A Symbolic Approach to Reasoning with Linguistic Quantifiers

TL;DR

This paper explores automated reasoning with linguistic quantifiers in probabilistic logic by propagating qualitative intervals instead of precise probabilities, aiming for a reasoning process aligned with human commonsense understanding.

Contribution

It introduces a symbolic method for probabilistic reasoning using linguistic intervals and demonstrates a qualitative syllogism that is threshold-independent and aligns with intuitive reasoning.

Findings

Qualitative syllogism is meaningful and threshold-independent.

The approach approximates commonsense probabilistic reasoning.

It offers a less precise but more intuitive reasoning framework.

Abstract

This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions. Then instead of propagating numbers, qualitative terms are propagated in accordance with the numerical interpretation of these terms. The quantified syllogism, modelling the chaining of probabilistic rules, is studied in this context. It is shown that a qualitative counterpart of this syllogism makes sense, and is relatively independent of the threshold defining the linguistically meaningful intervals, provided that these threshold values remain in accordance with the intuition. The inference power is less than that of a full-fledged probabilistic con-quaint propagation device but better corresponds to what could be thought of as commonsense probabilistic reasoning.