This paper presents a logic language for expressing NP search and optimization problems. Specifically, first a language obtained by extending (positive) Datalog with intuitive and efficient constructs (namely, stratified negation, constraints and exc
lusive disjunction) is introduced. Next, a further restricted language only using a restricted form of disjunction to define (non-deterministically) subsets (or partitions) of relations is investigated. This language, called NP Datalog, captures the power of Datalog with unstratified negation in expressing search and optimization problems. A system prototype implementing NP Datalog is presented. The system translates NP Datalog queries into OPL programs which are executed by the ILOG OPL Development Studio. Our proposal combines easy formulation of problems, expressed by means of a declarative logic language, with the efficiency of the ILOG System. Several experiments show the effectiveness of this approach.
This paper addresses the problem of representing the set of repairs of a possibly inconsistent database by means of a disjunctive database. Specifically, the class of denial constraints is considered. We show that, given a database and a set of denia
l constraints, there exists a (unique) disjunctive database, called canonical, which represents the repairs of the database w.r.t. the constraints and is contained in any other disjunctive database with the same set of minimal models. We propose an algorithm for computing the canonical disjunctive database. Finally, we study the size of the canonical disjunctive database in the presence of functional dependencies for both repairs and cardinality-based repairs.
