Both the phenomenon of presupposition and that of vagueness have motivated the use of one form or another of trivalent logic, in which a declarative sentence can not only receive the standard values true and false , but also a third, non-standard truth-value which is usually understood as ‘undefined’ . The goal of this paper is to propose a multivalent framework which can deal simultaneously with presupposition and vagueness, and, more specifically, capture their projection properties as well as their (...) different roles in language. Now, there is a prima facie simple way of doing this, which simply consists in assimilating the two phenomena, and using an appropriate type of trivalent logic. On this view, we just need a compositional system that deals with the ‘undefined’ truth-value, and does not care about whether the source of undefinedness is ‘presuppositional’ or related to vagueness. I will argue that such a simple solution cannot succeed, and point out a number of desiderata that any successful approach must meet. I will then present and discuss two seven-valued semantics, inspired, respectively, by the Strong Kleene semantics and by supervaluationism, which meet these desiderata. (shrink)

Predicates are supposed to slice reality neatly in two halves, one for which the predicate holds, the other for which it fails. Yet far from being razors, predicates tend to be dull knives that mangle reality. If reality is a tomato and predicates are knives, then when these knives divide the tomato, plenty of mush remains unaccounted for. Of course some knives are sharper than others, just as some predicates are less vague than others. “x is water” is certainly sharper (...) than “x is beautiful.” But perfect sharpness, perfect boundaries, and perfect separation seem only to obtain in mathematics. The vagueness inherent in many predicates became particularly evident in the twentieth century. Quantum mechanics, the revival of certain ancient paradoxes, and the philosophy of science all contributed to a growing awareness that vagueness was ineliminable from many predicates. Quantum mechanical superposition seems to allow mutually exclusive simultaneous states. In searching for plausible interpretations of quantum mechanics, some researchers attempted to do away with classical bivalent logic. In its place they substituted multivalent quantum logics. Any logic with more than two values forces its predicates to slice reality into more than two parts. Ancient paradoxes involving heaps and baldness also pointed up the 1 Random Predicate Logic 2.. (shrink)

In the paper, we tackle the matter of non-classical logics, in particular, paraconsistent ones, for which not every formula follows in general from inconsistent premisses. Our benchmark is Jaśkowski’s logic, modeled with the help of discussion. The second key origin of this paper is the matter of being tabular, i.e. being adequately expressible by finitely many finite matrices. We analyse Jaśkowski’s non-tabular discussive (discursive) logic $ \textbf {D}_{2}$, one of the first paraconsistent logics, from the perspective of a (...) trivalent tabular logic. We are motivated to step down from the ongoing modal $ \textbf {S5}$-perspective of developing $ \textbf {D}_{2}$ both by certain mysteries that have been surrounding it and by gaps in Jaśkowski’s arguments contra the multivalent tabular perspective. Although Jaśkowski’s idea to use $ \textbf {S5}$ in order to define $ \textbf {D}_{2}$ is very attractive since it allows one to benefit from the tools and results of modal logic, it also gives a ‘non-direct’ formulation and, as it appeared later, is superfluous with respect to what is meant to be achieved since one can define the very same logic but using modal logics weaker than S5. It is also known, due to Kotas, that discussive logic is not finite-valued. So, in light of Kotas’s result that $ \textbf {D}_{2}$ is non-tabular, we propose to associate it with a few dozen discussive formulae that Jaśkowski unequivocally and illustratively suggests to be its theorems or non-theorems rather than with axioms of its modern axiomatizations (one of which Kotas employs) in order to be capable of performing a computer-aided brute-force search for suitable trivalent matrices in the cases of one and two designated values. As a result, we find trivalent matrices with two designated values that might be dubbed ‘discussive’ because they meet Jaśkowski’s suggestion to validate and invalidate the litmus theorems and non-theorems, respectively, despite the fact that none of them validates all the negation axioms in the modern axiomatizations of $ \textbf {D}_{2}$. The matrices found are then analysed along with highlighting the ones that were previously mentioned in the literature. We conclude the paper with a comparative analysis of Omori’s results and a test of Karpenko’s hypothesis. (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in (...) the foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

