Introducing taxonomic reasoning in LOGIDATA⁺

Abstract

In this paper we give a syntax and define a denotational semantics for describing classes in LOGIDATA^*, and give a subsumption algorithm that is sound, complete, and polynomial. The syntax allows us to describe both primitive and defined acyclic classes by means of the tuple and set type constructors; in particular, it is also possible to state cardinality constraints on sets. Semantics is defined by means of an interpretation function that maps the descriptions given at an intensional level into the value domain. This interpretation also takes the undefined element nil into account, thus allowing us to deal with a form of incomplete knowledge in a way that is semantically correct. After introducing defined classes and the notion of interpretation function, it is possible to formally define the concept of subsumption, an inference technique that makes it possible reasoning about objects and classes on the basis of their descriptions.