ON EQUATIONAL COMPLETENESS THEOREMS

Abstract A logic is said to admit an equational completeness theorem when it can be interpreted into the consequence relative some class of algebras. We characterize logics admitting that are either locally tabular or have tautology. In particular, shown a protoalgebraic admits precisely has two distinct logically equivalent formulas. While problem determining whether decidable both for presented by finite set matrices and Hilbert calculus, becomes undecidable arbitrary calculi.