The ancient problem of fatalism, more particularly theological fatalism, has resurfaced with surprising vigour in the second half of the twentieth century. Two questions predominate in the debate: (1) Is divine foreknowledge compatible with human freedom and (2) How can God foreknow future free acts? Having surveyed the historical background of this debate in "The Problem of Divine Foreknowledge" and "Future Contingents from Aristotle to Suarez" (Brill: 1988), William Lane Craig now attempts to address these issues critically. His wide-ranging discussion (...) brings together a thought- provoking array of related topics such as logical fatalism, multivalent logic, backward causation, precognition, time travel, counterfactual logic, temporal necessity, Newcomb's Problem, middle knowledge, and relativity theory. The present work serves both as a useful survey of the extensive literature on theological fatalism and related fields and as a stimulating assessment of the possibility of divine foreknowledge of future free acts. (shrink)

English summary: Jan Lukasiewicz (1878-1956) was one of the most important members of the Lwow-Warsaw school of logic. The thirteen translated articles in this volume demonstrate the protean form of Lukasiewiczs work, from his texts on Aristotle and the principle of non-contradiction and syllogistics to modal logic, intuitionism, and multivalent logics. The articles show in particular his preoccupations with logical precision and the problem of human liberty. French description: Avec Kazimierz Twardowski, Stanislaw Lesniewski et Alfred Tarski, le logicien (...) et philosophe polonais Jan Lukasiewicz (1878-1956) est l'un des membres les plus importants de l'Ecole de Lvov-Varsovie. Celebre pour ses ouvrages consacres a Aristote, notamment sur le principe de non-contradiction et sur la syllogistique, il a egalement publie des articles majeurs sur la logique propositionnelle, la logique modale, l'intuitionnisme et les logiques multivalentes, dont il fut l'un des fondateurs. Enfin, il a contribue a faire reconnaitre l'importance des travaux en logique de l'ecole megarico-stoicienne, trop longtemps eclipses par ceux d'Aristote sur la syllogistique. Mais Lukasiewicz ne fut pas seulement un logicien et un historien brillant, il s'engagea aussi dans les polemiques philosophiques de son temps. Il defendit ainsi la methode logique en philosophie. Proche sur ce point des membres du Cercle de Vienne, il ne rejetait pas pour autant les questions metaphysiques, commecelle du determinisme qui l'occupa toute sa vie. Les treize articles de ce recueil, fruit d'un travail collectif de traduction, ont pour ambition de montrer le caractere proteiforme de l'oeuvre de Lukasiewicz, preoccupe autant par la precision logique que par le probleme de la liberte humaine. (shrink)

This book addresses two questions: "How is genuine future contingency compatible with divine foreknowledge?" and "How is foreknowledge possible?" Craig attempts to reconcile future contingency within the constraints of a Biblically informed conception of God. This volume, a companion to Craig's historical survey The Problem of Divine Foreknowledge and Future Contingents from Aristotle to Suarez, is in contrast to that study, is a synoptic and critical survey of the recent literature on theological fatalism. It discusses such intriguing related topics as (...) logical fatalism, multivalent logic, backward causation, time travel, counterfactuals, Newcomb's problem, and middle knowledge. (shrink)

In this paper I argue that logical multivalency is necessary for epistemology and has desirable structural properties. In support of this claim, I discuss the nonclassical logical values from an epistemological point of view. The question addressed is how many logical values logicians and philosophers need. Two standpoints are usually adopted regarding this issue: the fundamentality of bivalence and the necessity of multivalence. The first position, supported by Suszko, is summarized in the statement that due to the very nature of (...) logic, bivalency is all we need. The second position, motivated by research practice which requires making inferences under imperfect conditions, admits the multivalence. In the first part of the article, I focus on the very first manyvalued system L3, invented and explored by Jan Łukasiewicz. I recount the critique of L3, and then discuss Suszko’s thesis and Malinowski’s response. I also analyze the epistemological background of the Suszko-Łukasiewicz controversy which was related to the relation between logic, antirealism and externalism. I conclude fundamentalism regarding logical bivalence generates more problems than the adoption of multivalency. (shrink)

