A resolution-based system for symbolic approximate reasoning

Abstract The aim of this paper is twofold. First, it continues the development of a symbolic approach to approximate reasoning as an alternative to the well-known semantic approaches based on fuzzy sets. While this exacts a price in expressive power, it has the advantage of being computationally simpler. In addition, it accommodates formulation of certain aspects 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 techniques, are discussed. Second, this work shows how the proposed symbolic approach may be implemented in a Prolog-like question-answering system, known as SAR . To illustrate, an automated bank loan advisor based on this system might be presented the query “ Suitability(Jim) ?” and respond with something like “ Suitability(Jim ; very_good).” To this end we develop SAR resolution, an adaptation of the well-known SLD resolution which underlies Prolog. SAR resolution differs from the earlier version 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 being employed at that step, and (3) it requires incorporating a means for (symbolic) evidence combination. In generating and traversing the resolution tree, SAR resolution behaves essentially as SLD resolution when moving in the downward direction (from the root), and applies computational formulas and evidence combination procedures when moving in the upward direction. Thus it is more complex than SLD resolution, but is nonetheless simple enough for many real-world applications. In effect SAR is a general purpose “fuzzy classifier” and accordingly should find use in many expert systems of the classification genre, e.g., for diagnosis, troubleshooting, monitoring, and multicriteria decision making. The SAR resolution technique easily accommodates forms of inference other than the five discussed here. As examples: one could adjoin the well-known “compositional rule of inference,” or a mode of inference whose underlying computation is provided by a neural net. Thus this paper implicitly provides a general methodology by which one may devise reasoning systems that present the user with a variety of inferencing techniques, from which one may then choose as the situation demands.