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Substructural logics on display
Logic Journal of IGPL, 1998Belnap-style display characterizations admitting cut-elimination are presented for numerous substructural logics including non-commutative intuitionistic linear logic and its relevant, intuitionistic and classical extensions.
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2013
In this paper, we introduce substructural variants of Artemov's logic of proofs. We show a few things here. First, we introduce a bimodal logic that has both the exponential operator in linear logic and an S4 modal operator which does not bring in any structural feature.
Hidenori Kurokawa, Hirohiko Kushida
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In this paper, we introduce substructural variants of Artemov's logic of proofs. We show a few things here. First, we introduce a bimodal logic that has both the exponential operator in linear logic and an S4 modal operator which does not bring in any structural feature.
Hidenori Kurokawa, Hirohiko Kushida
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Finite Models of Some Substructural Logics
MLQ, 2002Summary: We give a proof of the finite model property (fmp) of some fragments of commutative and noncommutative linear logic: the Lambek calculus, BCI, BCK and their enrichments, MALL and Cyclic MALL. We essentially simplify our method used in Stud. Log.
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Modal and Substructural Logics
2019In this section, we will give a brief introduction to proof theory for two important branches of nonclassical logics, that is, modal logics and substructural logics. They are important because both of them include vast varieties of logics that have been actively studied.
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Kripke Semantics for Modal Substructural Logics
Journal of Logic, Language and Information, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Substructural Propositional Dynamic Logics
2019We prove completeness and decidability of a version of Propositional Dynamic Logic where the underlying non-modal propositional logic is a substructural logic in the vicinity of the Full Distributive Non-associative Lambek Calculus. Extensions of the result to stronger substructural logics are briefly discussed.
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Semantics for Substructural Logics
1993Abstract In this paper, we will discuss algebraic and Kripke-type semantics for logics lacking some or all structural rules, which are now called sub structural logics(for general information on sub structural logics, see, for example, Dosen [6], Ono [23] and Troelstra [33]). Various kinds of semantics for sub structural logics have been
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A SAHLQVIST THEOREM FOR SUBSTRUCTURAL LOGIC
The Review of Symbolic Logic, 2013AbstractIn this paper, we establish the first-order definability of sequents with consistent variable occurrence on bi-approximation semantics by means of the Sahlqvist–van Benthem algorithm. Then together with the canonicity results in Suzuki (2011), this allows us to establish a Sahlqvist theorem for substructural logic.
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Equality in Substructural Logics
1996Abstract Standard axioms for equality, or standard definitions of equality in secondorder logic or set theory, permit to infer versions limited to equalities of structural rules otherwise banned in substructural logics. In the presence of settheoretic extensionality and a rather natural form of separation, these limited structural rules ...
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