Answer Set Solving in Practice

Answer Set Programming (ASP) is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning (KRR). More recently, its attractive combination of a rich yet simple modeling language with high-performance solving capacities has sparked interest in many other areas even beyond KRR. This book presents a practical introduction to ASP, aiming at using ASP languages and systems for solving application problems. Starting from the essential formal foundations, it introduces ASP's solving technology, modeling language and methodology, while illustrating the overall solving process by practical examples. Table of Contents: List of Figures / List of Tables / Motivation / Introduction / Basic modeling / Grounding / Characterizations / Solving / Systems / Advanced modeling / Conclusions

[1]  Francesco Ricca,et al.  ASPIDE: Integrated Development Environment for Answer Set Programming , 2011, LPNMR.

[2]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

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

[4]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Real-World SAT Instances , 1997, AAAI/IAAI.

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

[6]  Vladimir Lifschitz,et al.  Mathematical Foundations of Answer Set Programming , 2005, We Will Show Them!.

[7]  Wolfgang Faber,et al.  The DLV system for knowledge representation and reasoning , 2002, TOCL.

[8]  Adnan Darwiche,et al.  A Lightweight Component Caching Scheme for Satisfiability Solvers , 2007, SAT.

[9]  Martin Gebser,et al.  On the Implementation of Weight Constraint Rules in Conflict-Driven ASP Solvers , 2009, ICLP.

[10]  David Pearce,et al.  Strongly equivalent logic programs , 2001, ACM Trans. Comput. Log..

[11]  Marina De Vos,et al.  Debugging Logic Programs under the Answer Set Semantics , 2005, Answer Set Programming.

[12]  John McCarthy,et al.  Applications of Circumscription to Formalizing Common Sense Knowledge , 1987, NMR.

[13]  Vasco M. Manquinho,et al.  Pseudo-Boolean and Cardinality Constraints , 2021, Handbook of Satisfiability.

[14]  Marina De Vos,et al.  Automatic Composition of Melodic and Harmonic Music by Answer Set Programming , 2008, ICLP.

[15]  Cesare Tinelli,et al.  Solving SAT and SAT Modulo Theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T) , 2006, JACM.

[16]  Enrico Pontelli,et al.  Under Consideration for Publication in Theory and Practice of Logic Programming Justifications for Logic Programs under Answer Set Semantics , 2022 .

[17]  Martin Gebser,et al.  The Conflict-Driven Answer Set Solver clasp: Progress Report , 2009, LPNMR.

[18]  Allen Van Gelder,et al.  The Alternating Fixpoint of Logic Programs with Negation , 1993, J. Comput. Syst. Sci..

[19]  Yuliya Lierler,et al.  Abstract answer set solvers with backjumping and learning , 2010, Theory and Practice of Logic Programming.

[20]  C. R. Ramakrishnan,et al.  Fully Local and Efficient Evaluation of Alternating Fixed Points (Extended Abstract) , 1998, TACAS.

[21]  Giovambattista Ianni,et al.  Computable Functions in ASP: Theory and Implementation , 2008, ICLP.

[22]  Thomas Linke,et al.  Graph Theoretical Characterization and Computation of Answer Sets , 2001, IJCAI.

[23]  Emina Torlak,et al.  Kodkod: A Relational Model Finder , 2007, TACAS.

[24]  Hans Tompits,et al.  VIDEAS: A Development Tool for Answer-Set Programs Based on Model-Driven Engineering Technology , 2011, LPNMR.

[25]  Raymond Reiter On Closed World Data Bases , 1977, Logic and Data Bases.

[26]  Thomas Eiter,et al.  Preferred Answer Sets for Extended Logic Programs , 1999, Artif. Intell..

[27]  Armin Biere,et al.  Bounded Model Checking Using Satisfiability Solving , 2001, Formal Methods Syst. Des..

[28]  Martin Gebser,et al.  plasp: A Prototype for PDDL-Based Planning in ASP , 2011, LPNMR.

[29]  Kevin Leyton-Brown,et al.  SATzilla: Portfolio-based Algorithm Selection for SAT , 2008, J. Artif. Intell. Res..

[30]  Hans Tompits,et al.  dlvhex: A Prover for Semantic-Web Reasoning under the Answer-Set Semantics , 2006, 2006 IEEE/WIC/ACM International Conference on Web Intelligence (WI 2006 Main Conference Proceedings)(WI'06).

[31]  Chiaki Sakama,et al.  Updating Extended Logic Programs through Abduction , 1999, LPNMR.

