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  1. A quick guided tour to the modal logic S4.2.Aggeliki Chalki, Costas D. Koutras & Yorgos Zikos - 2018 - Logic Journal of the IGPL 26 (4):429-451.
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  • The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):733-783.
    In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible (...)
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  • Uncompactness of Stit Logics Containing Generalized Refref Conditionals.Ming Xu - 1998 - Notre Dame Journal of Formal Logic 39 (4):485-506.
    In this paper we prove the uncompactness of every stit logic that contains a generalized refref conditional and is a sublogic of the stit logic with refref equivalence, a syntactical condition of uncompactness that covers infinitely many stit logics. This result is established through the uncompactness of every stit logic whose semantic structures contain no chain of busy choice sequences with cardinality , where is any natural number . The basic idea in the proof is to apply the notion of (...)
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  • Worlds and Times.Ulrich Meyer - 2006 - Notre Dame Journal of Formal Logic 47 (1):25--37.
    There are many parallels between the role of possible worlds in modal logic and that of times in tense logic. But the similarities only go so far, and it is important to note where the two come apart. This paper argues that even though worlds and times play similar roles in the model theories of modal and tense logic, there is no tense analogue of the possible-worlds analysis of modal operators. An important corollary of this result is that presentism cannot (...)
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  • Busy choice sequences refraining formulas and modalities.Ming Xu - 1995 - Studia Logica 54 (3):267 - 301.
    The purpose of this paper is to present some results instit theory, a theory of agency proposed by N. Belnap and M. Perloff. We will establish a correspondence between the numbers ofstit modalities and the complexity degrees ofbusy choice sequences in semantic structures, and consequently, a correspondence between the number of modes of actions/inactions instit theory and the complexity degrees ofbusy choice sequences in semantic structures.
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  • There are infinitely many diodorean modal functions.D. C. Makinson - 1966 - Journal of Symbolic Logic 31 (3):406-408.
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  • (1 other version)The Orthologic of Epistemic Modals.Wesley H. Holliday & Matthew Mandelkern - 2024 - Journal of Philosophical Logic 53 (4):831-907.
    Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $$p\wedge \Diamond \lnot p$$ (‘p, but it might be that not p’) appears to be a contradiction, $$\Diamond \lnot p$$ does not entail $$\lnot p$$, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. (...)
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  • Algebraic semantics for modal logics I.E. J. Lemmon - 1966 - Journal of Symbolic Logic 31 (1):46-65.
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  • Embeddings of classical logic in S4 part II.Johannes Czermak - 1976 - Studia Logica 35 (3):257-271.
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  • Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...)
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  • Generalizations of the Weak Law of the Excluded Middle.Andrea Sorbi & Sebastiaan A. Terwijn - 2015 - Notre Dame Journal of Formal Logic 56 (2):321-331.
    We study a class of formulas generalizing the weak law of the excluded middle and provide a characterization of these formulas in terms of Kripke frames and Brouwer algebras. We use these formulas to separate logics corresponding to factors of the Medvedev lattice.
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  • Proof analysis in intermediate logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1):71-92.
    Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...)
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  • Modal logics with linear alternative relations.Krister Segerberg - 1970 - Theoria 36 (3):301-322.
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  • Fatal Heyting Algebras and Forcing Persistent Sentences.Leo Esakia & Benedikt Löwe - 2012 - Studia Logica 100 (1-2):163-173.
    Hamkins and Löwe proved that the modal logic of forcing is S4.2 . In this paper, we consider its modal companion, the intermediate logic KC and relate it to the fatal Heyting algebra H ZFC of forcing persistent sentences. This Heyting algebra is equationally generic for the class of fatal Heyting algebras. Motivated by these results, we further analyse the class of fatal Heyting algebras.
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  • Modal counterparts of Medvedev logic of finite problems are not finitely axiomatizable.Valentin Shehtman - 1990 - Studia Logica 49 (3):365 - 385.
    We consider modal logics whose intermediate fragments lie between the logic of infinite problems [20] and the Medvedev logic of finite problems [15]. There is continuum of such logics [19]. We prove that none of them is finitely axiomatizable. The proof is based on methods from [12] and makes use of some graph-theoretic constructions (operations on coverings, and colourings).
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  • Algebraic semantics for modal logics II.E. J. Lemmon - 1966 - Journal of Symbolic Logic 31 (2):191-218.
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  • The deliberative stit: A study of action, omission, ability, and obligation. [REVIEW]John F. Horty & Nuel Belnap - 1995 - Journal of Philosophical Logic 24 (6):583 - 644.
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  • Epistemologische betrachtungen zu [S4, S5].Wolfgang Lenzen - 1979 - Erkenntnis 14 (1):33-56.
