Abstract
Resolution is an useful tool for mechanical theorem proving in modelling the refutation proof procedure, which is mostly used in constructing a “proof” of a “theorem”. An attempt is made to utilize approximate reasoning methodology in fuzzy resolution. Approximate reasoning is a methodology which can deduce a specific information from general knowledge and specific observation. It is dependent on the form of general knowledge and the corresponding deductive mechanism. In ordinary approximate reasoning, we derive from A→B and by some mechanism. In inverse approximate reasoning, we conclude from A→B and using an altogether different mechanism. An important observation is that similarity is inherent in fuzzy set theory. In approximate reasoning methodology-similarity relation is used in fuzzification while, similarity measure is used in fuzzy inference mechanism. This research proposes that similarity based approximate reasoning-modelling generalised modus ponens/generalised modus tollens—can be used to derive a resolution—like inference pattern in fuzzy logic. The proposal is well-illustrated with artificial examples.
Highlights
In automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique
In approximate reasoning methodology-similarity relation is used in fuzzification while, similarity measure is used in fuzzy inference mechanism
This paper presented a resolution principle for fuzzy formulae based on similarity and approximate reasoning methodology
Summary
Resolution is a rule of inference leading to a refutation theorem-proving technique. It is proved a set S of fuzzy clauses is unsatisfiable if and only if, there is a deduction of empty clause with its confidence of resolvent cd 0 from S. S. Ray [12] presented a generalised resolution principle that handles the inexact situation effectively and is applicable for both well-defined and undefined propositions. Ray [12] presented a generalised resolution principle that handles the inexact situation effectively and is applicable for both well-defined and undefined propositions They associated a truth value to every proposition. Our idea is to present, a generalised resolution principle that deals with the fuzzy propositions by the technique of inverse approximate reasoning.
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