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We examine the meaning and the complexity of probabilistic logic programsthat consist of a set of rules and a set of independent probabilistic facts(that is, programs based on Sato's distribution semantics). We focus on twosemantics, respectively based on stable and on well-founded models. We showthat the semantics based on stable models (referred to as the "credalsemantics") produces sets of probability models that dominate infinitelymonotone Choquet capacities, we describe several useful consequences of thisresult. We then examine the complexity of inference with probabilistic logicprograms. We distinguish between the complexity of inference when aprobabilistic program and a query are given (the inferential complexity), andthe complexity of inference when the probabilistic program is fixed and thequery is given (the query complexity, akin to data complexity as used indatabase theory). We obtain results on the inferential and query complexity foracyclic, stratified, and cyclic propositional and relational programs,complexity reaches various levels of the counting hierarchy and evenexponential levels.

On the Semantics and Complexity of Probabilistic Logic Programs