    The numerous modal systems between S4 and S5 are investigated from an epistemological point of view by interpreting necessity either as knowledge or as (strong) belief. It is shown that-granted some assumptions about epistemic logic for which the author has argued elsewhere-the system S4.4 may be interpreted as the logic of true belief, while S4.3.2 and S4.2 may be taken to represent epistemic logic systems for individuals who accept the scheme knowledge = true belief only for certain special instances. There (...)
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  • Completeness of S4 with respect to the real line: revisited.Guram Bezhanishvili & Mai Gehrke - 2004 - Annals of Pure and Applied Logic 131 (1-3):287-301.
    We prove that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski 45 141). We also prove that the same result holds for the bimodal system S4+S5+C, which is a strengthening of a 1999 result of Shehtman 369).
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  • Logics With Several Modal Operators.Melvin Fitting - 1969 - Theoria 35 (3):259-266.
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  • On logics with coimplication.Frank Wolter - 1998 - Journal of Philosophical Logic 27 (4):353-387.
    This paper investigates (modal) extensions of Heyting-Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We first develop matrix as well as Kripke style semantics for those logics. Then, by extending the Gö;del-embedding of intuitionistic logic into S4, it is shown that all (modal) extensions of Heyting-Brouwer logic can be embedded into tense logics (with additional modal operators). An extension of the Blok-Esakia-Theorem is proved for this embedding.
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  • (1 other version)Tense-logic and the continuity of time.A. N. Prior - 1962 - Studia Logica 13 (1):133 - 151.
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  • Oxford realism: Knowledge and perception II.Mathieu Marion - 2000 - British Journal for the History of Philosophy 8 (3):485 – 519.
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  • Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus.V. V. Rybakov - 1990 - Annals of Pure and Applied Logic 50 (1):71-106.
    Questions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework. The main result is the decidability of the universal theory of the free modal algebra imageω extended in signature by adding constants for free generators. As corollaries we obtain: there exists an algorithm for the recognition of admissibility of rules with parameters in the modal system Grz, the substitution problem for Grz and for (...)
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  • Constructive theories through a modal lens.Matteo Tesi - forthcoming - Logic Journal of the IGPL.
    We present a uniform proof-theoretic proof of the Gödel–McKinsey–Tarski embedding for a class of first-order intuitionistic theories. This is achieved by adapting to the case of modal logic the methods of proof analysis in order to convert axioms into rules of inference of a suitable sequent calculus. The soundness and the faithfulness of the embedding are proved by induction on the height of the derivations in the augmented calculi. Finally, we define an extension of the modal system for which the (...)
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  • On Hamblin's 15 Tense Theorem.Manfred Kudlek - 2010 - Journal of Applied Non-Classical Logics 20 (1):63-80.
    It is demonstrated that Hamblin's 15 tense theorem does not only hold for temporal logic with linear time but also for branching time. Furthermore three other theorems with finitely many tenses are shown.
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  • The Modal Multilogic of Geometry.Philippe Balbiani - 1998 - Journal of Applied Non-Classical Logics 8 (3):259-281.
    ABSTRACT A spatial logic is a modal logic of which the models are the mathematical models of space. Successively considering the mathematical models of space that are the incidence geometry and the projective geometry, we will successively establish the language, the semantical basis, the axiomatical presentation, the proof of the decidability and the proof of the completeness of INC, the modal multilogic of incidence geometry, and PRO, the modal multilogic of projective geometry.
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  • (1 other version)Some structure results for propositional calculi.Ronald Harrop - 1965 - Journal of Symbolic Logic 30 (3):271-292.
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  • The intensional side of algebraic-topological representation theorems.Sara Negri - 2017 - Synthese 198 (Suppl 5):1121-1143.
    Stone representation theorems are a central ingredient in the metatheory of philosophical logics and are used to establish modal embedding results in a general but indirect and non-constructive way. Their use in logical embeddings will be reviewed and it will be shown how they can be circumvented in favour of direct and constructive arguments through the methods of analytic proof theory, and how the intensional part of the representation results can be recovered from the syntactic proof of those embeddings. Analytic (...)
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  • Failure of the Blok–Esakia Theorem in the monadic setting.G. Bezhanishvili & L. Carai - 2025 - Annals of Pure and Applied Logic 176 (4):103527.
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  • Proofs and Countermodels in Non-Classical Logics.Sara Negri - 2014 - Logica Universalis 8 (1):25-60.
    Proofs and countermodels are the two sides of completeness proofs, but, in general, failure to find one does not automatically give the other. The limitation is encountered also for decidable non-classical logics in traditional completeness proofs based on Henkin’s method of maximal consistent sets of formulas. A method is presented that makes it possible to establish completeness in a direct way: For any given sequent either a proof in the given logical system or a countermodel in the corresponding frame class (...)
