Semantics of property inheritance in a hierarchic system with explicit negation

Abstract

The purpose of this paper is to present a first step in a formal study of inheritance systems.

The kind of systems considered are those that support overriding (all definitions being taken as defaults) and multiple inheritance. The overriding is based on the explicit statement of negative information.

The basic entities are classes and properties. The system is hierarchic because it is made out of classes which are structured as a hierarchy. We consider both the basic case of properties restricted to atomic propositional formulas and their negations, and the extension to properties defined by rules in the Logic Programming style.

A formal definition of hierarchic systems is given for which a model-theoretic 3-valued semantics is in roduced. This semantics is explicitly stated in terms of sets of individuals. It defines the notion of interpretation, the characterization of models, and what is meant by validity of formulas in such structures.

The inheritance mechanism is able to choose from a set of inherited default properties which ones must be overriden in order to guarantee that the local program has a model.

The notion of characteristic individuals of classes, introduced in our semantics, turns out to play a clarifying role of the relationship between semantic and syntactic aspects of inheritance systems.

Work done under partial support of Esprit BRA 3020 ”Integration” and Portuguese JNICT project PEROLA

Owns a scholarship from INIC.