Complexity and Expressive Power of Deterministic Semantics for DATALOG

Deterministic models are (partial) stable models which are not contradicted by any other stable model; i.e., M is a deterministic model if there is no stable model N such that M ∪ N is not an interpretation. For instanced the well-founded model, which coincides with the intersection of all partial stable models, is a deterministic model. As the well-founded model is deterministic and unique for each program, well-founded model semantics has been proposed as the canonical deterministic semantics for partial stable models. But the well-founded model is not the unique deterministic model; indeed the family of deterministic (partial stable) models is not, in general, a singleton and admits a minimum (the well-founded model) and a maximum, the max-deterministic model. The latter model is, another candidate for a deterministic semantics. The aim of this paper is to study the complexity and the expressive power of deterministic semantics. In coherence with the deterministic nature of the model, the expressive power of max-deterministic semantics is shown to be able to express problems with unique solutions, whereas the well-founded model only captures a proper subset of the queries computable in polynomial time, the so-called fixpoint queries.