the world of phenomena is immensely large this means we can perceive only part of the world. We see, feel and hear parts of reality, not the whole of it, and it seems that a sentence containing a verb of perception like 'John sees a house burn' is most naturally treated as saying that the subject sees an incomplete world in which the embedded sentence is true (see Barwise (1981) for this analysis). But if we want to analyse perception verbs (...) thus, we must introduce some form of incompleteness into our formal system, the.. (shrink)

This book will attempt to achieve a constructive and positive correla tion between mythic-symbolic language and philosophical anthropolo gy. It is intended as a reflection on the philosophical accomplishment of Paul Ricoeur. The term mythic-symbolic language in this context means the language of the multivalent symbol given in the myth with its psychological and poetic counterparts. The term symbol is not con ceived as an abstract sign as it is used in symbolic logic, but rather as a concrete phenomenon (...) - religious, psychological, and poetic. The task inherent in this correlation is monumental when one considers the dual dilemma of problematic and possibility which is at its heart. The prob lematic arises out of the apparent difficulty presented by the so-called challenge of modernity which seems to require the elimination of my thic-symbolic language as an intelligible mode of communication. Mythic-symbolic language is sometimes eliminated because in a world molded by abstract conceptualizations conceptUalizations of science, such a language is thought to be unintelligible. The claim is that its "primitive" explana tions have been transcended by our modernity. Others believe that the problem of mythic-symbolic language is the problem of the myth. If the mythic forms of language could be eliminated, the truth of such language could be preserved through its translation into an intelligible mode of discourse. The problematic is heightened further by the relation of consider ations of language to philosophical anthropology. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Tyrant’s Writ: Myths and Images of Writing in Ancient GreeceThomas ColeDeborah T. Steiner. The Tyrant’s Writ: Myths and Images of Writing in Ancient Greece. Princeton: Princeton University Press, 1994. xiv + 279 pp. Cloth, price not stated.Literacy, as the author correctly points out in her introduction (5), tends to be seen nowadays as “a tool of cultural progress, of rational thought, of scientific analysis, a critical marker (...) that separates the developing from the developed world”; and so the spread of literacy in the Greek world of the Archaic and Classical periods is almost inevitably treated as an event that “heralds in a new rational, skeptical and objective approach,” leading to “advances... in logic, science and technology.” What follows this observation—by way of supplement or corrective to the communis opinio—is an attempt to show that for the Greeks themselves—insofar as their attitude can be documented down to the early fourth century B.C.—writing was something rather different: a multivalent and at times mysterious system of signifiers only partially differentiated from the nonalphabetic symbols and signs that preceded its introduction (chap. 1), a talismanic means of giving greater solemnity and efficacy to the contents of oaths, curses, prayers, and oracles (chap. 2), a frequent source of a “conservative and backward looking” vehicle (metaphor) for carrying on psychological and cosmological speculation (chap. 3), and a medium highly suspect as being the one preferred by tyrants, Greek or oriental, when communicating with their subjects or deputies (chap. 4) and by various types of subversives (conspiring oligarchs, religious fanatics, apolitical shunners of assembly and agora) when communicating among themselves (chap. 5).The attempt, though carried out with energy and imagination, strikes me as ultimately unsuccessful—inconclusive at best and at times dedicated to establishing theses which are refuted by the very evidence that has been assembled to support them. This is especially apparent in chapter 3, which suffers from a failure to allow for the existence of highly traditional modes of argumentation such as metaphor alongside the use of metaphorical vehicles in conjunction with highly “progressive” or revolutionary tenors. The habit of comparing perception, remembering, and forgetting to the inscribing, preservation, and erasure of texts on the wax tablets of the mind (100–5) is surely inseparable from the development both of an empiricist psychology and epistemology and of a materialistic view of the soul; and the atomist analogy between letters and the basic constituents of the cosmos (116–22) stands in equally close relationship to the concern of the scientist—be he ancient or modern—to draw distinctions between primary and secondary sensory qualities and to produce an accounting for the apparently qualitative differences between phenomena in ultimately quantitative terms.While not actually refuting the author’s theses, chapter 2 reveals the existence [End Page 145] of a fairly strong argumentum ex silentio against them. Its discussion is based almost entirely on inferences as to the attitudes whose existence might be posited to explain the frequency with which writing is used in certain contexts, and this frequency is, to my mind, more efficiently and plausibly accounted for as the result of nothing more mysterious than a general recognition of the superiority of written to verbal texts in situations where permanence, transportability, visibility, or reliability and authenticity are called for. We are still far from the skepticism, rationalism, and objectivity posited by the modern communis opinio, but much nearer to that than the obscurantism and authoritarianism of the alternative vision offered here. One would certainly not be surprised if, “as documents came to supplement and then to replace symbolic objects,” the former came to acquire some of the sacral character of the latter, and Steiner cites evidence (63 n. 8) to suggest that this actually occurred in medieval England. Parallels can also be cited from medieval Tibet, where monks sought to secure to themselves the spiritual benefits of Buddhist scriptures by wadding pages from the texts in question into small pellets and swallowing them; or even twentieth-century America, where college students seem to derive comparable reassurance from the photocopies of unread articles that line their bookshelves. But nothing in the evidence Steiner cites... (shrink)

