Fuzzy-Syllogistic Systems: a Generic Model for Approximate Reasoning

Abstract

The well known Aristotelian syllogistic system S consists of 256 moods. We have found earlier that 136 moods are distinct in terms of equal truth ratios that range in tau = [ 0,1]. The truth ratio of a particular mood is calculated by relating the number of true and false syllogistic cases that the mood matches. The introduction of (n -1) fuzzy existential quantifiers, extends the system to fuzzy-syllogistic systems S-n, 1 < n, of which every fuzzy-syllogistic mood can be interpreted as a vague inference with a generic truth ratio, which is determined by its syllogistic structure. Here we introduce two new concepts, the relative truth ratio (r)tau = [ 0,1] that is calculated from the cardinalities of the syllogistic cases of the mood and fuzzy-syllogistic ontology (FSO). We experimentally apply the fuzzy-syllogistic systems S-2 and S-6 as underlying logic of a FSO reasoner (FSR) and discuss sample cases for approximate reasoning.y