there are theoretical benefits to keeping distinct—more pervasively than the literature has done so far—the psychological states of imagining that p versus believing that in-the-story p, when it comes to cognition of fiction and other forms of narrative. Positing both in the minds of a story’s audience helps explain the full range of reactions characteristic of story consumption. This distinction also has interesting conceptual and explanatory dimensions that haven’t been carefully observed, and the two mental state (...) types make distinct contributions to generating emotional responses to stories. Finally, the differences between the mental states illuminate how a given story can be both shared with others and at the same time experienced as personal. (shrink)

The addition of "actually" operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing "actually" operators has concentrated entirely upon extensions of KT5 and has employed a particular modeltheoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing "actually" operators, the weakest of which are conservative (...) extensions of K, using a novel generalisation of the standard semantics. (shrink)

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...) random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)

Since the very begining of quantum theory there started a debate on the proper role of space and time in it. Some authors assumed that space and time have their own algebraic operators. On that basis they supposed that quantum particles had “coordinates of position”, even though those coordinates were not possible to determine with infinite precision. Furthermore, time in quantum physics was taken to be on an equal foot, by means of a so-called “Heisenberg’s fourth relation of indeterminacy” (...) concerning time and energy. In this paper, the proper role of space and time in the core of non-relativistic quantum phsysics is analyzed. We will find that, rigorously, that relation for time and energy shows a different root. For the role of space, it will be discussed that there is no “coordinate of position” in the conceptual structure of quantum physics because quantum particles are not point-like objects. (shrink)

Ewald considered tense operators G, H, F and P on intuitionistic propositional calculus and constructed an intuitionistic tense logic system called IKt. In 2014, Figallo and Pelaitay introduced the variety IKt of IKt-algebras and proved that the IKt system has IKt-algebras as algebraic counterpart. In this paper, we introduce and study the variety of tense Nelson algebras. First, we give some examples and we prove some properties. Next, we associate an IKt-algebra to each tense Nelson algebras. This result allowed (...) us to determine the congruence of the tense Nelson algebras and also to characterize the subdirectly irreducible tense Nelson algebras and particularly the simple tense Nelson algebras. Finally, we prove that there exists an equivalence between the category of IKt-algebras and the category of tense centered Nelson algebras. (shrink)

We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.

Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended (...) by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right. (shrink)

Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining (...) truth-functional modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics. (shrink)

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339-1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174: (...) 1339-1368, 2010) to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases. (shrink)

Research is a process that leads to new insights rupturing the existent fabric of knowledge. To prevent this process from disintegrating, its coherence must be assured. Under the heading transposition, seventeen artists, musicians, and theorists explain how one thing may turn into another in a spatio-temporal play of identity and difference that has the power to expand into the unknown. While it does not attempt to define the still evolving field of artistic research, through the idea of transposition this book (...) aims to grasp a quality increasingly important to artistic practice because representational approaches have been losing traction. Taking to heart the lessons of deconstruction, new modes of epistemic relationships are being invented that include aesthetic dimensions. Working with materially concrete positions in a manner familiar to artists can ensure that knowledge does not decay into relativism. (shrink)

We investigate operators which take a set X to a set relatively computably enumerable in and above X by studying which such sets X can be so mapped into the Turing degree of K. We introduce notions of nontriviality for such operators, and use these to study which additional properties can be required of sets which can be completed to the jump by given operators of this kind.

Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving a number of counterintuitive features, the work made an implicit assumption that the subject-matter (...) of an intensional conditional is a function of the subject-matters of its subformulae. This assumption—which I will call a principle of topic sufficiency—runs counter to some natural intuitions concerning topic. In this paper, we will investigate topic sufficiency and offer a semantic account that is state-sensitive, providing an implementation through the introduction of topic-sensitive logics related to William Parry’s prototypical $\mathsf {PAI}$. (shrink)

A philosophical discussion of the intuitive meaning of the formalism of modal propositional logics.

We investigate the join semilattice of modal operators on a Boolean algebra B. Furthermore, we consider pairs ⟨f,g⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle f,g \rangle $$\end{document} of modal operators whose supremum is the unary discriminator on B, and study the associated bi-modal algebras.