Elaborating decolonial and intersectional methods, aesthetics has developed rich tools for tackling power differences. A philosophical question arises about the nature of gendered embodied experience and materiality: How to comprehend the cultural field if it is at once a site of heinous expropriation and violence and one of vital social and political possibility? This essay explores this question through a reading of Claudia Llosa's film The Milk of Sorrow ( La teta asustada ) (2009). The film, we show, reworks racial, (...) gendered, and colonial logics and supplants a model of transculturation, magical realism, and syncretism and its attendant figuration of resistance by a cultural vision of a web of multivalent, pluri-directional aesthetic promises and threats. Thus it presents a young Indigenous woman as a contemporary decolonial actor who, in encounter with popular culture and the global marketplace, renders memory livable and opens up unforeseen futures for her young town and country. We signal the implications for the positioning of the decolonial feminist spectator or culture maker and for a decolonial aesthetics. Aesthetic existence at the intersection of oppression and liberation, although impure and troubled, functions as a bountiful font of feminist energy and sustenance and a site of communal caring and imagination. (shrink)

I argue that it is only on the condition of a preconceptual understanding that Zhuangzi's metaphors can be cognitive. Kim-chong Chong holds that the choice between metaphors as noncognitive and cognitive is a choice between Allinson and Davidson. Chong's view of metaphors possessing multivalence is reducible to Davidson's choice, because there is no built-in parameter between multivalence and limitless valence. If Zhuangzi's metaphors were multivalent, the text would be subject to infinite interpretive viewpoints and the logical consequence of relativism. (...) It is only if metaphors are cognitive that the text of the Zhuangzi can convey the message of transcendent freedom. (shrink)

The Editors express their gratitude and appreciation to the indi-viduals listed below who served as referees for Informal Logic for Volumes 31 (2011) and 32 (2012).

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general (...) method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. (shrink)

ABSTRACT:This study examines whether the empirical evidence on the relationship between corporate social performance (CSP) and corporate financial performance (CFP) differs depending on the publication outlet in which that evidence appears. This moderator meta-analysis, based on a total sample size of 33,878 observations, suggests that published CSP-CFP findings have been shaped by differences in institutional logics in different subdisciplines of organization studies. In economics, finance, and accounting journals, the average correlations were only about half the magnitude of the findings (...) published in Social Issues in Management, Business Ethics, or Business and Society journals (mean corrected correlation coefficientof.22 vs..49, respectively). Specifically, economists did not find null or negative CSP-CFP correlations, and average findings published in general management outlets (=.41) were closer to Social Issues in Management, Business Ethics, and Business and Society results than to findings reported in economics, finance, and accounting journals. (shrink)

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic (...) in terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. -/- . (shrink)

Retroduction -- Contextualized self-interpretations -- Causal mechanisms -- Ontology -- Logics -- Articulation.

