Justifications for Programs with Disjunctive and Causal-choice Rules

In this paper, we study an extension of the stable model semantics for disjunctive logic programs where each true atom in a model is associated with an algebraic expression (in terms of rule labels) that represents its justifications. As in our previous work for non-disjunctive programs, these justifications are obtained in a purely semantic way, by algebraic operations (product, addition and application) on a lattice of causal values. Our new definition extends the concept of causal stable model to disjunctive logic programs and satisfies that each (standard) stable model corresponds to a disjoint class of causal stable models sharing the same truth assignments, but possibly varying the obtained explanations. We provide a pair of illustrative examples showing the behaviour of the new semantics and discuss the need of introducing a new type of rule, which we call causal-choice. This type of rule intuitively captures the idea of "$A$ may cause $B$" and, when causal information is disregarded, amounts to a usual choice rule under the standard stable model semantics. (Under consideration for publication in Theory and Practice of Logic Programming)