Defeasible justification for the KLM Framework

Wang, Shun

Defeasible justification for the KLM Framework

Thesis / Dissertation

2023

Abstract

Knowledge Representation (KR) and Reasoning are essential aspects of Artificial Intelligence (AI) as they allow AI systems to conduct logical reasoning. Most classical logics, such as Propositional Logic (PL), are monotonic, which means that adding new knowledge to a knowledge base cannot cause the retraction of a previously drawn conclusion. These classical logics cannot easily handle exceptions to typical scenarios. Defeasible reasoning is a type of non-monotonic reasoning, which allows the notion of “defeasible implication”. The Kraus, Lehmann, and Magidor (KLM) Framework is an extension of PL that can perform defeasible reasoning. The results of defeasible reasoning using the KLM Framework are often challenging to understand. Therefore, one needs a framework to justify conclusions drawn from defeasible reasoning. We propose a theoretical framework for defeasible justification using the KLM Framework and a software tool that implements the framework. The theoretical framework is based on an existing theoretical framework for Description Logic (DL) which we translate to PL. The defeasible justification algorithm uses the statement ranking required by the KLM-style form of defeasible entailment, known as rational closure. Classical justifications are computed based on materialised formulas (classical counterparts of defeasible formulas). The resulting classical justifications are converted to defeasible justifications based on the input knowledge base. We provide a software tool with a graphical user interface (GUI) that implements the algorithm. Given a defeasible knowledge base and a query, such that the knowledge base defeasibly entails the query, the program produces a set of justifications for the defeasible entailment. We use a set of representative examples to evaluate the defeasible justification algorithm and argue that its results conform to intuition. The same examples are used to confirm the correctness of the algorithm implementation.

Keywords

Computer Science

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