We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions of (...) general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides. (shrink)

Natural language provides motivation for studying modal backwards-looking operators such as “now”, “then” and “actually” that evaluate their argument formula at some previously considered point instead of the current one. This paper investigates the expressive power over models of both propositional and first-order basic modal language enriched with such operators. Having defined an appropriate notion of bisimulation for first-order modal logic, I show that backwards-looking operators increase its expressive power quite mildly, contrary to beliefs widespread among philosophers (...) of language and formal semanticists. That in turn presents a strong argument for the use of operator-based systems in the semantics of natural language, instead of systems with explicit quantification over worlds and times that have become a de-facto standard for such applications. The popularity of such explicit-quantification systems is shown to be based on the misinterpretation of a claim by Cresswell, which led many philosophers and linguists to assume that introducing “now” and “then” is expressively equivalent to explicitly quantifying over worlds and times. (shrink)

The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety (...) of the algerabic models of the given logics, soundness and completeness with respect to these classes of Kripke-style models follows by using entirely algebraical arguments from the soundness and completeness of the logic with respect to its algebraic models. (shrink)

For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical embedding (...) algebras. Taken together, these properties imply that results about a Sahlqvist variety V van be obtained by reasoning in the elementary class of canonical structures of algebras in V.We give an example of this strategy in the variety of Cylindric Algebras: we show that an important identity calledHenkin's equation is equivalent to a simpler identity that uses only one variable. We give a conceptually simple proof by showing that the first-order correspondents of these two equations are equivalent over the class of cylindric atom structures. (shrink)

In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic _bringing it about that_. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a reduction (...) to more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules. (shrink)

In this paper, we present a way to translate the metainferences of a mixed metainferential system into formulae of an extended-language system, called its associated σ-system. To do this, the σ-system will contain new operators (one for each standard), called the σ operators, which represent the notions of "belonging to a (given) standard". We first prove, in a model-theoretic way, that these translations preserve (in)validity. That is, that a metainference is valid in the base system if and only (...) if its translation is a tautology of its corresponding σ-system. We then use these results to obtain other key advantages. Most interestingly, we provide a recipe for building unlabeled sequent calculi for σ-systems. We then exemplify this with a σ-system useful for logics of the ST family, and prove soundness and completeness for it, which indirectly gives us a calculus for the metainferences of all those mixed systems. Finally, we respond to some possible objections and show how our σ-framework can shed light on the “obeying” discussion within mixed metainferential contexts. (shrink)

As consistency is such an important topic in logic, researchers have for a long time investigated how to attain and maintain it. But consistency can also be studied from the point of view of its opposite, inconsistency. The problem with inconsistency in classical logic is that by the principle of explosion a single inconsistency leads to triviality. Paraconsistent logics were introduced to get around this problem by defining logics in such a way that the explosion principle does not apply to (...) them. Another approach stays in the classical framework and evaluates the amount of inconsistency in a set of formulas. The great bulk of this work has been done for propositional logic and presents many interesting issues about inconsistency. A previous paper introduced the concept of generalized propositional logic (GPL) to provide a uniform method for measuring inconsistency in logics that allow the application of unary operator pairs, such as for modality, time, and space, to propositional logic formulas. The universality of GPL manifests itself in the fact that such an operator pair is evaluated in a uniform manner across all such logics. The difference lies solely in the choice of a frame for each logic. But some logics also contain nonunary operators. For example, temporal logics typically contain a binary Until operator. The purpose of this paper is to show how to extend generalized propositional logic to extended generalized propositional logic (EGPL) by adding nonunary operator pairs and measure inconsistency in such logics. The universality of EGPL manifests itself in the fact that once the evaluation of the nonunary operators is given, it carries over to all such logics. For example, the temporal Until operator becomes applicable to modal logic. Furthermore, while relative inconsistency measures were previously considered for GPL, they are now extended to EGPL and a new approach removes an undesirable feature from the previous version. Also, this paper provides results about various properties of the new inconsistency measures. Many examples and explanations are given to illustrate the issues involving this extension. (shrink)

In this paper, we will study Heyting algebras endowed with tense negative operators, which we call tense H-algebras and we proof that these algebras are the algebraic semantics of the Intuitionistic Propositional Logic with Galois Negations. Finally, we will develop a Priestley-style duality for tense H-algebras.

This paper is devoted to the concepts of consequence and rejection, formulated as operators on a nonempty set of sentences, which may initially be unstructured. One of the issues that we pay attention to is the “cyclicity” of these concepts when they are defined one through the other. In addition, we explore this cyclicity, when the set of all sentences acquires some structure, or we can assume some structure of sentences in the sense that the operation of substitution can (...) be applied to them. (shrink)

This article presents the results of the evaluations of the mechanical stresses associated with the performance of manual lifting tasks of loads and those operators must endure in their workplaces, considering these the most recurrent cases and positions. This study is based on a static analysis of certainspecific positions of the human body, the transmission of forces through the musculoskeletal structure, and the generation of efforts at critical points of the body. In addition to this, it is considered a (...) revision of the criteria of the Spanish Technical Standard NTP-477. There are critical points of the musculoskeletal structure that support considerable efforts, the recommendations and criteria provided by the NTP-477 are relevant and although limited, provide an adequate margin of safety to avoid injury to workers. (shrink)