About this topic
Summary Several kinds of semantics for modal logic have been proposed, the most popular of which is Kripke semantics. (This is sometimes called possible worlds semantics, although the formal semantics doesn’t require us to think of the entities in its domain as possible worlds.) In Kripke semantics, models comprise a domain of entities, variously called pointssituationsscenarios or possible worlds, with one or more accessible relations between them. The truth-value of a sentence at a possible world w may depend on the truth-value of other sentences at worlds accessible from w. In modal logics, for example, ‘necessarily, A’ is true at a worldw iff A is true at all worlds u accessible from w, and ‘possibly, A’ is true at w iff A is true at some world u accessible from w. This approach can be applied to other kinds of modalities, including ‘agent a knows that’ in modal epistemic logics. One can also give algebraic, topological and categorical semantics for modal logics, in place of Kripke semantics. These approaches have intrinsic mathematical interest, but have received less attention in the philosophical literature (perhaps because they do not provide an analysis of modal concepts in the way that possible worlds semantics does).
Key works Possible worlds semantics was first presented as a formal semantics for modal logic in Kripke 1959, 1963 and for intuitionistic logic in Kripke 1963Carnap 1947 was an important precursor to possible worlds semantics. Hintikka 1962, 1967 develops the possible worlds semantics and applies it to epistemic concepts. van Benthem 1983 is the classic investigation of the relationship between accessibility relations in the semantics and modal axioms. Lewis 1968 develops counterpart theory in the context of (first-order) possible worlds semantics. Lewis 1986 argues for an extreme realist philosophical interpretation of the possible worlds semantics.
Introductions Girle 2003 and Girle 2000 are introductory textbooks on possible worlds and modal logic. Priest 2001 is a general introduction to propositional modal, intuitionistic and relevant logics. Cresswell & Hughes 1996 is a classic textbook in modal logic. Sider 2010 includes a good presentation of quantified first-order logic.
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  1. added 2018-10-27
    The Modal Logic of the Countable Random Frame.Valentin Goranko & Bruce Kapron - 2003 - Archive for Mathematical Logic 42 (3):221-243.
    We study the modal logic M L r of the countable random frame, which is contained in and `approximates' the modal logic of almost sure frame validity, i.e. the logic of those modal principles which are valid with asymptotic probability 1 in a randomly chosen finite frame. We give a sound and complete axiomatization of M L r and show that it is not finitely axiomatizable. Then we describe the finite frames of that logic and show that it has the (...)
  2. added 2018-07-24
    Non-Normal Modalities in Variants of Linear Logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.
    This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models (...)
  3. added 2018-05-10
    Partial Semantics for Quantified Modal Logic.Eric Johannesson - 2018 - Journal of Philosophical Logic 47 (6):1049-1060.
    When it comes to Kripke-style semantics for quantified modal logic, there’s a choice to be made concerning the interpretation of the quantifiers. The simple approach is to let quantifiers range over all possible objects, not just objects existing in the world of evaluation, and use a special predicate to make claims about existence. This is the constant domain approach. The more complicated approach is to assign a domain of objects to each world. This is the varying domain approach. Assuming that (...)
  4. added 2018-04-21
    Dov Gabbay, Reactive Kripke Semantics. [REVIEW]Valentin Goranko - 2017 - Studia Logica 105 (2):431-437.
  5. added 2018-04-21
    Foreword to Special Issue on Logics for Multi-Agent Systems.Valentin Goranko & Wojciech Jamroga - 2011 - Journal of Applied Non-Classical Logics 21 (1):7-8.
  6. added 2018-04-21
    From Linear to Branching-Time Temporal Logics: Transfer of Semantics and Definability.Valentin Goranko & Alberto Zanardo - 2007 - Logic Journal of the IGPL 15 (1):53-76.
    This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. We then consider (...)
  7. added 2018-04-21
    Modal Logics for Parallelism, Orthogonality, and Affine Geometries.Philippe Balbiani & Valentin Goranko - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):365-397.
    We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.
  8. added 2018-04-21
    Hyperboolean Algebras and Hyperboolean Modal Logic.Valentin Goranko & Dimiter Vakarelov - 1999 - Journal of Applied Non-Classical Logics 9 (2):345-368.
    Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the finite model property. The (...)