In this article complexity results for adaptive logics using the minimal abnormality strategy are presented. It is proven here that the consequence set of some recursive premise sets is $\Pi _1^1 - complete$ . So, the complexity results in (Horsten and Welch, Synthese 158:41–60,2007) are mistaken for adaptive logics using the minimal abnormality strategy.

According to Frege's principle the denotation of a sentence coincides with its truth-value. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense.A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A deductive system is a second-order matrix over the formula algebra of some fixed but arbitrary language. A second-order matrix A is (...) Fregean if, for any subset X of A, the set of all pairs a,b such that X{a} and X{b} have the same closure is a congruence relation on A. Hence a deductive system is Fregean if interderivability is compositional. The logics intermediate between the classical and intuitionistic propositional calculi are the paradigms for Fregean logics. Normal modal logics are non-Fregean while quasi-normal modal logics are generally Fregean.The main results of the paper: Fregean deductive systems that either have the deduction theorem, or are protoalgebraic and have conjunction, are completely characterized. They are essentially the intermediate logics, possibly with additional connectives. All the full matrix models of a protoalgebraic Fregean deductive system are Fregean, and, conversely, the deductive system determined by any class of Fregean second-order matrices is Fregean. The latter result is used to construct an example of a protoalgebraic Fregean deductive system that is not strongly algebraizable. (shrink)

In this paper, I will describe a technique for generating a novel kind of semantics for a logic, and explore some of its consequences. It would be natural to call the semantics produced by the technique in question ‘many-valued'; but that name is, of course, already taken. I call them, instead, ‘plurivalent'. In standard logical semantics, formulas take exactly one of a bunch of semantic values. I call such semantics ‘univalent'. In a plurivalent semantics, by contrast, formulas may take one (...) or more such values. The construction I shall describe can be applied to any univalent semantics to produce a corresponding plurivalent one. In the paper I will be concerned with the application of the technique to propositional many-valued logics. Sometimes going plurivalent does not change the consequence relation; sometimes it does. I investigate the possibilities in detail with respect to small family of many-valued logics. (shrink)

In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that (...) are generically invariant and faithful against the backdrop of the strongest large cardinal hypotheses. We show that there is a close correspondence between the two hierarchies and we characterize the strongest logic in each hierarchy. On the first-order side, this leads to a new presentation of Woodin's Ω-logic. On the second-order side, we compare the strongest logic with full second-order logic and argue that the comparison lends support to Quine's claim that second-order logic is really set theory in sheep's clothing. (shrink)

The novel notion of importing logics is introduced, subsuming as special cases several kinds of asymmetric combination mechanisms, like temporalization [8, 9], modalization [7] and exogenous enrichment [13, 5, 12, 4, 1]. The graph-theoretic approach proposed in [15] is used, but formulas are identified with irreducible paths in the signature multi-graph instead of equivalence classes of such paths, facilitating proofs involving inductions on formulas. Importing is proved to be strongly conservative. Conservative results follow as corollaries for temporalization, modalization and (...) exogenous enrichment. (shrink)

The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we (...) exploit not only to establish advantages and limitations of our approach with respect to related ones, but also to give, by means of a substructural analysis, a new proof-theoretic method for investigating decidability and complexity of (some of) the logics we consider. All of our deduction systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development. Labelled Non-Classical Logics is essential reading for researchers and practitioners interested in the theory and applications of non-classical logics. (shrink)

A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed. In the past decade, spatial logics have attracted much attention in response to developments in such diverse fields as Artificial Intelligence, Database Theory, Physics, and Philosophy. The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. (...) Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject. (shrink)

