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# Brock TR # CS-02-06 Abstract

*Tangent circle algebras * [PDF]

Ivo Düntsch and Marc Roubens, May 2002.

In relational reasoning, one is concerned with the algebras generated by a given set of relations, when one allows only basic relational operations such as the Boolean operations, relational composition, and converse. According to a result by A. Tarski, the relations obtained in this way are exactly the relations which are definable in the three--variable fragment of first order logic. Thus, a relation algebra is a first indicator of the expressive power of a given set of relations.In this paper, we investigate relation algebras which arise in the context of preference relations. In particular, we study the tangent circle orders introduced by Abbas and Vincke (1996).