Constructive logic with strong negation as a substructural logic.

BUSANICHE, MANUELA; CIGNOLI, ROBERTO

Nashville, USA

Workshop; •Shanks Workshop: Proof Theory and Algebra; 2008

Vanderbilt University

Recently, M. Spinks and R. Veroff showed that Nelson constructive logic with strong negation can be considered as a substructural logic. We show how this approach can be exploited to obtain information on the algebraic semantics of Nelson logic and to relate it to some non-classical logics existing in the literature.    Under this point of view it can be shown that Nilpotent Minimum logic is an axiomatic extension of Nelson constructive logic with strong negation. We shall extend some results concerning Nilpotent Minimum algebras to subvarieties of Nelson algebras. We will also use a well known representation of Nelson algebras to study subvarieties of involutive residuated lattices.