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An Essay in Classical Modal Logic

Dissertation, Stanford University (1971)

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  1. Liar-type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
    We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo’s (...)
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  • A logic for epistemic two-dimensional semantics.Peter Fritz - 2013 - Synthese 190 (10):1753-1770.
    Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe (...)
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  • Inference and necessity.P. K. Schotch & R. E. Jennings - 1980 - Journal of Philosophical Logic 9 (3):327-340.
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  • Decidable and undecidable logics with a binary modality.ágnes Kurucz, István Németi, Ildikó Sain & András Simon - 1995 - Journal of Logic, Language and Information 4 (3):191-206.
    We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.
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  • (1 other version)A Descending Chain of Classical Logics for Which Necessitation Implies Regularity.Roy A. Benton - 1979 - Mathematical Logic Quarterly 25 (19‐24):289-291.
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  • Singulary extensional connectives: A closer look. [REVIEW]I. L. Humberstone - 1997 - Journal of Philosophical Logic 26 (3):341-356.
    The totality of extensional 1-ary connectives distinguishable in a logical framework allowing sequents with multiple or empty (alongside singleton) succedents form a lattice under a natural partial ordering relating one connective to another if all the inferential properties of the former are possessed by the latter. Here we give a complete description of that lattice; its Hasse diagram appears as Figure 1 in §2. Simple syntactic descriptions of the lattice elements are provided in §3; §§4 and 5 give some additional (...)
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  • Omnitemporal logic and converging time.G. E. Hughes & M. J. Cresswell - 1975 - Theoria 41 (1):11-34.
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  • The logical study of science.Johan Benthem - 1982 - Synthese 51 (3):431 - 472.
    The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the (...)
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  • Non-adjunctive inference and classical modalities.Horacio Arló Costa - 2005 - Journal of Philosophical Logic 34 (5/6):581 - 605.
    The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A ∧ B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified (...)
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  • Some Embedding Theorems for Conditional Logic.Ming Xu - 2006 - Journal of Philosophical Logic 35 (6):599-619.
    We prove some embedding theorems for classical conditional logic, covering 'finitely cumulative' logics, 'preferential' logics and what we call 'semi-monotonic' logics. Technical tools called 'partial frames' and 'frame morphisms' in the context of neighborhood semantics are used in the proof.
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  • Around provability logic.Leo Esakia - 2010 - Annals of Pure and Applied Logic 161 (2):174-184.
    We present some results on algebraic and modal analysis of polynomial distortions of the standard provability predicate in Peano Arithmetic PA, and investigate three provability-like modal systems related to the Gödel–Löb modal system GL. We also present a short review of relational and topological semantics for these systems, and describe the dual category of algebraic models of our main modal system.
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  • Arithmetical necessity, provability and intuitionistic logic.Rob Goldblatt - 1978 - Theoria 44 (1):38-46.
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  • A symmetric approach to axiomatizing quantifiers and modalities.Melvin Fitting - 1984 - Synthese 60 (1):5 - 19.
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  • Cut-free tableau calculi for some propositional normal modal logics.Martin Amerbauer - 1996 - Studia Logica 57 (2-3):359 - 372.
    We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G 0(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G 0are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the (...)
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  • Remarks on the modal logic of Henry Bradford Smith.Mary C. MacLeod & Peter K. Schotch - 2000 - Journal of Philosophical Logic 29 (6):603-615.
    H. B. Smith, Professor of Philosophy at the influential 'Pennsylvania School' was (roughly) a contemporary of C. I. Lewis who was similarly interested in a proper account of 'implication'. His research also led him into the study of modal logic but in a different direction than Lewis was led. His account of modal logic does not lend itself as readily as Lewis' to the received 'possible worlds' semantics, so that the Smith approach was a casualty rather than a beneficiary of (...)
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  • Negation‐Free Modal Logics.George F. Schumm & Roy Edelstein - 1979 - Mathematical Logic Quarterly 25 (13‐18):281-288.
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  • How far can Hume's is-ought thesis be generalized?Gerhard Schurz - 1991 - Journal of Philosophical Logic 20 (1):37 - 95.
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  • (1 other version)A Descending Chain of Classical Logics for Which Necessitation Implies Regularity.Roy A. Benton - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (19-24):289-291.
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  • Rough polyadic modal logics.D. Vakarelov - 1991 - Journal of Applied Non-Classical Logics 1 (1):9-35.
    Rough polyadic modal logics, introduced in the paper, contain modal operators of many arguments with a relational semantics, based on the Pawlak's rough set theory. Rough set approach is developed as an alternative to the fuzzy set philosophy, and has many applications in different branches in Artificial Intelligence and theoretical computer science.
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  • On Finite Model Property for Admissible Rules.Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner - 1999 - Mathematical Logic Quarterly 45 (4):505-520.
    Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...)
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  • Willem Blok and Modal Logic.W. Rautenberg, M. Zakharyaschev & F. Wolter - 2006 - Studia Logica 83 (1):15-30.
    We present our personal view on W.J. Blok's contribution to modal logic.
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