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  1. Effective finite-valued approximations of general propositional logics.Matthias Baaz & Richard Zach - 2008 - In Arnon Avron & Nachum Dershowitz (eds.), Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Springer Verlag. pp. 107–129.
    Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways can (...)
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  • Variations on the Kripke Trick.Mikhail Rybakov & Dmitry Shkatov - forthcoming - Studia Logica:1-48.
    In the early 1960s, to prove undecidability of monadic fragments of sublogics of the predicate modal logic $$\textbf{QS5}$$ QS 5 that include the classical predicate logic $$\textbf{QCl}$$ QCl, Saul Kripke showed how a classical atomic formula with a binary predicate letter can be simulated by a monadic modal formula. We consider adaptations of Kripke’s simulation, which we call the Kripke trick, to various modal and superintuitionistic predicate logics not considered by Kripke. We also discuss settings where the Kripke trick does (...)
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  • Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability.Frederik Van De Putte & Dominik Klein - 2020 - Studia Logica 109 (1):47-93.
    We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De Putte and Klein. The definition of our canonical models combines standard techniques with a so-called “puzzle piece construction”, which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling modalities and investigate the technique’s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.
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  • Synonymous logics: A correction. [REVIEW]Francis Jeffry Pelletier & Alasdair Urquhart - 2008 - Journal of Philosophical Logic 37 (1):95 - 100.
    In an earlier paper entitled Synonymous Logics, the authors attempted to show that there are two modal logics so that each is exactly translatable into the other, but they are not translationally equivalent. Unfortunately, there is an error in the proof of this result. The present paper provides a new example of two such logics, and a proof of the result claimed in the earlier paper.
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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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  • Logics containing k4. part II.Kit Fine - 1985 - Journal of Symbolic Logic 50 (3):619-651.
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  • Decidability by filtrations for graded normal logics (graded modalities V).Claudio Cerrato - 1994 - Studia Logica 53 (1):61 - 73.
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  • Modal logic: A semantic perspective.Patrick Blackburn & Johan van Benthem - 1988 - Ethics 98:501-517.
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 BASIC MODAL LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.
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  • Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...)
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