Results for 'Multidimensional Modal Logic'

951 found
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  1. Cylindric modal logic.Yde Venema - 1995 - Journal of Symbolic Logic 60 (2):591-623.
    Treating the existential quantification ∃ν i as a diamond $\diamond_i$ and the identity ν i = ν j as a constant δ ij , we study restricted versions of first order logic as if they were modal formalisms. This approach is closely related to algebraic logic, as the Kripke frames of our system have the type of the atom structures of cylindric algebras; the full cylindric set algebras are the complex algebras of the intended multidimensional frames (...)
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  2.  66
    A multidimensional modal translation for a formal system motivated by situation semantics.Juan Barba Escriba - 1991 - Notre Dame Journal of Formal Logic 32 (4):598-608.
  3. Actuality, Tableaux, and Two-Dimensional Modal Logics.Fabio Lampert - 2018 - Erkenntnis 83 (3):403-443.
    In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux (...)
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  4. The Logic of Sequence Frames.Fabio Lampert - 2022 - Review of Symbolic Logic 15 (1):101-132.
    This paper investigates and develops generalizations of two-dimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction.
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  5.  52
    The bidimensionality of modal variety.Salim Hireche - 2021 - Inquiry: An Interdisciplinary Journal of Philosophy:1-36.
    It is widely accepted that necessity comes in different varieties, often called ‘kinds': metaphysical necessity, logical necessity, natural necessity, conceptual necessity, moral necessity, to name but a few – and the same goes for the varieties of possibility. What is usually not fully appreciated, however, is that modal variety is not simply ‘unidimensional': it does not only involve one main variable – kind, whose values are the particular kinds of necessity. Rather, I argue, it is ‘bidimensional', involving two distinct (...)
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  6. (2 other versions)Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
  7. (1 other version)A completeness theorem in modal logic.Saul Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
  8. (1 other version)Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
  9. Counterpart-theoretic semantics for modal logic.Allen Hazen - 1979 - Journal of Philosophy 76 (6):319-338.
  10.  90
    Intuitionistic tense and modal logic.W. B. Ewald - 1986 - Journal of Symbolic Logic 51 (1):166-179.
  11. (1 other version)Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi.Saul A. Kripke - 1965 - In J. W. Addison (ed.), The theory of models. Amsterdam,: North-Holland Pub. Co.. pp. 206-20.
  12.  93
    Normal forms in modal logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.
  13.  5
    (1 other version)Modal Logic.Johan van Benthem - 2002 - In Dale Jacquette (ed.), A Companion to Philosophical Logic. Malden, MA, USA: Wiley-Blackwell. pp. 389–409.
    This chapter contains sections titled: Enriching Extensional Logic with Intensional Notions Changing Views of Modal Logic A Précis of Basic Modal Logic The Major Applications Fine‐Structure of Expressive Power System Combination: Action and Information Back to the Heartland Conclusion.
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  14. Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: 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).
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  15.  73
    A New Semantics for Positive Modal Logic.S. Celani & R. Jansana - 1997 - Notre Dame Journal of Formal Logic 38 (1):1-18.
    The paper provides a new semantics for positive modal logic using Kripke frames having a quasi ordering on the set of possible worlds and an accessibility relation connected to the quasi ordering by the conditions (1) that the composition of with is included in the composition of with and (2) the analogous for the inverse of and . This semantics has an advantage over the one used by Dunn in "Positive modal logic," Studia Logica (1995) and (...)
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  16. (1 other version)ModelTtheory for Modal Logic. Part I — The de re/de Dicto distinction.Kit Fine - 1978 - Journal of Philosophical Logic 7 (1):125 - 156.
  17. Necessities and Necessary Truths: A Prolegomenon to the Use of Modal Logic in the Analysis of Intensional Notions.V. Halbach & P. Welch - 2009 - Mind 118 (469):71-100.
    In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one (...)
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  18. Essentialism and quantified modal logic.Terence Parsons - 1969 - Philosophical Review 78 (1):35-52.
  19.  34
    The predicate modal logic of provability.Franco Montagna - 1984 - Notre Dame Journal of Formal Logic 25 (2):179-189.
  20.  50
    An almost general splitting theorem for modal logic.Marcus Kracht - 1990 - Studia Logica 49 (4):455 - 470.
