A Boolean Extension of KLM-Style Conditional Reasoning

Paterson-Jones, Guy and Casini, Giovanni and Meyer, Thomas (2020) A Boolean Extension of KLM-Style Conditional Reasoning, First Southern African Conference for AI Research, SACAIR 2020 Muldersdrift, South Africa, Communications in Computer and Information Science, 1342, Springer.

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Abstract

Propositional KLM-style defeasible reasoning involves extending propositional logic with a new logical connective that can express defeasible (or conditional) implications, with semantics given by ordered structures known as ranked interpretations. KLM-style defeasi- ble entailment is referred to as rational whenever the defeasible entail- ment relation under consideration generates a set of defeasible implica- tions all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.

Item Type:	Book chapter
Subjects:	Computing methodologies > Artificial intelligence > Knowledge representation and reasoning
Alternate Locations:	https://doi.org/10.1007/978-3-030-66151-9_15
Date Deposited:	01 Sep 2021 09:59
Last Modified:	01 Sep 2021 09:59
URI:	http://pubs.cs.uct.ac.za/id/eprint/1426

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