[32]  Gerhard Brewka,et al.  Logic programming with ordered disjunction , 2002, NMR.

[33]  Martin Gebser,et al.  Engineering an Incremental ASP Solver , 2008, ICLP.

[34]  M De Vos ASP: The future is bright a position paper , 2009, ICLP 2009.

[35]  Hans Tompits,et al.  A Classification and Survey of Preference Handling Approaches in Nonmonotonic Reasoning , 2004, Comput. Intell..

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

[37]  Marina De Vos,et al.  TOAST: Applying Answer Set Programming to Superoptimisation , 2006, ICLP.

[38]  Camilla Schwind,et al.  A Tableau-Based Theorem Prover for a Decidable Subset of Default Logic , 1990, CADE.

[39]  Wolfgang Faber,et al.  Pruning Operators for Disjunctive Logic Programming Systems , 2006, Fundam. Informaticae.

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

[41]  David Pearce Default Logic and Constructive Logic , 1992, ECAI.

[42]  Stefan Woltran Equivalence between Extended Datalog Programs - A Brief Survey , 2010, Datalog.

[43]  Martin Gebser,et al.  Multi-Criteria Optimization in Answer Set Programming , 2011, ICLP.

[44]  Enrico Pontelli,et al.  Issues in parallel execution of non-monotonic reasoning systems , 2005, Parallel Comput..

[45]  Martin Gebser,et al.  On the Input Language of ASP Grounder Gringo , 2009, LPNMR.

[46]  Martin Gebser,et al.  Generic Tableaux for Answer Set Programming , 2007, ICLP.

[47]  Ilkka Niemelä,et al.  Answer Set Programming via Mixed Integer Programming , 2012, KR.

[48]  Martin Gebser,et al.  Repair and Prediction (under Inconsistency) in Large Biological Networks with Answer Set Programming , 2010, KR.

[49]  Andreas Pietz,et al.  Nothing but the Truth , 2013, J. Philos. Log..

[50]  Pedro Cabalar,et al.  Propositional theories are strongly equivalent to logic programs , 2007, Theory Pract. Log. Program..

[51]  Martin Gebser,et al.  Conflict-Driven Answer Set Solving , 2007, IJCAI.

[52]  Thomas Eiter,et al.  Uniform Equivalence of Logic Programs under the Stable Model Semantics , 2003, ICLP.

[53]  Tomi Janhunen,et al.  Some (in)translatability results for normal logic programs and propositional theories , 2006, J. Appl. Non Class. Logics.

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

[55]  Tommi Syrjänen,et al.  Logic programming and cardinality constraints : theory and practice , 2009 .

[56]  Marina De Vos,et al.  A pragmatic programmer’s guide to answer set programming , 2009 .

[57]  N. Meyers,et al.  H = W. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[58]  Martin Gebser,et al.  Constraint Answer Set Solving , 2009, ICLP.

[59]  Torsten Schaub,et al.  A Glimpse of Answer Set Programming , 2005, Künstliche Intell..

[60]  Hans Tompits,et al.  On properties of update sequences based on causal rejection , 2001, Theory and Practice of Logic Programming.

[61]  Joao Marques-Silva,et al.  Theory and Applications of Satisfiability Testing - SAT 2007, 10th International Conference, Lisbon, Portugal, May 28-31, 2007, Proceedings , 2007, SAT.

[62]  Miroslaw Truszczynski,et al.  Answer set programming at a glance , 2011, Commun. ACM.

[63]  Jussi Rintanen,et al.  Heuristics for Planning with SAT , 2010, CP.

[64]  Matti Järvisalo,et al.  Extended ASP Tableaux and rule redundancy in normal logic programs1 , 2008, Theory and Practice of Logic Programming.

[65]  Miroslaw Truszczynski,et al.  Properties and Applications of Programs with Monotone and Convex Constraints , 2006, J. Artif. Intell. Res..

[66]  Xiaoping Chen,et al.  Developing high-level cognitive functions for service robots , 2010, AAMAS.

[67]  Mark E. Stickel,et al.  10th International Conference on Automated Deduction , 1990, Lecture Notes in Computer Science.

[68]  Enrico Giunchiglia,et al.  Solving satisfiability problems with preferences , 2010, Constraints.

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

[70]  David G. Mitchell,et al.  A SAT Solver Primer , 2005, Bull. EATCS.

[71]  Stefan Woltran,et al.  Debugging ASP Programs by Means of ASP , 2007, LPNMR.

