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Modal Logic: Graph. Darst

New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema (2001)

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  1. Propositional Quantification in Bimodal S5.Peter Fritz - 2020 - Erkenntnis 85 (2):455-465.
    Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding is then extended to all sublogics containing the logic (...)
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  • Modal Ontology and Generalized Quantifiers.Peter Fritz - 2013 - Journal of Philosophical Logic 42 (4):643-678.
    Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...)
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  • Higher-Order Contingentism, Part 1: Closure and Generation.Peter Fritz & Jeremy Goodman - 2016 - Journal of Philosophical Logic 45 (6):645-695.
    This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to (...)
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  • Some remarks on restricting the knowability principle.Martin Fischer - 2013 - Synthese 190 (1):63-88.
    The Fitch paradox poses a serious challenge for anti-realism. This paper investigates the option for an anti-realist to answer the challenge by restricting the knowability principle. Based on a critical discussion of Dummett's and Tennant's suggestions for a restriction desiderata for a principled solution are developed. In the second part of the paper a different restriction is proposed. The proposal uses the notion of uniform formulas and diagnoses the problem arising in the case of Moore sentences in the different status (...)
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  • A New Algebraic Version of Monteiro’s Four-Valued Propositional Calculus.Aldo Victorio Figallo, Estela Bianco & Alicia Ziliani - 2014 - Open Journal of Philosophy 4 (3):319-331.
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  • Essay Review.[author unknown] - 2001 - History and Philosophy of Logic 22 (2):99-112.
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  • Frame constructions, truth invariance and validity preservation in many-valued modal logic.Pantelis E. Eleftheriou & Costas D. Koutras - 2005 - Journal of Applied Non-Classical Logics 15 (4):367-388.
    In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical (...)
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  • Establishing Connections between Aristotle's Natural Deduction and First-Order Logic.Edgar José Andrade & Edward Samuel Becerra - 2008 - History and Philosophy of Logic 29 (4):309-325.
    This article studies the mathematical properties of two systems that model Aristotle's original syllogistic and the relationship obtaining between them. These systems are Corcoran's natural deduction syllogistic and ?ukasiewicz's axiomatization of the syllogistic. We show that by translating the former into a first-order theory, which we call T RD, we can establish a precise relationship between the two systems. We prove within the framework of first-order logic a number of logical properties about T RD that bear upon the same properties (...)
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  • A logical characterisation of qualitative coalitional games.Paul E. Dunne, Wiebe van der Hoek & Michael Wooldridge - 2007 - Journal of Applied Non-Classical Logics 17 (4):477-509.
    Qualitative coalitional games (QCGs) were introduced as abstract formal models of goal-oriented cooperative systems. A QCG is a game in which each agent is assumed to have some goal to achieve, and in which agents must typically cooperate with others in order to satisfy their goals. In this paper, we show how it is possible to reason about QCGs using Coalition Logic (CL), a formalism intended to facilitate reasoning about coalitional powers in game-like multiagent systems. We introduce a correspondence relation (...)
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  • Coalgebraic logic for stochastic right coalgebras.Ernst-Erich Doberkat & Christoph Schubert - 2009 - Annals of Pure and Applied Logic 159 (3):268-284.
    We generalize stochastic Kripke models and Markov transition systems to stochastic right coalgebras. These are coalgebras for a functor with as an endofunctor on the category of analytic spaces, and is the subprobability functor. The modal operators are generalized through predicate liftings which are set-valued natural transformations involving the functor. Two states are equivalent iff they cannot be separated by a formula. This equivalence relation is used to construct a cospan for logical equivalent coalgebras under a separation condition for the (...)
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  • Mixed algebras and their logics.Ivo Düntsch, Ewa Orłowska & Tinko Tinchev - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):304-320.
    We investigate complex algebras of the form arising from a frame where, and exhibit their abstract algebraic and logical counterparts.
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  • Agreement Theorems in Dynamic-Epistemic Logic.Cédric Dégremont & Oliver Roy - 2012 - Journal of Philosophical Logic 41 (4):735-764.
    This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The static agreement (...)
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  • Dynamics we can believe in: a view from the Amsterdam School on the centenary of Evert Willem Beth.Cédric Dégremont & Jonathan Zvesper - 2011 - Synthese 179 (2):223 - 238.
    Logic is breaking out of the confines of the single-agent static paradigm that has been implicit in all formal systems until recent times. We sketch some recent developments that take logic as an account of information-driven interaction. These two features, the dynamic and the social, throw fresh light on many issues within logic and its connections with other areas, such as epistemology and game theory.
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  • Exploring the tractability border in epistemic tasks.Cédric Dégremont, Lena Kurzen & Jakub Szymanik - 2014 - Synthese 191 (3):371-408.
