On the construction of explosive relation algebras

Abstract

Fork algebras are an extension of relation algebras obtained by extending the set of logical symbols with a binary operator called fork. This class of algebras was introduced by Haeberer and Veloso in the early 90's aiming at enriching relation algebra, an already successful language for program specification, with the capability of expressing some form of parallel computation. The further study of this class of algebras led to many meaningful results linked to interesting properties of relation algebras such as representability and finite axiomatizability, among others. Also in the 90's, Veloso introduced a subclass of relation algebras that are expansible to fork algebras, admitting a large number of non-isomorphic expansions, referred to as explosive relation algebras. In this work we discuss some general techniques for constructing algebras of this type