On the semantics and expressive power of Datalog-like languages for NP search and optimization problems

It has been shown that NP (decision, search and optimization) problems can be expressed by means of DATALOG⇁ (Datalog with unstratified negation) queries under stable model semantics. Anyhow, the use of unrestricted negation is often neither simple nor intuitive and, besides, DATALOG⇁ does not allow to optimize queries and to discipline the expressive power. This paper analyzes the power of Datalog-like languages in expressing NP search and optimization problems. In more detail, in this paper we study the expressive power of several languages obtained by extending positive DATALOG with intuitive and efficient constructs, i.e. stratified negation, constraints and (exclusive) disjunction. Finally, we investigate a further restricted language, called NP Datalog, which uses disjunction only to define (nondeterministically) partitions of relations and which, in addition, captures the power of DATALOG⇁ in expressing search and optimization problems.