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Towards a Proof Theory of G\"odel Modal Logics [PDF]
Logical Methods in Computer Science, 2011 Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic.
George Metcalfe, Nicola Olivetti
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Propositional Logics Complexity and the Sub-Formula Property [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 In 1979 Richard Statman proved, using proof-theory, that the purely implicational fragment of Intuitionistic Logic (M-imply) is PSPACE-complete.
Edward Hermann Haeusler
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Exploring a Syntactic Notion of Modal Many-Valued Logics [PDF]
, 2008 We propose a general semantic notion of modal many-valued logic. Then, we explore the di culties to characterize this notion in a syntactic way and analyze the existing literature with respect to this frameworkPeer ...
Félix Bou +2 more
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Electronic Proceedings in Theoretical Computer ScienceWe combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the many-valued minimal normal modal logic, presented as a Gentzen-like sequent calculus, and prove its soundness and
Karniel, Amir, Kaminski, Michael
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Sequents in many valued logic II [PDF]
Fundamenta Mathematicae, 1967 G. S. Rousseau
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Two deductions systems for the Logic PM4N
Intermaths, 2022 The logic PM4N was introduced by Jean-Yves Beziau as a modal and 4-valued system. In this introductory paper, the author presented the system from a matrix logic with four values disposed in a Boolean algebra with a modal operator for the notion of ...
Hércules de Araújo Feitosa +2 more
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ON A NEW APPROACH TO PEIRCE’S THREE-VALUE PROPOSITIONAL LOGIC
Manuscrito, 2023 In 1909, Peirce recorded in a few pages of his logic notebook some experiments with matrices for three-valued propositional logic. These notes are today recognized as one of the first attempts to create non-classical formal systems.
JOSÉ RENATO SALATIEL
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A Variant of Material Connexive Logic
Bulletin of the Section of Logic, 2021 The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic.
Alexander Belikov, Dmitry Zaitsev
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Fractional-Valued Modal Logic and Soft Bilateralism
Bulletin of the Section of Logic, 2023 In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of proof-theoretic semantics for the base modal logic \(\mathbf{K}\), whose values lie in the closed interval \([0,1]\) of rational numbers [14].
Mario Piazza +2 more
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Characteristic Logics for Behavioural Hemimetrics via Fuzzy Lax Extensions [PDF]
Logical Methods in Computer Science, 2022 In systems involving quantitative data, such as probabilistic, fuzzy, or metric systems, behavioural distances provide a more fine-grained comparison of states than two-valued notions of behavioural equivalence or behaviour inclusion.
Paul Wild, Lutz Schröder
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