Constructive Logic with Strong Negation is a Substructural Logic. I

Studia Logica 88 (3):325-348 (2008)

Abstract

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL ew (namely, a certain variety of FL ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL ew.

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References found in this work

Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
A Semantical Study of Constructible Falsity.Richmond H. Thomason - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (16-18):247-257.
A Semantical Study of Constructible Falsity.Richmond H. Thomason - 1969 - Mathematical Logic Quarterly 15 (16‐18):247-257.

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