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...

In [3], we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the equational class of (pointed) F-quasigroups and the equational class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.

A longstanding open problem in lambda calculus is whether there exists a non-syntactical model of the untyped lambda calculus whose theory is exactly the least λ-theory λβ. In this paper we make use of the Visser topology for investigating the related question of whether the equational theory of a model can be recursively enumerable (r.e. for brevity). We introduce the notion of an effective mo...

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...

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...

We consider the problem of combining procedures that decide solvability of (dis)uniication problems over disjoint equational theories. Partial answers to the following questions are given: Which properties of the component theories imply intractability in the sense that there cannot be a polynomial combination algorithm, assuming P 6 = NP? Which general properties of the component theories guar...

We study generalized deduction rules of cut and weakening in the context of equational fragment of Pavelkastyle fuzzy logic using complete residuated lattices as the structures of truth degrees. The deduction rules in question are parameterized by a truth stresser, an additional unary operation on the structure of truth degrees. It is shown that the deductive system of fuzzy Horn logic can be r...

Positive MV-algebras are the subreducts of with respect to signature $\{\oplus, \odot, \lor, \land, 0, 1\}$. We provide a finite quasi-equational axiomatization for class such algebras.

An algebra A is uniquely generated by a set G if G is a subset of every set that generates A. We investigate uniquely generated algebras and focus especially on equational classes of algebras in which the free algebras are uniquely generated. We show that such classes possess a number of algebraic properties that are in some sense extremal. We also present algebraic conditions on an equational ...

This paper belongs to our series of works on algebraic geometry over arbitrary structures. In this one, there will be investigated seven equivalences (namely: geometric, universal quasi-equational, universal, elementary, and combinations thereof) in specific classes structures (equationally Noetherian, qω-compact, uω-compact, equational domains, co-domains, etc.). The main questions are the fol...