Circumscription in Data Logic for Data Type Specification

In this paper we present a logical speciication of data types. This speciication is built upon a previously given speciication for a data type that we want to extend by introducing new constructing objects and deened operations. The extended data type is speciied by superposing a circumscription principle to some speciication axioms. Circumscription formalizes in second-order logic some forms of (non-monotonic) common-sense reasoning in knowledge bases 11]. By means of circumscription we separate very clearly the rst-order speciication language (or axioms) from the speciication mechanism. By showing the logical equivalence to Zhang's non-circumscriptive data type speciication 17], we obtain the categoricity of our speciication when we start from a categorical speciication for the original data type.