Cut elimination and strong separation for substructural logics: An algebraic approach
نویسندگان
چکیده
منابع مشابه
Cut elimination and strong separation for substructural logics: An algebraic approach
We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on (associative) substructural logics over the full Lambek Calculus FL (see e.g. [36, 19, 18]). We present a Gentzen-style sequent system GL that lacks the structural rules of contraction, weakening, exchange and associa...
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We carry out a unified investigation of two prominent topics in proof theory and order algebra: cut-elimination and completion, in the setting of substructural logics and residuated lattices. We introduce the substructural hierarchy — a new classification of logical axioms (algebraic equations) over full Lambek calculus FL, and show that a stronger form of cutelimination for extensions of FL an...
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Substructural logics have been traditionally characterized as those logics such that, when presented by means of a (sequent) proof system, lack one or more of the usual structural rules: weakening, exchange and contraction. Nonetheless, it is well known that they can also be, very usefully, roughly described as the logics of residuated lattices. Indeed, from this point of view we have seen, spe...
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We introduce intuitionistic and classical substructural logics with structural rules mingle and connective strong negation, and investigate the cut-elimination property and the relevance principle for these logics. The relevance principle does not hold for substructural logics with mingle and usual negation, but holds for those with mingle and strong negation.
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We give two generic proofs for cut elimination in propositional modal logics, interpreted over coalgebras. We first investigate semantic coherence conditions between the axiomatisation of a particular logic and its coalgebraic semantics that guarantee that the cut-rule is admissible in the ensuing sequent calculus. We then independently isolate a purely syntactic property of the set of modal ru...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2010
ISSN: 0168-0072
DOI: 10.1016/j.apal.2010.01.003