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Following Jiang Guanghao and Xu Luoshan's concept of conjugative, dually conjugative, normal and dually normal relations on sets, the concept of quasi-regular relations is introduced. Characterizations of quasi-regular relations are obtained and it is shown when an anti-order relation is quasi-regular. Some nontrivial examples of quasi-regular relations are given. At the end we introduce dually quasi-regular relations and give a connection between these two types of relations. [ABSTRACT FROM AUTHOR]

We prove that the equational complexity function for the variety of representable relation algebras is bounded below by a log-log function. [ABSTRACT FROM AUTHOR]

In [10] it is claimed that the set of predicate tautologies of all complete BL-chains and the set of all standard tautologies (i. e., the set of predicate formulas valid in all standard BL-algebras) coincide. As noticed in [11], this claim is wrong. In this paper we show that a complete BL-chain B satisfies all standard BL-tautologies iff for any transfinite sequence (ai: i ∈ I) of elements of B, the condition ∧i ∈ I (a2i) = (∧i ∈ Iai)2 holds in B. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Letn > 2. A weakly representable relation algebra that is not strongly representable is constructed. It is proved that the set of all n by n basic matrices forms a cylindric basis that is also a weakly but not a strongly representable atom structure. This gives an example of a binary generated atomic representable cylindric algebra with no complete representation. An application to first order logic is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Abstract.??We study MV-relation-algebras, appearing by abstracting away from the concrete many-valued relations and the operations on them, such as composition and converse. MV-relation-algebras are MV generalizations of the relation algebras developed by A. Tarski and his school starting from the late forties. Some facts about ideals, congruences, and various types of elements are proved. A characterization of the ?natural? MV-relation-algebras (a parameterized analogue of the classicalfullproperrelation algebras) is also provided, as well as a first-order elementary description of matrix MV-relation algebras. [ABSTRACT FROM AUTHOR]

To solve problems of Magnus and Stallings stated in the 1960s, we construct a balanced presentation of the trivial group such that no defining relator of this presentation could be replaced by a free generator and the group, given by the altered presentation, would still be trivial. Some other related problems on balanced presentations of the trivial group are discussed. [ABSTRACT FROM AUTHOR]

In the article we characterize, in terms of quivers and relations, the admissible algebras with formal two-ray modules introduced in Bobiński and Skowroński (2003b). [ABSTRACT FROM AUTHOR]

Many formalisms for qualitative spatial and temporal reasoning fit into a pattern exemplified by Allen's temporal interval calculus. Constraint‐based reasoning using Allen's calculus can benefit from some of its main properties: (a) the underlying constraint algebra is a relation algebra, in Tarski's sense; (b) testing path‐consistency is a complete method for testing consistency for well‐determined subclasses of relations; (c) atomic path‐consistent networks are consistent and determine unique qualitative configurations; (d) the first order theory associated to the calculus is aleph‐zero categorical. When considering analogous calculi, many of the properties mentioned above no longer hold. The main object of this paper is to examine some of the new questions which arise. In order to do so, we use the idea of weak representations of the algebras as a unifying concept. [ABSTRACT FROM AUTHOR]

This note is an addendum to clarify credit for universal relational systems and their properties. [ABSTRACT FROM AUTHOR]