Remarks on special lattices and related constructive logics with strong negation.
Piero Pagliani · Notre Dame Journal of Formal Logic · 1990
The main purposes of this paper are to provide an algebraic analysis of a certain class of constructive logics with strong negation, and to investigate algebraically the relations between strong and nonconstructible negations definable in these logics.The tools used in this analysis are varieties of algebraic structures of ordered pairs called special NΊattices which were first introduced as algebraic models for Nelson's constructive logic with strong negation (CLSN).Via suitable restrictions of the domains, algebras of this type are shown to be algebraic models for the propositional fragments of E°, CLSN, Intuitionistic Logic, and E%.The differences between E° and CLSN are then studied, via the interrelations that the related algebras exhibit among strong and nonconstructible negations, properties of filters, and their behavior with respect to classically valid formulas.