    We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it possible to manipulate Alice in a way that she will have the same beliefs as Bob? The results show that these problems lie on both sides of the border between tractability (P) and intractability (NP-hard). In particular, we (...)
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  • You better play 7: mutual versus common knowledge of advice in a weak-link experiment.Giovanna Devetag, Hykel Hosni & Giacomo Sillari - 2013 - Synthese 190 (8):1351-1381.
    This paper presents the results of an experiment on mutual versus common knowledge of advice in a two-player weak-link game with random matching. Our experimental subjects play in pairs for thirteen rounds. After a brief learning phase common to all treatments, we vary the knowledge levels associated with external advice given in the form of a suggestion to pick the strategy supporting the payoff-dominant equilibrium. Our results are somewhat surprising and can be summarized as follows: in all our treatments both (...)
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  • Some remarks on the model theory of epistemic plausibility models.Lorenz Demey - 2011 - Journal of Applied Non-Classical Logics 21 (3-4):375-395.
    The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized (...)
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  • Separation logics and modalities: a survey.Stéphane Demri & Morgan Deters - 2015 - Journal of Applied Non-Classical Logics 25 (1):50-99.
    Like modal logic, temporal logic, and description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoare-style proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is often understood as a programming language, an assertion language and a family of rules involving Hoare triples. In this survey, we present similarities between separation logic as an assertion language and modal and temporal logics. Moreover, we (...)
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  • Agreeing to disagree in probabilistic dynamic epistemic logic.Lorenz Demey - 2014 - Synthese 191 (3):409-438.
    This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural formalizations of (...)
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  • A Note on Intensionalization.Philippe de Groote & Makoto Kanazawa - 2013 - Journal of Logic, Language and Information 22 (2):173-194.
    Building on Ben-Avi and Winter’s (2007) work, this paper provides a general “intensionalization” procedure that turns an extensional semantics for a language into an intensionalized one that is capable of accommodating “truly intensional” lexical items without changing the compositional semantic rules. We prove some formal properties of this procedure and clarify its relation to the procedure implicit in Montague’s (1973) PTQ.
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  • On Bellissima’s construction of the finitely generated free Heyting algebras, and beyond.Luck Darnière & Markus Junker - 2010 - Archive for Mathematical Logic 49 (7-8):743-771.
    We study finitely generated free Heyting algebras from a topological and from a model theoretic point of view. We review Bellissima’s representation of the finitely generated free Heyting algebra; we prove that it yields an embedding in the profinite completion, which is also the completion with respect to a naturally defined metric. We give an algebraic interpretation of the Kripke model used by Bellissima as the principal ideal spectrum and show it to be first order interpretable in the Heyting algebra, (...)
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  • Temporal Reference in Linear Tense Logic.M. J. Cresswell - 2010 - Journal of Philosophical Logic 39 (2):173-200.
    The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.
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  • Predicate Metric Tense Logic for 'Now' and 'Then'.M. J. Cresswell - 2013 - Journal of Philosophical Logic 42 (1):1-24.
    In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices as (...)
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  • On the strength and scope of DLS.Willem Conradie - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):279-296.
    We provide syntactic necessary and sufficient conditions on the formulae reducible by the second-order quantifier elimination algorithm DLS. It is shown that DLS is compete for all modal Sahlqvist and Inductive formulae, and that all modal formulae in a single propositional variable on which DLS succeeds are canonical.
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  • Algorithmic correspondence and completeness in modal logic. IV. Semantic extensions of SQEMA.Willem Conradie & Valentin Goranko - 2008 - Journal of Applied Non-Classical Logics 18 (2):175-211.
    In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions of (...)
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  • Vagueness: Subvaluationism.Pablo Cobreros - 2013 - Philosophy Compass 8 (5):472-485.
    Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short (...)
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  • Paraconsistent vagueness: a positive argument.Pablo Cobreros - 2011 - Synthese 183 (2):211-227.
    Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least as (...)
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  • An efficient approach to nominal equalities in hybrid logic tableaux.Serenella Cerrito & Marta Cialdea Mayer - 2010 - Journal of Applied Non-Classical Logics 20 (1-2):39-61.
    Basic hybrid logic extends modal logic with the possibility of naming worlds by means of a distinguished class of atoms (called nominals) and the so-called satisfaction operator, that allows one to state that a given formula holds at the world named a, for some nominal a. Hence, in particular, hybrid formulae include “equality” assertions, stating that two nominals are distinct names for the same world. The treatment of such nominal equalities in proof systems for hybrid logics may induce many redundancies. (...)
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  • A Common Frame for Formal Imagination.Joan Casas-Roma, M. Elena Rodríguez & Antonia Huertas - 2019 - Minds and Machines 29 (4):603-634.