[72]  Francesco Scarcello,et al.  Enhancing DLV instantiator by backjumping techniques , 2007, Annals of Mathematics and Artificial Intelligence.

[73]  Frank Wolter,et al.  We Will Show Them! Essays in Honour of Dov Gabbay, Volume Two , 2005, We Will Show Them!.

[74]  Wolfgang Faber,et al.  Logic Programming and Nonmonotonic Reasoning , 2011, Lecture Notes in Computer Science.

[75]  Armin Biere Adaptive Restart Strategies for Conflict Driven SAT Solvers , 2008, SAT.

[76]  Wolfgang Faber,et al.  A backjumping technique for Disjunctive Logic Programming , 2006, AI Commun..

[77]  Marius Thomas Lindauer,et al.  Potassco: The Potsdam Answer Set Solving Collection , 2011, AI Commun..

[78]  John K. Slaney,et al.  Blocks World revisited , 2001, Artif. Intell..

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

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

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

[82]  Thomas Eiter,et al.  Towards automated integration of guess and check programs in answer set programming: a meta-interpreter and applications , 2004, Theory and Practice of Logic Programming.

[83]  T. Syrjänen Debugging Inconsistent Answer Set Programs , 2006 .

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

[85]  Keith L. Clark,et al.  Negation as Failure , 1987, Logic and Data Bases.

[86]  Gilles Audemard,et al.  Predicting Learnt Clauses Quality in Modern SAT Solvers , 2009, IJCAI.

[87]  Jack Dongarra,et al.  Recent Advances in Parallel Virtual Machine and Message Passing Interface , 1998, Lecture Notes in Computer Science.

[88]  José Júlio Alferes,et al.  LUPSA language for updating logic programs , 1999, Artif. Intell..

[89]  Martin Gebser,et al.  Reactive Answer Set Programming , 2011, LPNMR.

[90]  Marina De Vos,et al.  ASPVIZ: Declarative Visualisation and Animation Using Answer Set Programming , 2008, ICLP.

[91]  Yuanlin Zhang,et al.  Fast SAT-based Answer Set Solver , 2006, AAAI.

[92]  Tommi Syrjänen,et al.  Cardinality Constraint Programs , 2004, JELIA.

[93]  Jeffrey D. Ullman,et al.  Principles Of Database And Knowledge-Base Systems , 1979 .

[94]  Vladimir Lifschitz,et al.  Splitting a Logic Program , 1994, ICLP.

[95]  Ilkka Niemelä,et al.  Bounded LTL model checking with stable models , 2003, Theory Pract. Log. Program..

[96]  Tomi Janhunen On the Effect of Default Negation on the Expressiveness of Disjunctive Rules , 2001, LPNMR.

[97]  Roman Schindlauer,et al.  OntoDLV: An ASP-based System for Enterprise Ontologies , 2009, J. Log. Comput..

[98]  Francesco Ricca,et al.  A Java Wrapper for DLV , 2003, Answer Set Programming.

[99]  Martin Gebser,et al.  Loops: Relevant or Redundant? , 2005, LPNMR.

[100]  Paolo Ferraris,et al.  Answer Sets for Propositional Theories , 2005, LPNMR.

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

[102]  Luigi Palopoli,et al.  The LP-OD system: logic programming meets outlier detection , 2007, ICLP 2007.

[103]  Miroslaw Truszczynski,et al.  The First Answer Set Programming System Competition , 2007, LPNMR.

[104]  Ilkka Niemelä,et al.  Computing Stable Models via Reductions to Difference Logic , 2009, LPNMR.

[105]  Michael Gelfond,et al.  On Stratified Autoepistemic Theories , 1987, AAAI.

[106]  Lawrence Ryan Efficient algorithms for clause-learning SAT solvers , 2004 .

[107]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[108]  Christine Froidevaux,et al.  Minimalism subsumes Default Logic and Circumscription in Stratified Logic Programming , 1987, LICS.

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

[110]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[111]  Martine De Cock,et al.  An introduction to fuzzy answer set programming , 2007, Annals of Mathematics and Artificial Intelligence.

[112]  Thomas Eiter,et al.  Answer Set Programming: A Primer , 2009, Reasoning Web.

[113]  Felip Manyà,et al.  Resolution-based lower bounds in MaxSAT , 2010, Constraints.

[114]  Stephen A. Cook,et al.  The Relative Efficiency of Propositional Proof Systems , 1979, Journal of Symbolic Logic.

