On finite and infinite fork algebras and their relational reducts

Paulo A.S. Veloso

Abstract


A fork algebra is a relational algebra enriched with a new binary operation, called fork. Such algebras have been introduced because their equational calculus has applications in program construction. They also have some interesting connections with algebraic logic. We examine the finite and infinite fork algebras and their relational reducts. The aim is twofold: contrasting finite and infinite fork algebras as well as comparing relational and fork algebras. First, we show that the finite fork algebras are essentially Boolean algebras, being somewhat uninteresting. Then, we argue that this is not the case with the infinite fork algebras: they display a large diversity of behaviours even if their relational reducts are kept fixed.

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