Goal-directed execution of answer set programs

Answer Set Programming (ASP) represents an elegant way of introducing non-monotonic reasoning into logic programming. ASP has gained popularity due to its applications to planning, default reasoning and other areas of AI. However, none of the approaches and current implementations for ASP are goal-directed. In this paper we present a technique based coinduction that can be employed to design SLD resolution-style, goal-directed methods for executing answer set programs. We also discuss advantages and applications of such goal-directed execution of answer set programs, and report results from our implementation.

[1]  Gopal Gupta,et al.  Coinductive Logic Programming and Its Applications , 2007, ICLP.

[2]  Victor W. Marek,et al.  Stable models and an alternative logic programming paradigm , 1998, The Logic Programming Paradigm.

[3]  Robert A. Kowalski,et al.  Abduction Compared with Negation by Failure , 1989, ICLP.

[4]  Konstantinos Sagonas,et al.  XSB as an efficient deductive database engine , 1994, SIGMOD '94.

[5]  Gopal Gupta,et al.  Towards Predicate Answer Set Programming via Coinductive Logic Programming , 2009, AIAI.

[6]  Jürgen Dix,et al.  A Classification Theory of Semantics of Normal Logic Programs: II. Weak Properties , 1995, Fundam. Informaticae.

[7]  Arthur B. Markman,et al.  Knowledge Representation , 1998 .

[8]  Antonis C. Kakas,et al.  Computing Argumentation in Logic Programming , 1999, J. Log. Comput..

[9]  Ilkka Niemelä,et al.  Smodels - An Implementation of the Stable Model and Well-Founded Semantics for Normal LP , 1997, LPNMR.

[10]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[11]  Luís Moniz Pereira,et al.  Layered Models Top-Down Querying of Normal Logic Programs , 2009, PADL.

[12]  Enrico Pontelli,et al.  Credulous Resolution for Answer Set Programming , 2008, AAAI.

[13]  Gopal Gupta,et al.  Coinductive Logic Programming , 2006, ICLP.

[14]  Peter Wegner,et al.  Mathematical Models of Interactive Computing , 1999 .

[15]  Paolo Mancarella,et al.  Abductive Logic Programming , 1992, LPNMR.

[16]  Chitta Baral Knowledge Representation, Reasoning and Declarative Problem Solving: Query answering and answer set computing systems , 2003 .

[17]  Yuliya Lierler,et al.  SAT-Based Answer Set Programming , 2004, AAAI.

[18]  Gopal Gupta,et al.  Towards next generation logic programming systems , 2007 .

[19]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[20]  Lawrence S. Moss,et al.  Vicious circles - on the mathematics of non-wellfounded phenomena , 1996, CSLI lecture notes series.

[21]  Gopal Gupta,et al.  Galliwasp: A Goal-Directed Answer Set Solver , 2012, LOPSTR.

[22]  Dina Q. Goldin,et al.  Interaction, evolution, and intelligence , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[23]  José Júlio Alferes,et al.  Abduction in well-founded semantics and generalized stable models via tabled dual programs , 2003, Theory and Practice of Logic Programming.

[24]  Piero A. Bonatti Resolution for Skeptical Stable Model Semantics , 2004, Journal of Automated Reasoning.

[25]  Chitta Baral,et al.  Logic Programming and Knowledge Representation , 1994, J. Log. Program..

[26]  Andrew D. Gordon A Tutorial on Co-induction and Functional Programming , 1994, Functional Programming.

[27]  Gopal Gupta,et al.  Predicate Answer Set Programming with Coinduction , 2010 .

[28]  Benjamin C. Pierce,et al.  Types and programming languages: the next generation , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[29]  Joseph A. Goguen,et al.  Behavioral verification of distributed concurrent systems with BOBJ , 2003, Third International Conference on Quality Software, 2003. Proceedings..

[30]  Martin Gebser,et al.  clasp : A Conflict-Driven Answer Set Solver , 2007, LPNMR.

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

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

[33]  Martin Gebser,et al.  Tableau Calculi for Answer Set Programming , 2006, ICLP.

[34]  Li-Yan Yuan,et al.  Enhancing global SLS-resolution with loop cutting and tabling mechanisms , 2004, Theor. Comput. Sci..

[35]  Jürgen Dix,et al.  A Classification Theory of Semantics of Normal Logic Programs: I. Strong Properties , 1995, Fundam. Informaticae.

[36]  Luís Moniz Pereira,et al.  Revised Stable Models - A Semantics for Logic Programs , 2005, EPIA.