Results 11 to 20 of about 690 (186)
Quantitative Equality in Substructural Logic via Lipschitz Doctrines [PDF]
Logical Methods in Computer ScienceSubstructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar, rather than ...
Francesco Dagnino, Fabio Pasquali
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Journal of Symbolic Logic, 2007 AbstractSubstructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0, 1]. In this paper, we introduce Uninorm logicULas Multiplicative additive intuitionistic linear logicMAILLextended with the prelinearity axiom((A → B) ∧ t) V ((B → A)∧ t).
George Metcalfe, Franco Montagna
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CONNEXIVE IMPLICATIONS IN SUBSTRUCTURAL LOGICS
The Review of Symbolic Logic, 2023 AbstractThis paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FL ${}_{\scriptsize\mbox{e}}$ -algebras).
Davide Fazio, Gavin St. John
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Constructive Logic with Strong Negation as a Substructural Logic [PDF]
Journal of Logic and Computation, 2008 Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some axiomatic extensions of CLSN. For instance, we prove that Nilpotent minimum logic is the extension of CLSN by the prelinearity axiom ...
Manuela Busaniche, Roberto Cignoli
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Modal translation of substructural logics [PDF]
Journal of Applied Non-Classical Logics, 2020 In an article dating back in 1992, Kosta Došen initiated a project of modal translations in substructural logics, aiming at generalizing the well-known Gödel-McKinsey-Tarski translation of intuitionistic logic into {\bf S4}. Došen's translation worked well for (variants of) {\bf BCI} and stronger systems ({\bf BCW}, {\bf BCK}), but not for systems ...
Hartonas C.
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Substructural logic and partial correctness [PDF]
ACM Transactions on Computational Logic, 2003 We formulate a noncommutative sequent calculus for partial correctness that subsumes propositional Hoare Logic. Partial correctness assertions are represented by intuitionistic linear implication. We prove soundness and completeness over relational and trace models.
Dexter Kozen +2 more
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A Substructural Epistemic Resource Logic [PDF]
, 2016 We present a substructural epistemic logic, based on Boolean BI, in which the epistemic modalities are parametrized on agents' local resources. The new modalities can be seen as generalizations of the usual epistemic modalities. The logic combines Boolean BI's resource semantics with epistemic agency.
Didier Galmiche +2 more
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Substructural Fuzzy-Relevance Logic [PDF]
Notre Dame Journal of Formal Logic, 2015 This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn’s weak relevance principle.
Eunsuk Yang
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Constructive Logic with Strong Negation is a Substructural Logic. I [PDF]
Studia Logica, 2008 This is the latter half of two papers in which the authors show that the constructive logic with strong negation is definitionally equivalent to a certain axiomatic extension of the substructural logic FLew, namely, the full Lambek calculus with exchange and weakening. In the first half [\textit{M. Spinks} and \textit{R. Veroff}, Stud. Log. 88, No.
Matthew Spinks +2 more
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A Substructural Modal Logic of Utility [PDF]
Journal of Logic and Computation, 2017 Abstract We introduce a substructural modal logic of utility that can be used to reason aboutoptimality with respect to properties of states. Our notion of state is quite general, and is able to represent resource allocation problems in distributed systems.
Pym, D, Anderson, G
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