Glivenko theorems for substructural logics over FL
نویسندگان
چکیده
منابع مشابه
Glivenko theorems for substructural logics over FL
It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko’s theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko’s theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via ...
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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. The Herbrand and Skolemization theorems therefore take various forms, applying either to the left or right of the consequence relation, and to restricted classe...
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In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior’s MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Int to MIPC. As a result we obtain two different versions of Glivenko’s theorem for logics over MIPC. Since MIPC can be thought of as a one-variable fragment of the i...
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We give a simple proof-theoretic argument showing that Glivenko’s theorem for propositional logic and its version for predicate logic follow as an easy consequence of the deduction theorem, which also proves some Glivenko type theorems relating intermediate predicate logics between intuitionistic and classical logic. We consider two schemata, the double negation shift (DNS) and the one consisti...
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Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation pro...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2006
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1164060460