Smodels with CLP?A Treatment of Aggregates in ASP

Many practical systems have been recently proposed to support execution of Answer Set Programming (ASP) [13,7,1,10]. Our objective is to introduce different types of aggregates in ASP. Database languages (e.g., SQL) use aggregate functions—e.g., sum, count, and max—to obtain summary information from a database. Aggregates have been shown to significantly improve compactness and clarity of programs in various flavors of logic programming [9,6]. We expect to gain similar advantages from the introduction of aggregations in ASP.

[1]  Vladimir Lifschitz,et al.  Answer set programming and plan generation , 2002, Artif. Intell..

[2]  Thom W. Frühwirth,et al.  Theory and Practice of Constraint Handling Rules , 1998, J. Log. Program..

[3]  Kenneth A. Ross,et al.  Monotonic aggregation in deductive databases , 1992, J. Comput. Syst. Sci..

[4]  Alessandro Dal Palù,et al.  Integrating finite domain constraints and CLP with sets , 2003, PPDP '03.

[5]  Gerald Pfeifer,et al.  The KR System dlv: Progress Report, Comparisons and Benchmarks , 1998, KR.

[6]  Alan Bundy,et al.  Computational Logic: Logic Programming and Beyond , 2002 .

[7]  Agostino Dovier,et al.  Intensional Sets in CLP , 2003, APPIA-GULP-PRODE.

[8]  Peter J. Stuckey,et al.  Semantics of Logic Programs with Aggregates , 1991, ISLP.

[9]  Chitta Baral,et al.  Knowledge Representation, Reasoning and Declarative Problem Solving , 2003 .

[10]  Fangzhen Lin,et al.  ASSAT: computing answer sets of a logic program by SAT solvers , 2002, Artif. Intell..

[11]  Maurice Bruynooghe,et al.  Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates , 2001, ICLP.

[12]  Kenneth A. Ross,et al.  Foundations of Aggregation Constraints , 1994, Theor. Comput. Sci..

[13]  Timo Soininen,et al.  Extending and implementing the stable model semantics , 2000, Artif. Intell..

[14]  Carlo Zaniolo,et al.  Compilation of Set Terms in the Logic Data Language (LDL) , 1992, J. Log. Program..

[15]  Vladimir Lifschitz,et al.  Computing answer sets using program completion , 2003 .

[16]  Allen Van Gelder,et al.  The well-founded semantics of aggregation , 1992, PODS.

[17]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[18]  Michael Gelfond,et al.  Representing Knowledge in A-Prolog , 2002, Computational Logic: Logic Programming and Beyond.