Tangent Circle Algebras

This paper investigates relation algebras which arise in the context of preference relations, and studies the tangent circle orders introduced in [1].

Abstract

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 in [1].