  9. added 2018-04-20
    Strategic Commitment and Release in Logics for Multi-Agent Systems.Thomas Ågotnes, Valentin Goranko & Wojciech Jamroga - manuscript
    In this paper we analyze how the semantics of the Alternating-time Temporal Logic ATL$^*$ deals with agents' commitments to strategies in the process of formula evaluation. In (\acro{atl}$^*$), one can express statements about the strategic ability of an agent (or a coalition of agents) to achieve a goal $\phi$ such as: ``agent $i$ can choose a strategy such that, if $i$ follows this strategy then, no matter what other agents do, $\phi$ will always be true''. However, strategies in \acro{atl} are (...)
  10. added 2018-04-20
    Algorithmic Correspondence and Completeness in Modal Logic. V. Recursive Extensions of SQEMA.Willem Conradie, Valentin Goranko & Dimitar Vakarelov - 2010 - Journal of Applied Logic 8 (4):319-333.
    The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, we prove that (...)
  11. added 2018-04-20
    Algorithmic Correspondence and Completeness in Modal Logic. IV. Semantic Extensions of SQEMA.Willem Conradie & Valentin Goranko - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):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 (...)
  12. added 2018-04-20
    Elementary Canonical Formulae: Extending Sahlqvist’s Theorem.Valentin Goranko & Dimiter Vakarelov - 2006 - Annals of Pure and Applied Logic 141 (1):180-217.
    We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...)
  13. added 2018-04-20
    Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects.W. Conradie, V. Goranko & D. Vakarelov - 2005 - In Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 5. Kings College London Publ.. pp. 17-51.
    In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...)
  14. added 2018-04-20
    Sahlqvist Formulas Unleashed in Polyadic Modal Languages.Valentin Goranko & Dimiter Vakarelov - 2002 - In Frank Wolter, Heinrich Wansing, Maarten de Rijke & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 3. World Scientific. pp. 221-240.
    We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.
  15. added 2018-04-20
    Modal Definability in Enriched Languages.Valentin Goranko - 1989 - Notre Dame Journal of Formal Logic 31 (1):81-105.
    The paper deals with polymodal languages combined with standard semantics defined by means of some conditions on the frames. So, a notion of "polymodal base" arises which provides various enrichments of the classical modal language. One of these enrichments, viz. the base £(R,-R), with modalities over a relation and over its complement, is the paper's main paradigm. The modal definability (in the spirit of van Benthem's correspondence theory) of arbitrary and ~-elementary classes of frames in this base and in some (...)
  16. added 2018-03-20
    Updating Data Semantics.Anthony S. Gillies - forthcoming - Mind:fzy008.
    This paper has three main goals. First, to motivate a puzzle about how ignorance-expressing language like \expression{maybe} and \expression{if} interact: they (surprisingly) iterate and when they do they exhibit scopelessness. Second, to argue that there is an ambiguity in our theoretical toolbox and that resolving that opens the door to a solution to the puzzle. And third, to explore the reach of that solution (it turns out to do work in unexpected places). Along the way, the paper highlights a number (...)
  17. added 2018-03-09
    Still in the Mood: The Versatility of Subjunctive Markers in Modal Logic.Kai F. Wehmeier & Helge Rückert - forthcoming - Topoi:1-17.
    We investigate and compare two major approaches to enhancing the expressive capacities of modal languages, namely the addition of subjunctive markers on the one hand, and the addition of scope-bearing actuality operators, on the other. It turns out that the subjunctive marker approach is not only every bit as versatile as the actuality operator approach, but that it in fact outperforms its rival in the context of cross-world predication.
  18. added 2018-03-09
    In the Mood.Kai Frederick Wehmeier - 2004 - Journal of Philosophical Logic 33 (6):607-630.
    The purpose of the present paper is to challenge some received assumptions about the logical analysis of modal English, and to show that these assumptions are crucial to certain debates in current philosophy of language. Specifically, I will argue that the standard analysis in terms of quantified modal logic mistakenly fudges important grammatical distinctions, and that the validity of Kripke's modal argument against description theories of proper names crucially depends on ensuing equivocations.
  19. added 2018-02-17
    On Conceiving the Inconsistent.Francesco Berto - 2014 - Proceedings of the Aristotelian Society 114 (1pt1):103-121.