[115]  Wolfgang Faber,et al.  Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity , 2004, JELIA.

[116]  John S. Schlipf,et al.  The Expressive Powers of the Logic Programming Semantics , 1995, J. Comput. Syst. Sci..

[117]  Stefan Woltran,et al.  "That is illogical, Captain!" : the debugging support tool spock for answer-set programs ; system description , 2007 .

[118]  Yuliya Lierler,et al.  Abstract Answer Set Solvers with Learning , 2010, ArXiv.

[119]  Martin Gebser,et al.  The nomore++ Approach to Answer Set Solving , 2005, LPAR.

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

[121]  Francesco Scarcello,et al.  Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation , 1997, Inf. Comput..

[122]  Georg Gottlob,et al.  On the computational cost of disjunctive logic programming: Propositional case , 1995, Annals of Mathematics and Artificial Intelligence.

[123]  John S. Schlipf,et al.  Answer Set Programming with Clause Learning , 2004, LPNMR.

[124]  Nicola Olivetti,et al.  Tableaux for Nonmonotonic Logics , 1999 .

[125]  Ilkka Niemelä,et al.  Developing a Declarative Rule Language for Applications in Product Configuration , 1999, PADL.

[126]  Martin Gebser,et al.  Coala: A Compiler from Action Languages to ASP , 2010, JELIA.

[127]  Jack Minker Foundations of deductive databases and logic programming , 1988 .

[128]  João Leite,et al.  On Semantic Update Operators for Answer-Set Programs , 2010, ECAI.

[129]  Melvin Fitting,et al.  A Kripke-Kleene Semantics for Logic Programs , 1985, J. Log. Program..

[130]  Ilkka Niemelä,et al.  Logic programs with stable model semantics as a constraint programming paradigm , 1999, Annals of Mathematics and Artificial Intelligence.

[131]  Alexander A. Razborov,et al.  Propositional proof complexity , 2003, JACM.

[132]  Tommi Syrjänen Omega-Restricted Logic Programs , 2001, LPNMR.

[133]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[134]  Michael Gelfond,et al.  An A Prolog decision support system for the Space Shuttle , 2001, Answer Set Programming.

[135]  V. Lifschitz,et al.  Foundations of Logic Programming , 1997 .

[136]  Jinbo Huang,et al.  The Effect of Restarts on the Efficiency of Clause Learning , 2007, IJCAI.

[137]  Robert C. Moore Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.

[138]  Martin Gebser,et al.  Advances in gringo Series 3 , 2011, LPNMR.

[139]  Enrico Pontelli,et al.  Planning with Preferences Using Logic Programming , 2004, LPNMR.

[140]  Mario Alviano,et al.  The Third Answer Set Programming Competition: Preliminary Report of the System Competition Track , 2011, LPNMR.

[141]  Yuliya Lierler,et al.  Answer Set Programming Based on Propositional Satisfiability , 2006, Journal of Automated Reasoning.

[142]  Stefan Woltran,et al.  Characterising equilibrium logic and nested logic programs: Reductions and complexity1,2 , 2009, Theory and Practice of Logic Programming.

[143]  Hans Tompits,et al.  A framework for compiling preferences in logic programs , 2002, Theory and Practice of Logic Programming.

[144]  Georg Dengler N.F. [1.] , 1873 .

[145]  Katsumi Inoue,et al.  Embedding Negation as Failure into a Model Generation Theorem Prover , 1992, CADE.

[146]  Eugene Goldberg,et al.  BerkMin: A Fast and Robust Sat-Solver , 2002, Discret. Appl. Math..

[147]  Adnan Darwiche,et al.  On the power of clause-learning SAT solvers as resolution engines , 2011, Artif. Intell..

[148]  Armin Biere,et al.  PicoSAT Essentials , 2008, J. Satisf. Boolean Model. Comput..

[149]  Martin Gebser,et al.  Challenges in Answer Set Solving , 2011, Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning.

[150]  Torsten Schaub,et al.  ASP modulo CSP: The clingcon system , 2012, Theory Pract. Log. Program..

[151]  David Pearce,et al.  A Tableau Calculus for Equilibrium Entailment , 2000, TABLEAUX.

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

[153]  Vladimir Lifschitz,et al.  Answer Sets in General Nonmonotonic Reasoning (Preliminary Report) , 1992, KR.

[154]  Vladimir Lifschitz,et al.  Answer Set Planning (Abstract) , 1999, LPNMR.

