Abducing through negation as failure: stable models within the independent choice logic

Abstract

The independent choice logic (ICL) is part of a project to combine logic and decision/game theory into a coherent framework. The ICL has a simple possible-worlds semantics characterised by independent choices and an acyclic logic program that specifies the consequences of these choices. This paper gives an abductive characterization of the ICL. The ICL is defined model-theoretically, but we show that it is naturally abductive: the set of explanations of a proposition g is a concise description of the worlds in which g is true. We give an algorithm for computing explanations and show it is sound and complete with respect to the possible-worlds semantics. What is unique about this approach is that the explanations of the negation of g can be derived from the explanations of g. The use of probabilities over choices in this framework and going beyond acyclic logic programs are also discussed.