    I present an approach to our conceiving absolute impossibilities—things which obtain at no possible world—in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds based on world similarity. The explicit content of a representation plays a role similar in some respects to the one of a ceteris paribus conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. Unlike what happens with ceteris paribus counterfactual (...)
  20. added 2018-02-17
    Topics in the Philosophy of Possible Worlds.Daniel Patrick Nolan - 2002 - Routledge.
    This book discusses a range of important issues in current philosophical work on the nature of possible worlds. Areas investigated include the theories of the nature of possible worlds, general questions about metaphysical analysis and questions about the direction of dependence between what is necessary or possible and what could be.
  21. added 2018-02-17
    Modal Logic As Dialogical Logic.Patrick Blackburn - 2001 - Synthese 127 (1):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 I will show how to lift the dialogical conception to modal proof theory. I argue that this shift (...)
  22. added 2018-02-17
    Pietroski on Possible Worlds Semantics for Belief Sentences.Joe Lau - 1995 - Analysis 55 (4):295.
    Pietroski (1993) offers a semantics for belief sentences that is supposed to address the problem of equivalence. This paper argues that his proposal fails to solve the problem.
  23. added 2018-01-11
    A Purely Recombinatorial Puzzle.Fritz Peter - 2017 - Noûs 51 (3):547-564.
    A new puzzle of modal recombination is presented which relies purely on resources of first-order modal logic. It shows that naive recombinatorial reasoning, which has previously been shown to be inconsistent with various assumptions concerning propositions, sets and classes, leads to inconsistency by itself. The context sensitivity of modal expressions is suggested as the source of the puzzle, and it is argued that it gives us reason to reconsider the assumption that the notion of metaphysical necessity is in good standing.
  24. added 2017-12-04
    Quantified Multimodal Logics in Simple Type Theory.Christoph Benzmüller & Lawrence C. Paulson - 2013 - Logica Universalis 7 (1):7-20.
    We present an embedding of quantified multimodal logics into simple type theory and prove its soundness and completeness. A correspondence between QKπ models for quantified multimodal logics and Henkin models is established and exploited. Our embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics. Moreover, it provides a starting point for further logic embeddings and their combinations in simple type theory.
  25. added 2017-12-04
    Multimodal and Intuitionistic Logics in Simple Type Theory.Christoph Benzmueller & Lawrence Paulson - 2010 - Logic Journal of the IGPL 18 (6):881-892.
    We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various non-classical logics. We report some experiments using the higher-order automated theorem prover LEO-II.
  26. added 2017-11-11
    Modelling Belief Revision Via Belief Bases Using Situation Semantics.Ayse Sena Bozdag - 2017 - Dissertation, Bogazici University
    The belief base approach to belief representation and belief dynamics is developed as an alternative to the belief set approaches, which are pioneered by the AGM model. The belief base approach models collections of information and expectations of an agent as possibly incomplete and possibly inconsistent foundations for her beliefs. Nevertheless, the beliefs of an agent are always consistent; this is ensured by a sophisticated inference relation. Belief changes take place on the information base instead of on the belief set, (...)
  27. added 2017-10-06
    La Connaissance Commune: Une Sémantique Pour la Logique Modale.L. Lismont & P. Mongin - 1993 - Logique Et Analyse 133 (134):133-149.
    This French paper is a prelimary report on the authors' work on the logics of common knowledge and common belief. See L. Lismont and P. Mongin, "On the logic of common belief and common knowledge", Theory and Decision 37 (1): 75-106. 1994 for a more complete report.
  28. added 2017-09-12
    Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic.Koji Tanaka - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 15--25.
    Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on classical logicians (...)
  29. added 2017-09-03
    On the Modal Logic of Subset and Superset: Tense Logic Over Medvedev Frames.Wesley H. Holliday - 2017 - Studia Logica 105 (1):13-35.
    Viewing the language of modal logic as a language for describing directed graphs, a natural type of directed graph to study modally is one where the nodes are sets and the edge relation is the subset or superset relation. A well-known example from the literature on intuitionistic logic is the class of Medvedev frames $\langle W,R\rangle$ where $W$ is the set of nonempty subsets of some nonempty finite set $S$, and $xRy$ iff $x\supseteq y$, or more liberally, where $\langle W,R\rangle$ (...)
