DATALOG with constraints - an answer-set programming system

Answer-set programming (ASP) has emerged recently as a viable programming paradigm well attuned to search problems in AI, constraint satisfaction and combinatorics. Propositional logic is, arguably, the simplest ASP system with an intuitive semantics supporting direct modeling of problem constraints. However, for some applications, especially those requiring that transitive closure be computed, it requires additional variables and results in large theories. Consequently, it may not be a practical computational tool for such problems. On the other hand, ASP systems based on nonmonotonic logics, such as stable logic programming, can handle transitive closure computation efficiently and, in general, yield very concise theories as problem representations. Their semantics is, however, more complex. Searching for the middle ground, in this paper we introduce a new nonmonotonic logic, DATALOG with constraints or DC. Informally, DC theories consist of propositional clauses (constraints) and of Horn rules. The semantics is a simple and natural extension of the semantics of the propositional logic. However, thanks to the presence of Horn rules in the system, modeling of transitive closure becomes straightforward. We describe the syntax and semantics of DC, and study its properties. We discuss an implementation of DC and present results of experimental study of the effectiveness of DC, comparing it with CSAT, a satisfiability checker and SMODELS implementation of stable logic programming. Our results show that DC is competitive with the other two approaches, in case of many search problems, often yielding much more efficient solutions.Comment: 6 pages, 5 figures, will appear in Proceedings of AAAI-200

NP Datalog: a Logic Language for Expressing NP Search and Optimization Problems

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 exclusive 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.Comment: To appear in Theory and Practice of Logic Programming (TPLP