Gradual inference rules in approximate reasoning. (English) Zbl 0736.68070

Summary: Gradual inference rules of the form “The more \(X\) is \(F\), the more \(Y\) is \(G\) (or of similar forms with “the less” instead of “the more”), which express a progressive change of the degree to which the entity \(Y\) satisfies the gradual property \(G\) when the degree to which the entity \(X\) satisfies the gradual property \(F\) is modified, are often encountered in commonsense reasoning. A representation of such rules by means of fuzzy sets is proposed and discussed. This representation turns out to be based on a special implication function already considered in multiple- valued logic. Patterns of reasoning involving gradual inference rules are formalized. Their links with interpolation mechanisms are pointed out.


68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
03B52 Fuzzy logic; logic of vagueness
68T30 Knowledge representation
Full Text: DOI


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