  30. added 2017-07-16
    A Free Logic with Intensions as Possible Values of Terms.G. H. Merrill - 1975 - Journal of Philosophical Logic 4 (3):293 - 326.
    This paper contains an axiomatic theory of first order modal logic with operations, identity, and descriptions together with a formal semantics which interprets the theory in such a manner that empty universes of discourse and denotationless terms are allowed for at each possible world. The intuitive basis of the theory is discussed in preliminary sections, the syntax and semantics of theory are then characterized, its semantical adequacy is demonstrated, and certain important axioms and theorems are discussed in detail in later (...)
  31. added 2017-07-15
    Modal Logic S4 as a Paraconsistent Logic with a Topological Semantics.Marcelo E. Coniglio & Leonardo Prieto-Sanabria - 2017 - In Carlos Caleiro, Francisco Dionisio, Paula Gouveia, Paulo Mateus & João Rasga (eds.), Logic and Computation: Essays in Honour of Amilcar Sernadas. London, UK: College Publications. pp. 171-196.
    In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof of (...)
  32. added 2017-07-01
    Chalmers, semantiikka ja välttämättömyys.Panu Raatikainen - 2016 - In Mahdollisuus. Helsinki: Suomen Filosofinen Yhdistys.
  33. added 2017-03-22
    Errata and Addenda to ‘Finite Non-Deterministic Semantics for Some Modal Systems’.Marcelo E. Coniglio, Luis Fariñas del Cerro & Newton M. Peron - 2016 - Journal of Applied Non-Classical Logics 26 (4):336-345.
    In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...)
  34. added 2017-02-20
    Worlds and Models in Bayart and Carnap.Max Cresswell - 2016 - Australasian Journal of Logic 13 (1).
    In the early days of the semantics for modal logic the `possible worlds' were thought of as models or interpretations. This was particularly so when the interpretation was of emph{logical} necessity or possibility, where this was understood in terms of validity. Arnould Bayart in 1958 may have been the first modal logician to argue explicitly against the identification of necessity and validity. This note contrasts his semantics with that provided by Rudolf Carnap in 1946, and examines Bayart's proof that if (...)
  35. added 2017-02-20
    Peacocke’s Principle-Based Account of Modality: “Flexibility of Origins” Plus S4.Sonia Roca Royes - 2007 - Erkenntnis 65 (3):405-426.
    Due to the influence of Nathan Salmon's views, endorsement of the "flexibility of origins" thesis is often thought to carry a commitment to the denial of S4. This paper rejects the existence of this commitment and examines how Peacocke's theory of the modal may accommodate flexibility of origins without denying S4. One of the essential features of Peacocke's account is the identification of the Principles of Possibility, which include the Modal Extension Principle, and a set of Constitutive Principles. Regarding their (...)
  36. added 2017-02-20
    Peacocke's Principle-Based Account of Modality:“Flexibility of Origins” P.Royes Sonia Roca - 2006 - Erkenntnis 65 (3):405-426.
    Due to the influence of Nathan Salmon's views, endorsement of the "flexibility of origins" thesis is often thought to carry a commitment to the denial of S4. This paper rejects the existence of this commitment and examines how Peacocke's theory of the modal may accommodate flexibility of origins without denying S4. One of the essential features of Peacocke's account is the identification of the Principles of Possibility, which include the Modal Extension Principle, and a set of Constitutive Principles. Regarding their (...)
  37. added 2017-02-20
    The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic.Charles S. Chihara - 2001 - Mind 110 (439):736-740.
  38. added 2017-02-20
    The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic.Charles Chihara - 2001 - Philosophical Quarterly 51 (202):108-110.
  39. added 2017-02-11
    Propositions, Possible Worlds, and Recursion.Andrzej Wiśniewski - 2011 - Logic and Logical Philosophy 20 (1-2):73-79.
    The issue of reduction of propositions to sets of possible worlds is addressed. It is shown that, under some natural assumptions, there always exist recursive propositions, i.e. decidable sets of possible worlds, which are not assigned to any sentence of a language. Some consequences of this result are discussed.
  40. added 2017-02-11
    Quantificational Modal Logic with Sequential Kripke Semantics.Stefano Borgo - 2005 - Journal of Applied Non-Classical Logics 15 (2):137-188.