[155]  Torsten Schaub,et al.  Profiling Answer Set Programming: The Visualization Component of the noMoRe System , 2004, JELIA.

[156]  Martin Gebser,et al.  Detecting inconsistencies in large biological networks with answer set programming , 2008, Theory and Practice of Logic Programming.

[157]  Wolfgang Faber,et al.  Computing preferred answer sets by meta-interpretation in answer set programming , 2003, Theory Pract. Log. Program..

[158]  Patrik Simons,et al.  Evaluating an Algorithm for Default Reasoning , 1995 .

[159]  Martin Gebser,et al.  Multi-threaded ASP solving with clasp , 2012, Theory and Practice of Logic Programming.

[160]  Robert A. Kowalski,et al.  Algorithm = logic + control , 1979, CACM.

[161]  Georg Gottlob,et al.  Complexity and expressive power of logic programming , 2001, CSUR.

[162]  Martin Gebser,et al.  GrinGo : A New Grounder for Answer Set Programming , 2007, LPNMR.

[163]  Hans Tompits,et al.  Combining answer set programming with description logics for the Semantic Web , 2004, Artif. Intell..

[164]  Esra Erdem,et al.  Combining high-level causal reasoning with low-level geometric reasoning and motion planning for robotic manipulation , 2011, 2011 IEEE International Conference on Robotics and Automation.

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

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

[167]  Nachum Dershowitz,et al.  Towards a Better Understanding of the Functionality of a Conflict-Driven SAT Solver , 2007, SAT.

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

[169]  Michael Gelfond,et al.  Answer Sets , 2008, Handbook of Knowledge Representation.

[170]  Chiaki Sakama,et al.  Prioritized logic programming and its application to commonsense reasoning , 2000, Artif. Intell..

[171]  Michael Gelfond,et al.  Towards an Integration of Answer Set and Constraint Solving , 2005, ICLP.

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

[173]  Norman Y. Foo,et al.  A Unified Framework for Representing Logic Program Updates , 2005, AAAI.

[174]  Robert E. Mercer,et al.  Platypus: A Platform for Distributed Answer Set Solving , 2005, LPNMR.

[175]  Toby Walsh,et al.  Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications , 2009 .

[176]  Victor W. Marek,et al.  Nonmonotonic logic - context-dependent reasoning , 1997, Artificial intelligence.

[177]  Bart Selman,et al.  Planning as Satisfiability , 1992, ECAI.

[178]  Michael Gelfond,et al.  Integrating answer set programming and constraint logic programming , 2008, Annals of Mathematics and Artificial Intelligence.

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

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

[181]  Rupak Majumdar,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2010, Lecture Notes in Computer Science.

[182]  Michael Gelfond,et al.  Integrating Answer Set Reasoning with Constraint Solving Techniques , 2008, FLOPS.

[183]  V. S. Costa,et al.  Theory and Practice of Logic Programming , 2010 .

[184]  Enrico Pontelli,et al.  Non-monotonic Reasoning on Beowulf Platforms , 2003, PADL.

[185]  Torsten Schaub,et al.  Graphs and colorings for answer set programming , 2005, Theory and Practice of Logic Programming.

[186]  Hans Tompits,et al.  A Preference-Based Framework for Updating Logic Programs , 2007, LPNMR.

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

[188]  Frank van Harmelen,et al.  Handbook of Knowledge Representation , 2008, Handbook of Knowledge Representation.

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

[190]  Torsten Schaub,et al.  A semantic framework for preference handling in answer set programming , 2003, Theory and Practice of Logic Programming.

[191]  Bettina Schnor,et al.  Experiences Running a Parallel Answer Set Solver on Blue Gene , 2009, PVM/MPI.

[192]  Torsten Schaub,et al.  Unsatisfiability-based optimization in clasp , 2012, ICLP.

[193]  H. Tompits,et al.  Catching the Ouroboros: On debugging non-ground answer-set programs , 2010, Theory and Practice of Logic Programming.

[194]  Martin Gebser,et al.  Heuristics in Conflict Resolution , 2010, ArXiv.

[195]  Michael Gelfond,et al.  Knowledge Representation and Logic Programming , 2002, Artif. Intell..

[196]  Aaron Stump,et al.  SMT-COMP: Satisfiability Modulo Theories Competition , 2005, CAV.

[197]  Hans Tompits,et al.  A Meta-Programming Technique for Debugging Answer-Set Programs , 2008, AAAI.

