On Non-monotonic Conditional Reasoning

TL;DR

This paper provides a formal analysis of non-monotonic reasoning in intelligent systems, establishing a connection between logic and probability through a non-quantitative conditional logic that supports evidence combination.

Contribution

It introduces a non-monotonic conditional logic compatible with conditional probability, unifying multi-valued and non-monotonic reasoning frameworks.

Findings

Defines a formal structure linking logic and probability without quantitative measures

Shows the non-monotonic nature of the introduced conditional logic

Highlights the role of this logic in evidence combination and reasoning

Abstract

This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is established by introducing conditioning notions by means of formal structures that do not rely on quantitative measures. The associated conditional logic, compatible with conditional probability evaluations, is non-monotonic relative to additional evidence. Computational aspects of conditional probability logic are mentioned. The importance of this development lies on its role to provide a conceptual basis for various forms of evidence combination and on its significance to unify multi-valued and non-monotonic logics