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Distribution-Free Normal Modal Logics [PDF]
LogicsThis article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different approach, as a
Chrysafis Hartonas
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Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics [PDF]
Axioms, 2021 Aristotelian diagrams, such as the square of opposition, are well-known in the context of normal modal logics (i.e., systems of modal logic which can be given a relational semantics in terms of Kripke models). This paper studies Aristotelian diagrams for
Lorenz Demey
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Theorem Provers For Every Normal Modal Logic
EPiC Series in Computing, 2018 We present a procedure for algorithmically embedding problems formulated in higher-order modal logic into classical higher-order logic. The procedure was implemented as a stand-alone tool and can be used as a preprocessor for turning TPTP THF-compliant ...
Tobias Gleißner +2 more
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Natural deduction in normal modal logic. [PDF]
Notre Dame Journal of Formal Logic, 1990 A natural deduction system for a wide range of normal modal logics is presented, which is based on Segerberg's idea that classical validity should be preserved «in any modal context».
John Hawthorn
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Intuitionistic Non-normal Modal Logics: A General Framework [PDF]
Journal of Philosophical Logic, 2020 We define a family of intuitionistic non-normal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility.
Tiziano Dalmonte +2 more
semanticscholar +9 more sources
Some Additional Axioms for T-normal Logics. Defining K45, KB4, KD45 and S5 without Using Modal Rules
Bulletin of the Section of LogicThe paper studies extensions of t-normal logics S0.5o and S0.5 obtained by means of some axioms of normal logics. We will prove determination theorems for these extensions by appropriate Kripke-style models.
Andrzej Pietruszczak
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Explicit non-normal modal logic [PDF]
Journal of Logic and Computation, 2021 Abstract Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of deontic situations. To overcome this issue, we introduce novel justification logics as hyperintensional analogues to non-normal modal logics. We establish soundness and completeness with respect
Atefeh Rohani, Thomas Studer
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A modal logic internalizing normal proofs [PDF]
Information and Computation, 2011 AbstractIn the proof-theoretic study of logic, the notion of normal proof has been understood and investigated as a metalogical property. Usually we formulate a system of logic, identify a class of proofs as normal proofs, and show that every proof in the system reduces to a corresponding normal proof.
Sungwoo Park, Hyeonseung Im
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Rosser provability and normal modal logics [PDF]
Studia Logica, 2018 In this paper, we investigate Rosser provability predicates whose provability logics are normal modal logics. First, we prove that there exists a Rosser provability predicate whose provability logic is exactly the normal modal logic ${\sf KD}$. Secondly, we introduce a new normal modal logic ${\sf KDR}$ which is a proper extension of ${\sf KD}$, and ...
Taishi Kurahashi
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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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