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

[199]  Marius Thomas Lindauer,et al.  A Portfolio Solver for Answer Set Programming: Preliminary Report , 2011, LPNMR.

[200]  David Pearce,et al.  A New Logical Characterisation of Stable Models and Answer Sets , 1996, NMELP.

[201]  Bettina Schnor,et al.  A Simple Distributed Conflict-Driven Answer Set Solver , 2009, LPNMR.

[202]  Sharad Malik,et al.  Efficient conflict driven learning in a Boolean satisfiability solver , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[203]  D. Gabbay,et al.  Handbook of tableau methods , 1999 .

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

[205]  Alan Robinson,et al.  The Inverse Method , 2001, Handbook of Automated Reasoning.

[206]  Martin Gebser,et al.  Conflict-Driven Answer Set Enumeration , 2007, LPNMR.

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

[208]  Marco Cadoli,et al.  : Compiling problem specifications into SAT , 2005, Artif. Intell..

[209]  Michael Gelfond,et al.  Logic Programs with Classical Negation , 1990, ICLP.

[210]  Maarten Mariën,et al.  On the Relation Between ID-Logic and Answer Set Programming , 2004, JELIA.

[211]  David Pearce,et al.  Equilibrium logic , 2006, Annals of Mathematics and Artificial Intelligence.

[212]  Henry A. Kautz,et al.  Towards Understanding and Harnessing the Potential of Clause Learning , 2004, J. Artif. Intell. Res..

[213]  Yuliya Lierler,et al.  One More Decidable Class of Finitely Ground Programs , 2009, ICLP.

[214]  Michael Gelfond,et al.  Classical negation in logic programs and disjunctive databases , 1991, New Generation Computing.

[215]  Giorgio Terracina,et al.  Enhancing a DLP System for Advanced Database Applications , 2008, RR.

[216]  Jussi Rintanen Planning and SAT , 2009, Handbook of Satisfiability.

[217]  Miroslaw Truszczynski,et al.  Answer Set Optimization , 2003, IJCAI.

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

[219]  J. McCarthy Circumscription|a Form of Nonmonotonic Reasoning , 1979 .

[220]  A RossKenneth,et al.  The well-founded semantics for general logic programs , 1991 .

[221]  Martin Gebser,et al.  Conflict-Driven Disjunctive Answer Set Solving , 2008, KR.

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

[223]  J. P. Marques,et al.  GRASP : A Search Algorithm for Propositional Satisfiability , 1999 .

[224]  A. Tarski A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[225]  Miroslaw Truszczynski,et al.  Properties of Programs with Monotone and Convex Constraints , 2005, AAAI.

[226]  A. Heyting Die formalen Regeln der intuitionistischen Logik , 1930 .

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

[228]  Miroslaw Truszczynski Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs , 2011, Theory Pract. Log. Program..

[229]  Martin Gebser,et al.  Conflict-driven answer set solving: From theory to practice , 2012, Artif. Intell..

[230]  Michael Gelfond,et al.  Knowledge Representation, Reasoning, and the Design of Intelligent Agents: The Answer-Set Programming Approach , 2014 .

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

[232]  Wolfgang Faber,et al.  The INFOMIX system for advanced integration of incomplete and inconsistent data , 2005, SIGMOD '05.

[233]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[234]  Mario Alviano,et al.  Unfounded Sets and Well-Founded Semantics of Answer Set Programs with Aggregates , 2011, J. Artif. Intell. Res..

[235]  Michael Gelfond,et al.  Logic programming and knowledge representation—The A-Prolog perspective , 2002 .

[236]  Yuliya Lierler,et al.  On elementary loops of logic programs , 2010, Theory and Practice of Logic Programming.

[237]  Alexander A. Razborov,et al.  Why are there so many loop formulas? , 2006, TOCL.

[238]  Bettina Schnor,et al.  Cluster-Based ASP Solving with claspar , 2011, LPNMR.

[239]  Xiaoping Chen,et al.  Integrating NLP with Reasoning about Actions for Autonomous Agents Communicating with Humans , 2009, 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology.

[240]  Miroslaw Truszczynski,et al.  The Second Answer Set Programming Competition , 2009, LPNMR.

[241]  Eugenia Ternovska,et al.  A logic of nonmonotone inductive definitions , 2008, TOCL.

[242]  Martin Gebser,et al.  Complex optimization in answer set programming , 2011, Theory and Practice of Logic Programming.

[243]  Martin Gebser,et al.  Advanced Preprocessing for Answer Set Solving , 2008, ECAI.