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 present...

Birkhoff [1935] initiated the general study of algebraic structure. Importantly for our concerns here, his development was from (universal) algebra to (equational) logic. Birkhoff’s starting point was the informal conception of algebra based on familiar concrete examples. Abstracting from these, he introduced the concepts of signature and equational presentation, and thereby formalised what is ...

Lawvere theories provide a category theoretic view of equational logic, identifying equational theories with small categories equipped with finite products. This formulation allows equational theories to be investigated as first class mathematical entities. However, many formal systems, particularly in computer science, are described by equations modulated by side conditions asserting the “fres...

The equational complexity function βV : N → N of an equational class of algebras V bounds the size of equation required to determine membership of n-element algebras in V. Known examples of finitely generated varieties V with unbounded equational complexity have growth in Ω(nc), usually for c ≥ 1 2 . We show that much slower growth is possible, exhibiting O(log 2 (n)) growth amongst varieties o...