Abduction in Logic Programming as Second-Order Quantifier Elimination

It is known that skeptical abductive explanations with respect to classical logic can be characterized semantically in a natural way as formulas with second-order quantifiers. Computing explanations is then just elimination of the second-order quantifiers. By using application patterns and generalizations of second-order quantification, like literal projection, the globally weakest sufficient condition and circumscription, we transfer these principles in a unifying framework to abduction with three non-classical semantics of logic programming: stable model, partial stable model and well-founded semantics. New insights are revealed about abduction with the partial stable model semantics.

[1]  Christoph Wernhard.  Computing with Logic as Operator Elimination: The ToyElim System , 2011, INAP/WLP.

[2]  Fangzhen Lin.  A study of nonmonotonic reasoning , 1992 .

[3]  Joohyung Lee,et al.  Stable models and circumscription , 2011, Artif. Intell..

[4]  Christoph Wernhard,et al.  Tableaux for Projection Computation and Knowledge Compilation , 2009, TABLEAUX.

[5]  Christoph Wernhard.  Projection and scope-determined circumscription , 2012, J. Symb. Comput..

[6]  Jia-Huai You,et al.  Unfolding partiality and disjunctions in stable model semantics , 2000, TOCL.

[7]  Teodor C. Przymusinski.  Stable semantics for disjunctive programs , 1991, New Generation Computing.

[8]  Jorge Lobo,et al.  Abductive Consequence Relations , 1997, Artif. Intell..

[9]  Valentin Goranko,et al.  SCAN Is Complete for All Sahlqvist Formulae , 2003, RelMiCS.

[10]  Katsumi Inoue,et al.  Linear Resolution for Consequence Finding , 1992, Artif. Intell..

[11]  Diego Calvanese,et al.  View-Based Query Processing: On the Relationship Between Rewriting, Answering and Losslessness , 2005, ICDT.

[12]  Hans Tompits.  Expressing default abduction problems as quantified Boolean formulas , 2003, AI Commun..

[13]  Vladimir Lifschitz,et al.  Twelve Definitions of a Stable Model , 2008, ICLP.

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

[15]  Armin Biere,et al.  Effective Preprocessing in SAT Through Variable and Clause Elimination , 2005, SAT.

[16]  Georg Gottlob,et al.  Abduction from Logic Programs: Semantics and Complexity , 1997, Theor. Comput. Sci..

[17]  Carlo Zaniolo,et al.  Deterministic and Non-Deterministic Stable Models , 1997, J. Log. Comput..

[18]  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.

[19]  Antonis C. Kakas,et al.  Abduction in Logic Programming , 2002, Computational Logic: Logic Programming and Beyond.

[20]  Chiaki Sakama,et al.  Equivalence issues in abduction and induction , 2009, J. Appl. Log..

[21]  Kewen Wang,et al.  Semantic forgetting in answer set programming , 2008, Artif. Intell..

[22]  Paolo Mancarella,et al.  Generalized Stable Models: A Semantics for Abduction , 1990, ECAI.

[23]  Christoph Wernhard,et al.  Literal Projection for First-Order Logic , 2008, JELIA.

[24]  Norbert Manthey.  Coprocessor 2.0 - A Flexible CNF Simplifier - (Tool Presentation) , 2012, SAT.

[25]  Fangzhen Lin,et al.  Abduction in logic programming: A new definition and an abductive procedure based on rewriting , 2001, Artif. Intell..

[26]  Antonis C. Kakas,et al.  Computational Logic: Logic Programming and Beyond , 2002, Lecture Notes in Computer Science.

[27]  Martin Gebser,et al.  Solution Enumeration for Projected Boolean Search Problems , 2009, CPAIOR.

[28]  Ken Satoh,et al.  Computing abduction by using TMS with top-down expectation , 2000, J. Log. Program..

[29]  Patrick Doherty,et al.  Computing Strongest Necessary and Weakest Sufficient Conditions of First-Order Formulas , 2001, IJCAI.

[30]  Antonis C. Kakas,et al.  The role of abduction in logic programming , 1998 .

[31]  Patrick Doherty,et al.  Computing Circumscription Revisited: A Reduction Algorithm , 1997, Journal of Automated Reasoning.

[32]  Christoph Wernhard.  Circumscription and Projection as Primitives of Logic Programming , 2010, ICLP.

[33]  Fangzhen Lin,et al.  On strongest necessary and weakest sufficient conditions , 2000, Artif. Intell..

[34]  Teodor C. Przymusinski.  The Well-Founded Semantics Coincides with the Three-Valued Stable Semantics , 1990, Fundam. Inform..

[35]  Laurence A. Wolsey,et al.  Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007, Proceedings , 2007, CPAIOR.

[36]  Chiaki Sakama,et al.  Negation as Failure in the Head , 1998, J. Log. Program..

[37]  Stefan Woltran,et al.  Solving Advanced Reasoning Tasks Using Quantified Boolean Formulas , 2000, AAAI/IAAI.

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

[39]  Dov M. Gabbay,et al.  Quantifier Elimination in Second-Order Predicate Logic , 1992, KR.

[40]  Roy Dyckhoff.  Automated Reasoning with Analytic Tableaux and Related Methods , 2000, Lecture Notes in Computer Science.

[41]  Dov M. Gabbay,et al.  Second-Order Quantifier Elimination - Foundations, Computational Aspects and Applications , 2008, Studies in logic : Mathematical logic and foundations.