A Fuzzy Syllogistic Reasoning Schema for Generalized Quantifiers

TL;DR

This paper introduces a new fuzzy syllogistic reasoning schema that handles various types of generalized quantifiers and multiple premises by formulating the reasoning process as a mathematical optimization problem.

Contribution

It extends existing approaches by incorporating diverse quantifier types and premises, providing a systematic optimization-based reasoning procedure.

Findings

Effective handling of different quantifier types

Ability to process multiple premises simultaneously

Reasoning formulated as an optimization problem

Abstract

In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of premises can be taken into account within the reasoning process. Furthermore, a systematic reasoning procedure to solve the syllogism is also proposed, interpreting it as an equivalent mathematical optimization problem, where the premises constitute the constraints of the searching space for the quantifier in the conclusion.