A Revised Concept of Safety for General Answer Set Programs

To ensure a close relation between the answer sets of a program and those of its ground version, some answer set solvers deal with variables by requiring a safety condition on program rules. If we go beyond the syntax of disjunctive programs, for instance by allowing rules with nested expressions, or perhaps even arbitrary first-order formulas, new definitions of safety are required. In this paper we consider a new concept of safety for formulas in quantified equilibrium logic where answer sets can be defined for arbitrary first-order formulas. The new concept captures and generalises two recently proposed safety definitions: that of Lee, Lifschitz and Palla (2008) as well as that of Bria, Faber and Leone (2008). We study the main metalogical properties of safe formulas.

[1]  Vladimir Lifschitz,et al.  Nested expressions in logic programs , 1999, Annals of Mathematics and Artificial Intelligence.

[2]  Jos de Bruijn,et al.  Quantified Equilibrium Logic and Hybrid Rules , 2007, RR.

[3]  Joohyung Lee,et al.  On Loop Formulas with Variables , 2008, KR.

[4]  Joohyung Lee,et al.  Safe Formulas in the General Theory of Stable Models (Preliminary Report) , 2008, ICLP.

[5]  A. Campbell,et al.  Progress in Artificial Intelligence , 1995, Lecture Notes in Computer Science.

[6]  David Pearce,et al.  Towards a First Order Equilibrium Logic for Nonmonotonic Reasoning , 2004, JELIA.

[7]  Dirk van Dalen,et al.  Logic and structure , 1980 .

[8]  Pedro Cabalar,et al.  Safety Preserving Transformations for General Answer Set Programs , 2009 .

[9]  David Pearce,et al.  A Characterization of Strong Equivalence for Logic Programs with Variables , 2007, LPNMR.

[10]  Frank Wolter,et al.  Semi-qualitative Reasoning about Distances: A Preliminary Report , 2000, JELIA.

[11]  Stephen Cole Kleene,et al.  On notation for ordinal numbers , 1938, Journal of Symbolic Logic.

[12]  David Pearce,et al.  Reducing Propositional Theories in Equilibrium Logic to Logic Programs , 2005, Answer Set Programming.

[13]  David Pearce,et al.  Minimal Logic Programs , 2007, ICLP.

[14]  Joohyung Lee,et al.  A Reductive Semantics for Counting and Choice in Answer Set Programming , 2008, AAAI.

[15]  Joohyung Lee,et al.  Yet Another Proof of the Strong Equivalence Between Propositional Theories and Logic Programs , 2007, CENT.

[16]  Joohyung Lee,et al.  A New Perspective on Stable Models , 2007, IJCAI.

[17]  Stijn Heymans,et al.  Guarded Open Answer Set Programming , 2005, LPNMR.

[18]  David Pearce,et al.  Quantified Equilibrium Logic and Foundations for Answer Set Programs , 2008, ICLP.

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

[20]  Wolfgang Faber,et al.  Normal Form Nested Programs , 2009, Fundam. Informaticae.

[21]  David Pearce,et al.  A First Order Nonmonotonic Extension of Constructive Logic , 2005, Stud Logica.

[22]  Davy Van Nieuwenborgh,et al.  G-Hybrid Knowledge Bases , 2003 .

[23]  Stijn Heymans,et al.  Open answer set programming with guarded programs , 2006, TOCL.

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