On the disjunctive rational closure of a conditional knowledge base

Abstract

One of the most widely investigated decision problems in symbolic AI is that of which conditional sentences of the form “if α, then normally β” should follow from a knowledge base containing this type of statements. Probably, the most notable approach to this problem is the rational closure construction put forward by Lehmann and Magidor in the'90s, which has been adapted to logical languages of various expressive powers since then. At the core of rational closure is the Rational Monotonicity property, which allows one to retain existing (defeasible) conclusions whenever new information cannot be negated by existing conclusions. As it turns out, Rational Monotonicity is not universally accepted, with many researchers advocating the investigation of weaker versions thereof leading to a larger class of consequence relations. A case in point is that of the Disjunctive Rationality property, which states that if one may draw a (defeasible) conclusion from a disjunction of premises, then one should be able to draw this conclusion from at least one of the premises taken alone. While there are convincing arguments that the rational closure forms the ‘simplest’ rational consequence relation extending a given set of conditionals, the question of what the simplest disjunctive consequence relation in this setting is has not been explored in depth. In this article, we do precisely that by motivating and proposing a concrete construction of the disjunctive rational closure of a conditional knowledge base, of which the properties and consequences of its adoption we also investigate in detail. (Previous versions of this work have been selected for presentation at the 18th International Workshop on Nonmonotonic Reasoning (NMR 2020) [1] and at the 35th AAAI Conference on Artificial Intelligence (AAAI 2021) [2]. The present submission extends and elaborates on both papers.)