Abstract

MORRIS, Matthew; ROSS, Tala  and  MEYER, Thomas. Algorithmic definitions for KLM-style defeasible disjunctive Datalog. SACJ [online]. 2020, vol.32, n.2, pp.141-160. ISSN 2313-7835.  http://dx.doi.org/10.18489/sacj.v32i2.846.

Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasible reasoning into classical Datalog. We present a systematic approach for extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog extensions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure. We provide algorithmic definitions for these forms of defeasible entailment and prove that the definitions are LM-rational.CATEGORIES: • Theory of computation ~ Automated reasoning • Theory of computation ~ Logic and databases • Computing methodologies ~ Nonmonotonic, default reasoning and belief revision

Keywords : knowledge representation and reasoning; defeasible reasoning; KLM approach; Rational Closure; Relevant Closure; Datalog.

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