The “semilattices of Mal’cev blocks”, for short SMB algebras, were defined by A. Bulatov. In a recently accepted paper P. Đapić, Marković, R. McKenzie, and Prokić, the class all algebras its subclass regular proved to be varieties algebras. this paper, we find an equational base first variety simplify previously known second variety.

We propose and study a logic able to state and reason about equational constraints, by combining aspects of classical propositional logic, equational logic, and quantifiers. The logic has a classical structure over an algebraic base, and a form of universal quantification distinguishing between local and global validity of equational constraints. We present a sound and complete axiomatization f...

Using the left merge and communication merge from ACP, we present an equational base (i.e., a ground-complete and ω-complete set of valid equations) for the fragment of CCS without recursion, restriction and relabelling. Our equational base is finite if the set of actions is finite.

This document describes developing an environment for effective use of functional/equational programs and rule-based expert systems. There are significant advantages in using these paradigms for reliability, parallelism, and accumulation of expertise in knowledge bases. The environment will make it easier to understand and use these paradigms, construct more reliable systems, and automatically ...

We investigate the equational theory of several fragments of CCS modulo (strong) bisimilarity with special attention to restriction and relabelling. The largest fragment we consider includes action prefixing, choice, parallel composition without communication, restriction and relabelling. We present a finite equational base (i.e., a finite groundcomplete and omega-complete axiomatisation) for i...

Suppose that T is an equational theory of groups or of rings. If T is finitely axiomatizable, then there is a least number μ so that T can be axiomatized by μ equations. This μ can depend on the operation symbols that occur in T . In the 1960’s, Alfred Tarski and Thomas C. Green completely determined the values of μ for arbitrary equational theories of groups and of rings. While Tarski and Gree...

By an equational theory we mean a set of equations from some fixed language which is closed with respect to logical consequences. We regard equations as universal sentences whose quantifierfree parts are equations between terms. In our notation, we suppress the universal quantifiers. Once a language has been fixed, the collection of all equational theories for that language is a lattice ordered...

‎‎The investigation of equational compactness was initiated by‎ ‎Banaschewski and Nelson‎. ‎They proved that pure injectivity is‎ ‎equivalent to equational compactness‎. ‎Here we define the so‎ ‎called sequentially compact acts over semigroups and study‎ ‎some of their categorical and homological properties‎. ‎Some‎ ‎Baer conditions for injectivity of S-acts are also presented‎.

We present an axiomatization of Conway theories which yields, as a corollary, a very concise axiomatization of iteration theories satisfying the functorial implication for base morphisms. It has been shown that most fixed point operations in computer science share the same equational properties. These equational properties are captured by the notion of iteration theories [1, 3]. Several axiomat...