Equational deduction is generalised within a category-based abstract model theory framework, and proved complete under a hypothesis of quantiier projectivity, using a semantic treatment that regards quantiiers as models rather than variables, and regards valuations as model morphisms rather than functions. Applications include many and order sorted conditional] equational logics, Horn clause lo...

in this paper we continue development of formal theory of a special class offuzzy logics, called eq-logics. unlike fuzzy logics being extensions of themtl-logic in which the basic connective is implication, the basic connective ineq-logics is equivalence. therefore, a new algebra of truth values calledeq-algebra was developed. this is a lower semilattice with top element endowed with two binary...

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 ...

The behavioral equivalence of hidden terms in an equational specification logic is not itself specifiable in general (Buss and Roşu 2000). But much recent work has been done on its partial specification, in particular using coinduction. In this paper we consider the more general notion of conditional behavioral equivalence introduced by Reichel in 1984. We investigate the behavioral proof theor...

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...