    In this paper, we review three influential theories of imagination in order to understand how the dynamics of imagination acts could be modeled using formal languages. While reviewing them, we notice that they are not detailed enough to account for all the mechanisms involved in creating and developing imaginary worlds. We claim those theories could be further refined into what we call the Common Frame for Imagination Acts, which defines a framework that can be used to study the dynamics of (...)
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  • Variants of multi-relational semantics for propositional non-normal modal logics.Erica Calardo & Antonino Rotolo - 2014 - Journal of Applied Non-Classical Logics 24 (4):293-320.
    A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study multi-relational structures, (...)
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  • Quantification in Some Non-normal Modal Logics.Erica Calardo & Antonino Rotolo - 2017 - Journal of Philosophical Logic 46 (5):541-576.
    This paper offers a semantic study in multi-relational semantics of quantified N-Monotonic modal logics with varying domains with and without the identity symbol. We identify conditions on frames to characterise Barcan and Ghilardi schemata and present some related completeness results. The characterisation of Barcan schemata in multi-relational frames with varying domains shows the independence of BF and CBF from well-known propositional modal schemata, an independence that does not hold with constant domains. This fact was firstly suggested for classical modal systems (...)
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  • Determining the environment: a modal logic for closed interaction.Jan Broersen, Rosja Mastop, John-Jules Meyer & Paolo Turrini - 2009 - Synthese 169 (2):351-369.
    The aim of the work is to provide a language to reason about Closed Interactions, i.e. all those situations in which the outcomes of an interaction can be determined by the agents themselves and in which the environment cannot interfere with they are able to determine. We will see that two different interpretations can be given of this restriction, both stemming from Pauly Representation Theorem. We will identify such restrictions and axiomatize their logic. We will apply the formal tools to (...)
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  • From KLM-style conditionals to defeasible modalities, and back.Katarina Britz & Ivan Varzinczak - 2018 - Journal of Applied Non-Classical Logics 28 (1):92-121.
    We investigate an aspect of defeasibility that has somewhat been overlooked by the non-monotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal osperators with which to formalise the notion of defeasible (...)
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  • Constrained Consequence.Katarina Britz, Johannes Heidema & Ivan Varzinczak - 2011 - Logica Universalis 5 (2):327-350.
    There are various contexts in which it is not pertinent to generate and attend to all the classical consequences of a given premiss—or to trace all the premisses which classically entail a given consequence. Such contexts may involve limited resources of an agent or inferential engine, contextual relevance or irrelevance of certain consequences or premisses, modelling everyday human reasoning, the search for plausible abduced hypotheses or potential causes, etc. In this paper we propose and explicate one formal framework for a (...)
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  • Nonclassical Probability and Convex Hulls.Seamus Bradley - 2017 - Erkenntnis 82 (1):87-101.
    It is well known that the convex hull of the classical truth value functions contains all and only the probability functions. Work by Paris and Williams has shown that this also holds for various kinds of nonclassical logics too. This note summarises the formal details of this topic and extends the results slightly.
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  • Quantificational modal logic with sequential Kripke semantics.Stefano Borgo - 2005 - Journal of Applied Non-Classical Logics 15 (2):137-188.
    We introduce quantificational modal operators as dynamic modalities with (extensions of) Henkin quantifiers as indices. The adoption of matrices of indices (with action identifiers, variables and/or quantified variables as entries) gives an expressive formalism which is here motivated with examples from the area of multi-agent systems. We study the formal properties of the resulting logic which, formally speaking, does not satisfy the normality condition. However, the logic admits a semantics in terms of (an extension of) Kripke structures. As a consequence, (...)
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  • Logics of left variable inclusion and Płonka sums of matrices.S. Bonzio, T. Moraschini & M. Pra Baldi - 2020 - Archive for Mathematical Logic (1-2):49-76.
    The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic \. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic \ is related to the construction of Płonka sums of the matrix models of \. This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate (...)
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  • Inexact Knowledge with Introspection.Denis Bonnay & Paul Égré - 2009 - Journal of Philosophical Logic 38 (2):179-227.
    This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.
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  • Pure Extensions, Proof Rules, and Hybrid Axiomatics.Patrick Blackburn & Balder Ten Cate - 2006 - Studia Logica 84 (2):277-322.
    In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a (...)
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  • Modal Logic As Dialogical Logic.Patrick Blackburn - 2001 - Synthese 127 (1-2):57-93.
    The title reflects my conviction that, viewed semantically,modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notably the use of nominals, special proposition symbols which ‘name’ worlds) I will show how to lift the dialogical (...)
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  • Arthur Prior and Hybrid Logic.Patrick Blackburn - 2006 - Synthese 150 (3):329-372.
