Knowledge Embedding in the Description System Omega

Knowledge Embedding in the Description System Omega Carl Mewitt, 6iuseppe Attardi, and Maria Simi M.I.T. 545 Technology Square Cambridge, Mass 02139 Omega is a description system for knowledge embedding which combines mechanisms of the predicate calculus, type systems, and pattern matching systems. It can express arbitrary predicates (achieving the power of the o-order quantificational calculus), type declarations in programming systems (Algal, Simula, etc.), pattern matching languages (Planner, Merlin, KRL, etc.). Omega gains much of its power by unifying these mechanisms in a single formalism In this paper we present an axiomatization of basic constructs in Omega which serves as an important component of the interface between implementors and users+ Omega is based on a small number of primitive concepts. It is sufficiently powerful to be able to express its own rules of inference In this way Omega represents a self-describing system in which a great deal of knowledge about itself can be embedded. The techniques in Omega represent an important advance in the creation of self-describing systems without engendering the problems discovered by Russell Meta-descriptions (in the sense used in mathematical logic) are ordinary descriptions in Omega. Together with Jerry Barber we have constructed a preliminary implementation of Omega on the MLT. CADR System and used it in the development of an office workstation prototype. I -Introduction First Order Logic is a powerful formalism for representing mathematical theories and formalizing hypotheses about the world. Logicians have developed a mathematical semantics in which a number of important results have been established such as completeness. These circumstances have motivated the development of deductive systems based on first order predicate calculus [FOL, PROLOG, Bledsoe’s Verifier, etc. ] However, First Order Logic is unsatisfactory as a language for embedding knowledge in computer systems. Therefore tnany recent reasoning system have tried to develop their own formalisms [PLANNER, FRL, KL-ONE, KRL, LMS, NETL, AMORD, XPRT, ETHERJ The semantics and deductive theory of these new systems however has not been satisfactorily developed. The only rigorous description of most of them has been their implementations which are rather large and convoluted programs. 2 -Overview The syntax of Omega is a version of template English, For example we use the indefinite article in instance descriptions such as the one below: