ASP Solving for Expanding Universes

Over the last years, Answer Set Programming has significantly extended its range of applicability, and moved beyond solving static problems to dynamic ones, even in online environments. However, its nonmonotonic nature as well as its upstream instantiation process impede a seamless integration of new objects into its reasoning process, which is crucial in dynamic domains such as logistics or robotics. We address this problem and introduce a simple approach to successively incorporating new information into ASP systems. Our approach rests upon a translation of logic programs and thus refrains from any dedicated algorithms. We prove its modularity as regards the addition of new information and show its soundness and completeness. We apply our methodology to two domains of the Fifth ASP Competition and evaluate traditional one-shot and incremental multi-shot solving approaches.

[1]  Martin Gebser,et al.  An incremental answer set programming based system for finite model computation , 2011, AI Commun..

[2]  Ilkka Niemelä,et al.  Planning as satisfiability: parallel plans and algorithms for plan search , 2006, Artif. Intell..

[3]  Martin Gebser,et al.  Design and results of the Fifth Answer Set Programming Competition , 2016, Artif. Intell..

[4]  Alessandro Dal Palù,et al.  Answer Set Programming with Constraints Using Lazy Grounding , 2009, ICLP.

[5]  Peter J. Stuckey,et al.  Lazy Model Expansion by Incremental Grounding , 2012, ICLP.

[6]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[7]  Dov M. Gabbay,et al.  What Is Negation as Failure? , 2012, Logic Programs, Norms and Action.

[8]  Martin Gebser,et al.  The Design of the Fifth Answer Set Programming Competition , 2014, ArXiv.

[9]  K. Claessen,et al.  New Techniques that Improve MACE-style Finite Model Finding , 2007 .

[10]  François Fages,et al.  Consistency of Clark's completion and existence of stable models , 1992, Methods Log. Comput. Sci..

[11]  Martin Gebser,et al.  The Design of the Sixth Answer Set Programming Competition - - Report - , 2014, LPNMR.

[12]  Joohyung Lee,et al.  A Model-Theoretic Counterpart of Loop Formulas , 2005, IJCAI.

[13]  Jeffrey D. Uuman Principles of database and knowledge- base systems , 1989 .

[14]  Tomi Janhunen,et al.  Modular Equivalence for Normal Logic Programs , 2006, ECAI.

[15]  Martin Gebser,et al.  Clingo = ASP + Control: Preliminary Report , 2014, ArXiv.

[16]  Antonius Weinzierl,et al.  OMiGA : An Open Minded Grounding On-The-Fly Answer Set Solver , 2012, JELIA.

[17]  Niklas Sörensson,et al.  Temporal induction by incremental SAT solving , 2003, BMC@CAV.

[18]  Pascal Nicolas,et al.  The First Version of a New ASP Solver : ASPeRiX , 2009, LPNMR.

[19]  Inês Lynce,et al.  Conflict-Driven Clause Learning SAT Solvers , 2009, Handbook of Satisfiability.

[20]  Stefan Woltran,et al.  Modularity Aspects of Disjunctive Stable Models , 2007, LPNMR.

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

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

[23]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[24]  Thomas Eiter,et al.  Grounding HEX-Programs with Expanding Domains ? , 2013 .

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