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A Substructural Logic for Inconsistent Mathematics
2019A logic for inconsistent mathematics must be strong enough to support reasoning in proofs, while weak enough to avoid paradoxes. We present a substructural logic intended to meet the needs of a working dialetheic mathematician—specifically, by adding a de Morgan negation to light linear logic, and extending the logic with a relevant conditional.
Badia, Guillermo, Weber, Zach
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Substructural logics, pluralism and collapse
Synthese, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eduardo Alejandro Barrio +2 more
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1993
Abstract Sub structural logics are non classical logics, which arose in response to problems in foundations of mathematics and logic, theoretical computer science, mathematical linguistics, and category theory. They include intuitionistic logic, relevant logic, BCK logic, linear logic, and Lambek's calculus of syntactic categories.
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Abstract Sub structural logics are non classical logics, which arose in response to problems in foundations of mathematics and logic, theoretical computer science, mathematical linguistics, and category theory. They include intuitionistic logic, relevant logic, BCK logic, linear logic, and Lambek's calculus of syntactic categories.
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Modal translations in substructural logics
Journal of Philosophical Logic, 1992The Gödel-Tarski translation of the intuitionistic predicate logic into S4 by prefixing \(\square\) to all subformulas is sound and faithful. The author proves a similar result for translations of the intuitionistic versions of linear logic, relevance logic and BCK-logic into their classical S4-analogs.
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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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Information, Awareness and Substructural Logics
2013The paper outlines a generalisation of the awareness-based epistemic semantics by Fagin and Halpern. Awareness is construed as a relation between agents and pieces of information instead of formulas. The main motive for introducing the generalisation is that it shows substructural logics to be a natural component of information-based epistemic logic ...
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A Paraconsistent and Substructural Conditional Logic
2012I introduce and motivate a conditional logic based on the substructural system HL from Paoli (Substructural logics: a primer, Kluwer, Dordrecht, 2002). Its hallmark is the presence of three logical levels (each one of which contains its own conditional connective), linked to one another by means of appropriate distribution principles.
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Logic for two: The semantics of distributive substructural logics
1997This is an account of the semantics of a family of logics whose paradigm member is the relevant logic R of Anderson and Belnap. The formal semantic theory is well worn, having been discussed in the literature of such logics for over a quarter of a century.
John K. Slaney, Robert K. Meyer
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A substructural connective for possibilistic logic
1995We investigate the use of substructural logics for dealing with uncertainty. In this paper possibilistic logic is enriched with a new connective for combining information; the language allows then for two combinators: the usual ”and” for performing expansion and the new ”and” for combining information from distinct independent sources, as argued in ...
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Substructural Nuclear (Image-Based) Logics and Operational Kripke-Style Semantics
Studia Logica, 2023Eunsuk Yang, Yang Eunsuk
exaly