    Contemporary hybrid logic is based on the idea of using formulas as terms, an idea invented and explored by Arthur Prior in the mid-1960s. But Prior’s own work on hybrid logic remains largely undiscussed. This is unfortunate, since hybridisation played a role that was both central to and problematic for his philosophical views on tense. In this paper I introduce hybrid logic from a contemporary perspective, and then examine the role it played in Prior’s work.
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  • Subspaces of $${\mathbb{Q}}$$ whose d-logics do not have the FMP.Guram Bezhanishvili & Joel Lucero-Bryan - 2012 - Archive for Mathematical Logic 51 (5-6):661-670.
    We show that subspaces of the space ${\mathbb{Q}}$ of rational numbers give rise to uncountably many d-logics over K4 without the finite model property.
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  • Tree-like constructions in topology and modal logic.G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan & J. Van Mill - 2020 - Archive for Mathematical Logic 60 (3):265-299.
    Within ZFC, we develop a general technique to topologize trees that provides a uniform approach to topological completeness results in modal logic with respect to zero-dimensional Hausdorff spaces. Embeddings of these spaces into well-known extremally disconnected spaces then gives new completeness results for logics extending S4.2.
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  • Connected modal logics.Guram Bezhanishvili & David Gabelaia - 2011 - Archive for Mathematical Logic 50 (3-4):287-317.
    We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing the McKinsey-Tarski theorem. As a consequence, we obtain that each intermediate logic with the finite model property is the logic of a subalgebra of the Heyting algebra of all open subsets of R.
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  • Admissible Bases Via Stable Canonical Rules.Nick Bezhanishvili, David Gabelaia, Silvio Ghilardi & Mamuka Jibladze - 2016 - Studia Logica 104 (2):317-341.
    We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.
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  • Duality for the Logic of Quantum Actions.Jort M. Bergfeld, Kohei Kishida, Joshua Sack & Shengyang Zhong - 2015 - Studia Logica 103 (4):781-805.
    In this paper we show a duality between two approaches to represent quantum structures abstractly and to model the logic and dynamics therein. One approach puts forward a “quantum dynamic frame” :2267–2282, 2005), a labelled transition system whose transition relations are intended to represent projections and unitaries on a Hilbert space. The other approach considers a “Piron lattice”, which characterizes the algebra of closed linear subspaces of a Hilbert space. We define categories of these two sorts of structures and show (...)
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  • The information in intuitionistic logic.Johan Benthem - 2008 - Synthese 167 (2):251-270.
    Issues about information spring up wherever one scratches the surface of logic. Here is a case that raises delicate issues of 'factual' versus 'procedural' information, or 'statics' versus 'dynamics'. What does intuitionistic logic, perhaps the earliest source of informational and procedural thinking in contemporary logic, really tell us about information? How does its view relate to its 'cousin' epistemic logic? We discuss connections between intuitionistic models and recent protocol models for dynamic-epistemic logic, as well as more general issues that emerge.
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  • Logic in a Social Setting.Johan van Benthem - 2011 - Episteme 8 (3):227-247.
    Taking Backward Induction as its running example, this paper explores avenues for a logic of information-driven social action. We use recent results on limit phenomena in knowledge updating and belief revision, procedural rationality, and a ‘Theory of Play’ analyzing how games are played by different agents.
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  • Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences.Johan Van Benthem, Patrick Girard & Olivier Roy - 2009 - Journal of Philosophical Logic 38 (1):83 - 125.
    This paper presents a new modal logic for ceteris paribus preferences understood in the sense of "all other things being equal". This reading goes back to the seminal work of Von Wright in the early 1960's and has returned in computer science in the 1990' s and in more abstract "dependency logics" today. We show how it differs from ceteris paribus as "all other things being normal", which is used in contexts with preference defeaters. We provide a semantic analysis and (...)
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  • On the Ternary Relation and Conditionality.Jc Beall, Ross T. Brady, J. Michael Dunn, A. P. Hazen, Edwin D. Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney & Richard Sylvan - 2012 - Journal of Philosophical Logic 41 (3):595 - 612.
    One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...)
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  • Continuous propositional modal logic.Stefano Baratella - 2018 - Journal of Applied Non-Classical Logics 28 (4):297-312.
    We introduce a propositional many-valued modal logic which is an extension of the Continuous Propositional Logic to a modal system. Otherwise said, we extend the minimal modal logic to a Continuous Logic system. After introducing semantics, axioms and deduction rules, we establish some preliminary results. Then we prove the equivalence between consistency and satisfiability. As straightforward consequences, we get compactness, an approximated completeness theorem, in the vein of Continuous Logic, and a Pavelka-style completeness theorem.
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