Abstract
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.
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Notes
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 ⋆.
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.
Notice that this formula has four variables ranging over individuals.
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© 1997 Springer-Verlag Wien
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Haeberer, A., Frias, M., Baum, G., Veloso, P. (1997). Fork Algebras. In: Brink, C., Kahl, W., Schmidt, G. (eds) Relational Methods in Computer Science. Advances in Computing Sciences. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6510-2_4
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DOI: https://doi.org/10.1007/978-3-7091-6510-2_4
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82971-4
Online ISBN: 978-3-7091-6510-2
eBook Packages: Springer Book Archive