FROM TYPE SYSTEMS TO KNOWLEDGE REPRESENTATION: NATURAL SEMANTICS SPECIFICATIONS FOR DESCRIPTION LOGICS

Abstract

We first explore the similarities and differences between concept definitions in description/terminological logics such as KL-ONE, Classic, Back, Loom, etc. and the types normally encountered in programming languages. The similarities lead us to consider the application of natural semantics — the mechanism most frequently used to describe type systems — to the definition of knowledge base management systems that use such description logics. The paper presents inference rules in the natural semantics style for a variety of judgments involving descriptions, such as “subsumption” and “object membership”, and provides the full definition of subsumption in the Classic KBMS as a proof system. One of our objectives is to document some advantages of this approach, including the utility of multiple complementary semantics, and especially the characterization of implementations that are computationally tractable but are incomplete relative to standard denotational semantics.