In this chapter we present the class of fork algebras, an extension of relation algebras with an extra operator called fork. We will present results relating fork algebras both to logic and to computer science. The interpretability of first-order theories as equational theories in fork algebras will provide a tool for expressing program specifications as fork algebra equations. Furthermore, the finite axiomatizability of this class of algebras will be shown to have deep influence in the process of program development within a relational calculus based on fork algebras.
KeywordsBinary Relation Equational Theory Relation Algebra Pairing Operation Common Extension
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- 1.It is important to remark that proper fork algebras are quasi-concrete structures, since, as was pointed out by Andréka and Németi in a private communication, concrete structures must be fully characterized by their underlying domain, which does not happen with proper fork algebras because of the (hidden) operation ⋆.Google Scholar
- 2.Along the next theorems, by S we denote the operation of taking subalgebras of a given class of algebras. P takes direct products of algebras in a given class, and I takes isomorphic copies.Google Scholar
- 3.Notice that this formula has four variables ranging over individuals.Google Scholar