  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)