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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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  • Hereditarily Structurally Complete Intermediate Logics: Citkin’s Theorem Via Duality.Nick Bezhanishvili & Tommaso Moraschini - 2023 - Studia Logica 111 (2):147-186.
    A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally complete if all its extensions are structurally complete. Citkin (1978) proved that an intermediate logic is hereditarily structurally complete if and only if the variety of Heyting algebras associated with it omits five finite algebras. Despite its importance in the theory of admissible rules, a direct proof of Citkin’s theorem is not widely accessible. In this paper we offer (...)
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  • Completeness of S4 with respect to the real line: revisited.Gurman Bezhanishvili & Mai Gehrke - 2005 - Annals of Pure and Applied Logic 131 (1-3):287-301.
    We prove that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski 45 141). We also prove that the same result holds for the bimodal system S4+S5+C, which is a strengthening of a 1999 result of Shehtman 369).
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  • Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
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  • Propositional Logics Related to Heyting's and Johansson's.Krister Segerberg - 1968 - Theoria 34 (1):26-61.
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  • On superintuitionistic logics as fragments of proof logic extensions.A. V. Kuznetsov & A. Yu Muravitsky - 1986 - Studia Logica 45 (1):77 - 99.
    Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms (...)
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  • On variable separation in modal and superintuitionistic logics.Larisa Maksimova - 1995 - Studia Logica 55 (1):99 - 112.
    In this paper we find an algebraic equivalent of the Hallden property in modal logics, namely, we prove that the Hallden-completeness in any normal modal logic is equivalent to the so-called super-embedding property of a suitable class of modal algebras. The joint embedding property of a class of algebras is equivalent to the Pseudo-Relevance Property. We consider connections of the above-mentioned properties with interpolation and amalgamation. Also an algebraic equivalent of of the principle of variable separation in superintuitionistic logics will (...)
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  • Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
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  • Canonical formulas for k4. part I: Basic results.Michael Zakharyaschev - 1992 - Journal of Symbolic Logic 57 (4):1377-1402.
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  • Kripke models and the intuitionistic theory of species.D. H. J. de Jongh - 1976 - Annals of Mathematical Logic 9 (1):157.
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  • Annual meeting of the Association for Symbolic Logic, New York City, December 1987.Nicholas Goodman, Harold T. Hodes, Carl G. Jockusch & Kenneth McAloon - 1988 - Journal of Symbolic Logic 53 (4):1287-1299.
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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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  • The algebraic significance of weak excluded middle laws.Tomáš Lávička, Tommaso Moraschini & James G. Raftery - 2022 - Mathematical Logic Quarterly 68 (1):79-94.
    For (finitary) deductive systems, we formulate a signature‐independent abstraction of the weak excluded middle law (WEML), which strengthens the existing general notion of an inconsistency lemma (IL). Of special interest is the case where a quasivariety algebraizes a deductive system ⊢. We prove that, in this case, if ⊢ has a WEML (in the general sense) then every relatively subdirectly irreducible member of has a greatest proper ‐congruence; the converse holds if ⊢ has an inconsistency lemma. The result extends, in (...)
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  • Modal companions of intermediate propositional logics.Alexander Chagrov & Michael Zakharyashchev - 1992 - Studia Logica 51 (1):49 - 82.
    This paper is a survey of results concerning embeddings of intuitionistic propositional logic and its extensions into various classical modal systems.
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  • Fictions within fictions.Reina Hayaki - 2008 - Philosophical Studies 146 (3):379 - 398.
    This paper examines the logic of fictions within fictions. I argue that consistently nested consistent fictions must have certain formal characteristics. The most important is that they form a tree structure. Depending on one’s theory of fictional objects, additional constraints may apply regarding the appearance of a fictional object in two or more fictional universes. The background motivation for the paper is to use iterated fiction operators as a tool for making sense of iterated modal operators; I conclude by noting (...)
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  • Reference and perspective in intuitionistic logics.John Nolt - 2006 - Journal of Logic, Language and Information 16 (1):91-115.
    What an intuitionist may refer to with respect to a given epistemic state depends not only on that epistemic state itself but on whether it is viewed concurrently from within, in the hindsight of some later state, or ideally from a standpoint “beyond” all epistemic states (though the latter perspective is no longer strictly intuitionistic). Each of these three perspectives has a different—and, in the last two cases, a novel—logic and semantics. This paper explains these logics and their semantics and (...)
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  • The undecidability of the disjunction property of propositional logics and other related problems.Alexander Chagrov & Michael Zakharyaschev - 1993 - Journal of Symbolic Logic 58 (3):967-1002.
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  • A logical and algebraic characterization of adjunctions between generalized quasi-varieties.Tommaso Moraschini - 2018 - Journal of Symbolic Logic 83 (3):899-919.
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  • An algebraic study of diodorean modal systems.R. A. Bull - 1965 - Journal of Symbolic Logic 30 (1):58-64.
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