    Given a normal (multi-)modal logic a characterization is given of the finitely presentable algebras A whose logics L A split the lattice of normal extensions of . This is a substantial generalization of Rautenberg [10] and [11] in which is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite A L A splits the lattice of normal extensions of K. (...)
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  21.  62
    Repairing the interpolation theorem in quantified modal logic.Carlos Areces, Patrick Blackburn & Maarten Marx - 2003 - Annals of Pure and Applied Logic 124 (1-3):287-299.
    Quantified hybrid logic is quantified modal logic extended with apparatus for naming states and asserting that a formula is true at a named state. While interpolation and Beth's definability theorem fail in a number of well-known quantified modal logics , their counterparts in quantified hybrid logic have these properties. These are special cases of the main result of the paper: the quantified hybrid logic of any class of frames definable in the bounded fragment of (...)
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  22. Model theory for modal logic—part II The elimination of de re modality.Kit Fine - 1978 - Journal of Philosophical Logic 7 (1):277 - 306.
  23.  19
    A note on non-monotonic modal logic.Robert Stalnaker - 1993 - Artificial Intelligence 64 (2):183-196.
  24. Modal logic and classical logic.Johan van Benthem - 1983 - Atlantic Highlands, N.J.: Distributed in the U.S.A. by Humanities Press.
  25.  39
    A Sahlqvist theorem for distributive modal logic.Mai Gehrke, Hideo Nagahashi & Yde Venema - 2004 - Annals of Pure and Applied Logic 131 (1-3):65-102.
    In this paper we consider distributive modal logic, a setting in which we may add modalities, such as classical types of modalities as well as weak forms of negation, to the fragment of classical propositional logic given by conjunction, disjunction, true, and false. For these logics we define both algebraic semantics, in the form of distributive modal algebras, and relational semantics, in the form of ordered Kripke structures. The main contributions of this paper lie in extending (...)
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  26. An actualistic semantics for quantified modal logic.Thomas Jager - 1982 - Notre Dame Journal of Formal Logic 23 (3):335-349.
  27. Topology and modality: The topological interpretation of first-order modal logic: Topology and modality.Steve Awodey - 2008 - Review of Symbolic Logic 1 (2):146-166.
    As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to (...)
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  28.  6
    Decidability of IF Modal Logic of Perfect Recall.T. Hyttinen & T. Tulenheimo - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 111-131.
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  29.  23
    Cut-free Sequent Calculus and Natural Deduction for the Tetravalent Modal Logic.Martín Figallo - 2021 - Studia Logica 109 (6):1347-1373.
    The tetravalent modal logic is one of the two logics defined by Font and Rius :481–518, 2000) in connection with Monteiro’s tetravalent modal algebras. These logics are expansions of the well-known Belnap–Dunn’s four-valued logic that combine a many-valued character with a modal character. In fact, TML{\mathcal {TML}} TML is the logic that preserves degrees of truth with respect to tetravalent modal algebras. As Font and Rius observed, the connection between the logic $${\mathcal (...)
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  30.  26
    Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences.Benthem Johan, Girard Patrick & Roy Olivier - 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 (...)
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  31. A purely syntactic and cut-free sequent calculus for the modal logic of provability.Francesca Poggiolesi - 2009 - Review of Symbolic Logic 2 (4):593-611.
    In this paper we present a sequent calculus for the modal propositional logic GL (the logic of provability) obtained by means of the tree-hypersequent method, a method in which the metalinguistic strength of hypersequents is improved, so that we can simulate trees shapes. We prove that this sequent calculus is sound and complete with respect to the Hilbert-style system GL, that it is contraction free and cut free and that its logical and modal rules are invertible. (...)
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  32. The surprise examination in modal logic.Robert Binkley - 1968 - Journal of Philosophy 65 (5):127-136.
  33.  38
    Capturing equilibrium models in modal logic.Luis Fariñas del Cerro, Andreas Herzig & Ezgi Iraz Su - 2014 - Journal of Applied Logic 12 (2):192-207.
  34. Model theory for modal logic—part III existence and predication.Kit Fine - 1981 - Journal of Philosophical Logic 10 (3):293 - 307.
