Algorithmic definitions for KLM-style defeasible disjunctive Datalog

Matthew Morris, Tala Ross, Thomas Meyer

Abstract:

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.