A note on the logic of signed equations

Abstract

A signed ∑-equation is an expression of the form t ≈ t′ or t ≉ t′, where t and t′ are ∑-terms (for some ranked set ∑). We characterize those classes of ∑-algebras which are models of a set of signed ∑-equations. Further we consider the problem of finding a complete deductive system analogous to equational logic for the logical consequence operation restricted to signed equations.