  41. added 2017-02-11
    Maximal Kripke-Type Semantics for Modal and Superintuitionistic Predicate Logics.D. P. Skvortsov & V. B. Shehtman - 1993 - Annals of Pure and Applied Logic 63 (1):69-101.
    Recent studies in semantics of modal and superintuitionistic predicate logics provided many examples of incompleteness, especially for Kripke semantics. So there is a problem: to find an appropriate possible- world semantics which is equivalent to Kripke semantics at the propositional level and which is strong enough to prove general completeness results. The present paper introduces a new semantics of Kripke metaframes' generalizing some earlier notions. The main innovation is in considering "n"-tuples of individuals as abstract "n"-dimensional vectors', together with some (...)
  42. added 2017-02-11
    Review: Richmond H. Thomason, Philosophy and Formal Semantics. [REVIEW]Melvin Fitting - 1977 - Journal of Symbolic Logic 42 (2):317-317.
  43. added 2017-02-11
    Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - University of Chicago Press.
    This is identical with the first edition (see 21: 2716) except for the addition of a Supplement containing 5 previously published articles and the bringing of the bibliography (now 73 items) up to date. The 5 added articles present clarifications or modifications of views expressed in the first edition. (PsycINFO Database Record (c) 2009 APA, all rights reserved).
  44. added 2017-02-09
    Kripke Sheaf Completeness of Some Superintuitionistic Predicate Logics with a Weakened Constant Domains Principle.Dmitrij Skvortsov - 2012 - Studia Logica 100 (1-2):361-383.
    The completeness w.r.t. Kripke frames with equality (or, equivalently, w.r.t. Kripke sheaves, [ 8 ] or [4, Sect. 3.6]) is established for three superintuitionistic predicate logics: ( Q - H + D *), ( Q - H + D *&K), ( Q - H + D *& K & J ). Here Q - H is intuitionistic predicate logic, J is the principle of the weak excluded middle, K is Kuroda’s axiom, and D * (cf. [ 12 ]) is a (...)
  45. added 2017-02-09
    Review of David Lewis, On the Plurality of Worlds. [REVIEW]Michael Clark - 1987 - Philosophical Books 28.
  46. added 2017-02-08
    Modality and Databases.Melvin Fitting - unknown
    Two things are done in this paper. First, a modal logic in which one can quantify over both objects and concepts is presented; a semantics and a tableau system are given. It is a natural modal logic, extending standard versions, and capable of addressing several well-known philosophical difficulties successfully. Second, this modal logic is used to introduce a rather different way of looking at relational databases. The idea is to treat records as possible worlds, record entries as objects, and attributes (...)
  47. added 2017-02-08
    The Logic of Fiction and the 'Sayso' Semantics.Graeme Hunter - 1978 - Dialogue 17 (2):344-366.
  48. added 2017-02-07
    Propositional Quantification in the Topological Semantics for S.Philip Kremer - 1997 - Notre Dame Journal of Formal Logic 38 (2):295-313.
    Fine and Kripke extended S5, S4, S4.2 and such to produce propositionally quantified systems , , : given a Kripke frame, the quantifiers range over all the sets of possible worlds. is decidable and, as Fine and Kripke showed, many of the other systems are recursively isomorphic to second-order logic. In the present paper I consider the propositionally quantified system that arises from the topological semantics for S4, rather than from the Kripke semantics. The topological system, which I dub , (...)
  49. added 2017-02-07
    The Ontology of Impossible Worlds.David A. Vander Laan - 1997 - Notre Dame Journal of Formal Logic 38 (4):597-620.
    The best arguments for possible worlds as states of affairs furnish us with equally good arguments for impossible worlds of the same sort. I argue for a theory of impossible worlds on which the impossible worlds correspond to maximal inconsistent classes of propositions. Three objections are rejected. In the final part of the paper, I present a menu of impossible worlds and explore some of their interesting formal properties.
  50. added 2017-02-07
    On an Unsound Proof of the Existence of Possible Worlds.Christopher Menzel - 1989 - Notre Dame Journal of Formal Logic 30 (4):598-603.
    In this paper, an argument of Alvin Plantinga's for the existence of abstract possible worlds is shown to be unsound. The argument is based on a principle Plantinga calls "Quasicompactness", due to its structural similarity to the notion of compactness in first-order logic. The principle is shown to be false.
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