A RESOLUTION-BASED SYSTEM FOR SYMBOLIC APPROXIMATE REASONING

The aim of this paper is twofold. First, it continues the development of a symbolic approach to approximate reasoning as an alternative to t he well-known semantic approaches based on fuzzy sets. While this exac ts a price in expressive power; it has the advantage of being computat ionally simpler. In addition, it accommodates formulation of certain a spects of approximate reasoning that are not easily expressed in terms of fuzzy sets, or where the notion of a fuzzy set might not naturally apply. Five different such forms of inference, or reasoning technique s, are discussed. Second, this work shows how the proposed symbolic ap proach may be implemented in a Prolog-like question-answering system, known as SAR. To illustrate, an automated bank loan advisor based on t his system might be presented the query ''Suitability(Jim)?'' and resp ond with something like ''Suitability(Jim; very-good).'' To this end w e develop SAR resolution, an adaptation of the well-known SLD resoluti on which under lies Prolog. SAR resolution differs from the earlier ve rsion in that (1) it requires generation of a resolution tree, rather than a single path, (2) it requires attaching a computational formula to each resolvent, reflecting the particular inferencing technique bei ng employed at that step, and (3) it requires incorporating a means fo r (symbolic) evidence combination. In generating and traversing the re solution tree, SAR resolution behaves essentially as SLD resolution wh en moving in the downward direction (from the root), and applies compu tational formulas and evidence combination procedures when moving in t he upward direction. Thus it is more complex than SLD resolution, but is nonetheless simple enough for many real-world applications. In effe ct SAR is a general purpose ''fuzzy classifier'' and accordingly shoul d find use in many expert systems of the classification genre, e.g., f or diagnosis, troubleshooting, monitoring, and multicriteria decision making. The SAR resolution technique easily accommodates forms of infe rence inference other than the jive discussed here. As examples: one c ould adjoin the well-known ''compositional rule of inference,'' or a m ode of inference whose underlying computation is provided by a neural net. Thus this paper implicitly provides a general methodology by whic h one may devise reasoning systems that present the user with a variet y of inferencing techniques, from which one may then choose as the sit uation demands.