On the analysis of set-based fuzzy quantified reasoning using classical syllogistics

TL;DR

This paper compares fuzzy syllogistic reasoning models with classical Aristotelian logic to evaluate their validity, plausibility, and potential as extensions for approximate reasoning in logic systems.

Contribution

It analyzes and compares fuzzy syllogistic models by Zadeh and Dubois et al. against classical logic, assessing their coverage of valid syllogistic patterns.

Findings

Fuzzy models replicate many classical syllogistic patterns

Some fuzzy approaches extend classical reasoning plausibly

The models show potential for approximate syllogistic reasoning

Abstract

Syllogism is a type of deductive reasoning involving quantified statements. The syllogistic reasoning scheme in the classical Aristotelian framework involves three crisp term sets and four linguistic quantifiers, for which the main support is the linguistic properties of the quantifiers. A number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main support is cardinality calculus. In this paper we analyze fuzzy syllogistic models previously described by Zadeh and Dubois et al. and compare their behavior with that of the classical Aristotelian framework to check which of the 24 classical valid syllogistic reasoning patterns or moods are particular crisp cases of these fuzzy approaches. This allows us to assess to what extent these approaches can be considered as either plausible extensions of the classical crisp syllogism or a basis for a general approach to the problem of approximate syllogism.