An intensional semantics for a hybrid language

摘要

One of the major assumptions in designing knowledge representation formalisms in the KL-One family, was the so-called ‘intensional representation’. An intensional representation is required when two descriptions have to be compared, or when they are interpreted by qualitative processes; in other words, many processes can be activated by using the global structure of a concept, and by interpreting its properties and the relationships between these properties.In this perspective, an intensional semantics for a typical terminological language has been designed, which is quite different from the extensional models proposed so far. The semantics of the language is similar to that of data types in programming languages. Primitive concepts are denoted by a set of values. Defined concepts are denoted by their properties. A denotation thus contains the minimum number of properties which are required for an individual to be an instance of a generic concept. More precisely, the denotation is the Cartesian product of the sets denoting the properties of the genetic concept (deduced from its syntax). A role is denoted by a function which, given a tuple, returns the values of the property which individuates the role. An individual is created by instantiating the properties of the relative generic concept, used as a guide. As a result, this process creates a tuple whose elements are the instantiating properties. The instantiation chain terminates by instantiating primitive concepts on the basis of their denotation.A deeper integration between the entire system and any programming language can be reached, which implicitly gives rise to an object-oriented system. In other words, it is possible to introduce an individual concept into a programming language, like any other data type. For instance, an individual concept is passed to a function as a parameter; once it has been verified that this individual is an instance of a generic concept, or of one of its subconcepts, the function will be executed.Furthermore, an increase in the expressive power is obtained, since it makes it possible to give a formal meaning to all kinds of recursive definitions of individual and generic concepts.