Author: de Freitas R.P. Viana J.P. Benevides M.R.F. Veloso S.R.M. Veloso P.A.S.
Publisher: Springer Publishing Company
ISSN: 0022-3611
Source: Journal of Philosophical Logic, Vol.32, Iss.4, 2003-08, pp. : 343-355
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Abstract
In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is
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