## Abstract

In its modern form the algebra of relations has been under investigation by mathematicians since Tarski’s seminal paper of (1941). The main line of development has been the study of a class of algebras called *relation algebras* (Chin and Tarski 1951, Jónsson 1982), in parallel with developments such as Boolean algebras with operators (Jónsson and Tarski 1951/1952) and cylindric algebras (Henkin, Monk and Tarski 1985). Since the early seventies the algebra of relations has increasingly become of interest to computer scientists. Just as the notion of a partial function provides a natural model for deterministic programs, so the more general notion of a (binary) relation provides a natural model for nondeterministic programs. This idea has been exploited by various authors. For example, it is evident in Floyd-Hoare logic for program verification, it has been extended to specification in Hoare and He, Jifeng (1987), it figures in logics of programs such as dynamic logic (Parikh 1981, Harel 1984), and it was used in the early seventies to model recursive procedures (de Bakker and de Roever 1973, Hitchcock and Park 1972). Recently the algebra of relations has been extensively used in a graph-theoretic approach to programs by Schmidt and Ströhlein (1991). In modal logic, relation algebra features strongly in the Dutch-Hungarian cooperation on van Benthem’s (1991) new *arrow logic* (see *Logic at Work, Proceedings of the Applied Logic Conference* (1992)). Venema (1992) is another interdisciplinary study of relation algebra and multi-modal logic. The proof theory of relations is also of interest to computer scientists, and several relational inference systems are available (Wadge 1975, Hennessy 1980, Maddux 1983, Orlowska 1991).

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