Once the Kripke semantics for normal modal logics were introduced, a whole family of modal logics other than the Lewis systems S1 to S5 were discovered. These logics were obtained by changing the semantics in natural ways. The same can be said of the Kripke-style semantics for relevant logics: a whole range of logics other than the standard systems R, E and T were unearthed once a semantics was given (cf. Priest and Sylvan [6], Restall (...) [7], and Routley et al. [8]). In a similar way, weakening the structural rules of the Gentzen formulation of classical logic gives rise to other ‘substructural’ logics such as linear logic (as in Girard [4]). This process of ‘strategic weakening’ is becoming popular today, with the discovery of applications of these logics to areas such as linguistics and the theory of computation (cf. van Benthem [1]). Until now no-one has (to my knowledge) examined what the process of weakening does to the Kripke-style semantics of intuitionistic logic. This paper remedies the deficiency, introducing the family of subintuitionistic logics. These systems have some appealing features. Unlike other substructural logics such as linear logic (which lack distribution of extensional disjunction over conjunction) they have a very natural Kripke-style worlds semantics. Also, the difficulties with regard to modelling quantification in these systems may be able to shed some light on the difficulties in naturally modelling quantification in relevant logics, as it must be admitted that the semantics currently available for quantified relevant logics are rather baroque (cf. Fine [3]). But most importantly, delving in the undergrowth of logics such as intuitionistic logic gives us a ‘feel’ for how such systems are put together, and what job is being done by each aspect of the modelling conditions in.. (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense reasoning, expert systems implementation, (...) deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found in human (...) reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

This article proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this article we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, (...) expansions of MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs. (shrink)

This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FL ${}_{\scriptsize\mbox{e}}$ -algebras). In particular, we inquire into sufficient and necessary conditions under which generalizations of the connexive implication-like operation defined in [6] for Heyting algebras still satisfy connexive theses. It will turn out that, in most cases, connexive principles are equivalent to the equational Glivenko property with respect to Boolean algebras. Furthermore, (...) we provide some philosophical upshots like, e.g., a discussion on the relevance of the above operation in relationship with G. Polya’s logic of plausible inference, and some characterization results on weak and strong connexivity. (shrink)

We define prenormal modal logics and show that S1, S1, S0.9, and S0.9 are Lewis versions of certain prenormal logics, determination and decidability for which are immediate. At the end we characterize Cresswell logics and ponder C. I. Lewis's idea of strict implication in S1.

This chapter contains sections titled: 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9.

We generalize Moss and Parikh's logic of knowledge, effort, and topological reasoning, in two ways. We develop both a multi-agent and a multi-method setting for it. In each of these cases, we prove a corresponding soundness and completeness theorem, and we show that the new logics are decidable. Our methods of proof rely on those for the original system. This might have been expected, since that system is conservatively extended for the given situation. Several technical details are different nevertheless (...) here. (shrink)

In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.

Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes clear (...) (despite some of our hopes and utterances) that the One True Logic does not exist. This is as true for relevant logics as Kripke et al., showed it to be for modal logics. In both cases, subtle (and not so subtle) variations on semantical postulates produce different logics in the same family. The question of which semantical postulates are correct makes no sense without further context, i.e., the questioner needs to answer the question: Correct for what? The question that does remain is: What motivates the relevant family of logics? And this is the question that is the main job for this chapter to investigate. (shrink)

In this paper1 we study admissible consecutions in multi-modal logics with the universal modality. We consider extensions of multi-modal logic S4n augmented with the universal modality. Admissible consecutions form the largest class of rules, under which a logic is closed. We propose an approach based on the context effective finite model property. Theorem 7, the main result of the paper, gives sufficient conditions for decidability of admissible consecutions in our logics. This theorem also provides an explicit algorithm for (...) recognizing such consecutions. Some applications to particular logics with the universal modality are given. (shrink)

We present a number of equivalent calculi for many-valued logics and prove soundness and strong completeness theorems. The calculi are obtained from the truth tables of the logic under consideration in a straightforward manner and there is a natural duality among these calculi. We also prove the cut elimination theorems for the sequent-like systems.