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  1. Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects.W. Conradie, V. Goranko & D. Vakarelov - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. 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 (...)
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  • Two simple incomplete modal logics.J. F. A. K. van Benthem - 1978 - Theoria 44 (1):25-37.
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  • Modal languages for topology: Expressivity and definability.Balder ten Cate, David Gabelaia & Dmitry Sustretov - 2009 - Annals of Pure and Applied Logic 159 (1-2):146-170.
    In this paper we study the expressive power and definability for modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language.
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  • Expressivity of second order propositional modal logic.Balder ten 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 and SOPML.
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  • Modal logic and the theory of modal aggregation.P. K. Schotch & R. E. Jennings - 1980 - Philosophia 9 (2):265-278.
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  • A comparison of two approaches to parainconsistency: Flemish and Polish.Marek Nasieniewski - 2001 - Logic and Logical Philosophy 9:47.
    In this paper we present a comparison of certain inconsistencyadaptive logics and Jaśkowski’s logic.
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  • Universal First‐Order Definability in Modal Logic.R. E. Jennings, D. K. Johnston & P. K. Schotch - 1980 - Mathematical Logic Quarterly 26 (19-21):327-330.
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  • 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 (...)
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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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  • Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
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  • Algorithmic problems concerning first-order definability of modal formulas on the class of all finite frames.A. V. Chagrov & L. A. Chagrova - 1995 - Studia Logica 55 (3):421 - 448.
    The main result is that is no effective algorithmic answer to the question:how to recognize whether arbitrary modal formula has a first-order equivalent on the class of finite frames. Besides, two known problems are solved: it is proved algorithmic undecidability of finite frame consequence between modal formulas; the difference between global and local variants of first-order definability of modal formulas on the class of transitive frames is shown.
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  • A framework for the transfer of proofs, lemmas and strategies from classical to non classical logics.Ricardo Caferra, Stéphane Demri & Michel Herment - 1993 - Studia Logica 52 (2):197 - 232.
    There exist valuable methods for theorem proving in non classical logics based on translation from these logics into first-order classical logic (abbreviated henceforth FOL). The key notion in these approaches istranslation from aSource Logic (henceforth abbreviated SL) to aTarget Logic (henceforth abbreviated TL). These methods are concerned with the problem offinding a proof in TL by translating a formula in SL, but they do not address the very important problem ofpresenting proofs in SL via a backward translation. We propose a (...)
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  • Two simple incomplete modal logics.J. F. A. K. Benthem - 1978 - Theoria 44 (1):25-37.
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  • On Sahlqvist Formulas in Relevant Logic.Guillermo Badia - 2018 - Journal of Philosophical Logic 47 (4):673-691.
    This paper defines a Sahlqvist fragment for relevant logic and establishes that each class of frames in the Routley-Meyer semantics which is definable by a Sahlqvist formula is also elementary, that is, it coincides with the class of structures satisfying a given first order property calculable by a Sahlqvist-van Benthem algorithm. Furthermore, we show that some classes of Routley-Meyer frames definable by a relevant formula are not elementary.
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  • Modern Origins of Modal Logic.Roberta Ballarin - 2010 - Stanford Encyclopedia of Philosophy.
     
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  • Logika a logiky.Jaroslav Peregrin - manuscript
    Kniha, jako je tato, nemůže být tak docela dílem jediného člověka. Dovést ji do podoby koherentního celku bych nedokázal bez pomoci svých kolegů, kteří po mně text četli a upozornili mě na spoustu chyb a nedůsledností, které se v něm vyskytovaly. Můj dík v tomto směru patří zejména Vojtěchu Kolmanovi, Liboru Běhounkovi a Martě Bílkové. Za připomínky k různým částem rukopisu jsem vděčen i Pavlu Maternovi, Milanu Matouškovi, Prokopu Sousedíkovi, Vladimíru Svobodovi, Petru Hájkovi a Grahamu Priestovi. Kniha vznikla v rámci (...)
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