BKLM - An expressive logic for defeasible reasoning

Paterson-Jones, Guy and Casini, Giovanni and Meyer, Thomas (2020) BKLM - An expressive logic for defeasible reasoning, Proceedings of 18th INTERNATIONAL WORKSHOP ON NON-MONOTONIC REASONING, 12-14 September, Onlone, 170-178.

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Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or con- ditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consider- ation generates a set of defeasible implications 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 im- possibility 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 dis- junctions, conjunctions, and negations, but not nesting, of de- feasible 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 entail- ment proposed by Booth et al. to apply to BKLM.

Item Type: Conference paper
Subjects: Computing methodologies > Artificial intelligence > Knowledge representation and reasoning
Alternate Locations: https://nmr2020.dc.uba.ar/WorkshopNotes.pdf
Date Deposited: 01 Sep 2021 09:59
Last Modified: 01 Sep 2021 09:59
URI: http://pubs.cs.uct.ac.za/id/eprint/1424

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