  35.  50
    Topos Semantics for Higher-Order Modal Logic.Steve Awodey, Kohei Kishida & Hans-Cristoph Kotzsch - 2014 - Logique Et Analyse 228:591-636.
    We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E. In contrast to the well-known interpretation of higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE, but rather by a suitable complete Heyting algebra H. The canonical map relating H and ΩE both serves to interpret equality and provides a modal operator on H in the form of a comonad. Examples of such structures arise (...)
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  36. Fischer Servi's Intuitionistic Modal Logic has the Finite Modal Property.Carsten Grefe - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 85-98.
     
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  37.  24
    Medieval modal logic & science: Augustine on necessary truth & Thomas on its impossibility without a first cause.Robert C. Trundle - 1999 - Lanham, MD: University Press of America.
    Medieval Modal Logic & Science uses modal reasoning in a new way to fortify the relationships between science, ethics, and politics. Robert C. Trundle accomplishes this by analyzing the role of modal logic in the work of St. Augustine and St. Thomas Aquinas, then applying these themes to contemporary issues. He incorporates Augustine's ideas involving thought and consciousness, and Aquinas's reasoning to a First Cause. The author also deals with Augustine's ties to Aristotelian modalities of (...)
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  38.  58
    Modal logic: the Lewis-modal systems.Joseph Jay Zeman - 1973 - London,: Clarendon Press.
  39.  31
    Second-order propositional modal logic and monadic alternation hierarchies.Antti Kuusisto - 2015 - Annals of Pure and Applied Logic 166 (1):1-28.
  40.  13
    Decidability of IF Modal Logic of Perfect Recall.T. Hyttinen & T. Tulenheimo - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 111-131.
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  41. The logic of common nouns: an investigation in quantified modal logic.Anil Gupta - 1980 - New Haven: Yale University Press.
  42.  40
    Uniform interpolation and sequent calculi in modal logic.Rosalie Iemhoff - 2019 - Archive for Mathematical Logic 58 (1-2):155-181.
    A method is presented that connects the existence of uniform interpolants to the existence of certain sequent calculi. This method is applied to several modal logics and is shown to cover known results from the literature, such as the existence of uniform interpolants for the modal logic \. New is the result that \ has uniform interpolation. The results imply that for modal logics \ and \, which are known not to have uniform interpolation, certain sequent (...)
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  43.  53
    Counterpart Theory as a Semantics for Modal Logic.Lin Woollaston - 1994 - Logique Et Analyse 37 (147-148):255-263.
    A claim by David K. Lewis (1986) that his counterpart theory provides a semantics for intensional languages is critiqued by showing that basic principles of modal logic fail to be valid in counterpart theory & by investigating problematic counterpart-theoretical translations of instances of universal instantiation. From Lewis's postulate that individuals inhabit only one world & have counterparts in other worlds, it follows that the relation between an object & its counterparts is nontransitive & nonsymmetric; consequently, an object does (...)
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  44. G. E. Hughes & M. J. Cresswell, A New Introduction to Modal Logic[REVIEW]Paolo Crivelli & Timothy Williamson - 1998 - Philosophical Review 107 (3):471.
    This volume succeeds the same authors' well-known An Introduction to Modal Logic and A Companion to Modal Logic. We designate the three books and their authors NIML, IML, CML and H&C respectively. Sadly, George Hughes died partway through the writing of NIML.
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  45.  12
    Expressivity of Second Order Propositional Modal Logic.Balder Cate - 2006 - Journal of Philosophical Logic 35 (2):209-223.
    We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic (...)
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  46. Modal Logic: An Introduction.Brian F. Chellas - 1980 - New York: Cambridge University Press.
    A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical (...)
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  47. Post completeness in modal logic.Krister Segerberg - 1972 - Journal of Symbolic Logic 37 (4):711-715.
  48. 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 (...)
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  49.  67
    (2 other versions)Reduction of tense logic to modal logic. I.S. K. Thomason - 1974 - Journal of Symbolic Logic 39 (3):549-551.
  50. Quantified Modal Logic and the Plural De Re.Phillip Bricker - 1989 - Midwest Studies in Philosophy 14 (1):372-394.
    Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" (...)
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