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Semi-Substructural Logics à la Lambek with Symmetry
Bulletin of the Section of LogicThis work studies the proof theory and ternary relational semantics of left (right) skew monoidal closed categories and skew monoidal bi-closed categories, both symmetric and non-symmetric, from the perspective of non-associative Lambek calculus ...
Cheng-Syuan Wan
doaj +3 more sources
Skolemization for Substructural Logics
, 2015 The usual Skolemization procedure, which removes strong quantifiers by introducing new function symbols, is in general unsound for first-order substructural logics defined based on classes of complete residuated lattices.
Metcalfe, George +5 more
core +3 more sources
Herbrand Theorems for Substructural Logics [PDF]
, 2013 Herbrand and Skolemization theorems are obtained for a broad family of first-order substructural logics. These logics typically lack equivalent prenex forms, a deduction theorem, and reductions of semantic consequence to satisfiability.
Metcalfe, George +3 more
core +3 more sources
Generalized quantification as substructural logic [PDF]
Journal of Symbolic Logic, 1996 AbstractWe show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables.
Natasha Alechina, Michiel van Lambalgen
openalex +4 more sources
Constructive logic with strong negation as a substructural logic
Journal of Logic and Computation, 2010 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
openalex +3 more sources
Craig interpolation for semilinear substructural logics
Mathematical Logic Quarterly, 2012 The Craig interpolation property is investigated for substructural logics whose algebraic semantics are varieties of semilinear (subdirect products of linearly ordered) pointed commutative residuated lattices.
Enrico Marchioni, George Metcalfe
exaly +2 more sources
Disjunction property and complexity of substructural logics
Theoretical Computer Science, 2011 We systematically identify a large class of substructural logics that satisfy the disjunction property (DP), and show that every consistent substructural logic with the DP is PSPACE-hard. Our results are obtained by using algebraic techniques.
Rostislav Horčík, Kazushige Terui
exaly +2 more sources
Substructural Logics and Residuated Lattices — an Introduction
Trends in Logic, 2003 This is an introductory survey of substructural logics and of residuated lattices which are algebraic structures for substructural logics. Our survey starts from sequent systems for basic substructural logics and develops the proof theory of them.
Hiroakira Ono, Ono Hiroakira
exaly +2 more sources
A General Framework for Hybrid Substructural Categorial Logics
, 1994 this paper to propose an alternative general model of hybrid substructural systems, which should eliminate the need for structural modalities, and avoid their associated problems.
Categorial Logics +3 more
core +3 more sources
Nonassociative substructural logics and their semilinear extensions: Axiomatization and completeness properties [PDF]
, 2013 Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices.
Horcik R., Cintula P., Noguera C.
core +4 more sources