On the construction of explosive relation algebras

TL;DR

This paper explores methods for constructing explosive relation algebras, a subclass of fork algebras that can be expanded in numerous ways, enhancing the expressive power of relation algebra for program specification.

Contribution

It introduces general techniques for constructing explosive relation algebras, advancing understanding of their properties and potential applications.

Findings

Developed methods for constructing explosive relation algebras

Analyzed properties related to representability and axiomatizability

Enhanced the theoretical framework for fork algebra extensions

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.