Answer Sets

Publisher Summary This chapter discusses Answer Set Prolog, which is a language for knowledge representation and reasoning based on the answer set/stable model semantics of logic programs. The language has roots in the declarative programming, syntax, and semantics of standard Prolog, disjunctive databases, and nonmonotonic logic. Unlike standard Prolog, it allows expressing disjunction and classic or strong negation. It differs from many other knowledge representation languages by its ability to represent defaults. A substantial part of education consists in learning various defaults, exceptions to these defaults, and the ways of using this information to draw reasonable conclusions about the world and the consequences of one's actions. Answer Set Prolog provides a powerful logical model of this process. Its syntax allows a simple representation of defaults and their exceptions, its consequence relation characterizes the corresponding set of valid conclusions, and its inference mechanisms allow a program to find these conclusions in a reasonable amount of time.

[1]  Michael Gelfond,et al.  Action Languages , 1998, Electron. Trans. Artif. Intell..

[2]  Hudson Turner,et al.  Order-consistent programs are cautiously monotonic , 2000, Theory and Practice of Logic Programming.

[3]  Murray Shanahan Solving the frame problem - a mathematical investigation of the common sense law of inertia , 1997 .

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

[5]  Chitta Baral,et al.  Reasoning agents in dynamic domains , 2000 .

[6]  Jack Minker,et al.  Logic and Databases: A 20 Year Retrospective , 1996, Logic in Databases.

[7]  Victor W. Marek,et al.  Stable Semantics for Logic Programs and Default Theories , 1989, NACLP.

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

[9]  Marcello Balduccini,et al.  USA-Smart: Improving the Quality of Plans in Answer Set Planning , 2004, PADL.

[10]  Marek J. Sergot,et al.  A logic-based calculus of events , 1989, New Generation Computing.

[11]  Enrico Pontelli,et al.  Smodels with CLP and Its Applications: A Simple and Effective Approach to Aggregates in ASP , 2004, ICLP.

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

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

[14]  Georg Gottlob,et al.  Disjunctive datalog , 1997, TODS.

[15]  Teodor C. Przymusinski On the Declarative Semantics of Deductive Databases and Logic Programs , 1988, Foundations of Deductive Databases and Logic Programming..

[16]  David Makinson,et al.  General patterns in nonmonotonic reasoning , 1994 .

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

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

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

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

[21]  Robert A. Kowalski,et al.  Logic for problem solving , 1982, The computer science library : Artificial intelligence series.

[22]  Chitta Baral,et al.  Reasoning about Intended Actions , 2005, AAAI.

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

[24]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

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

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

[27]  Stefan Woltran,et al.  Semantical characterizations and complexity of equivalences in answer set programming , 2005, TOCL.

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

[29]  Wolfgang Faber,et al.  Unfounded Sets for Disjunctive Logic Programs with Arbitrary Aggregates , 2005, LPNMR.

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

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

[32]  Raymond Reiter,et al.  Logical Foundations for Cognitive Agents: Contributions in Honor of Ray Reiter , 2001 .

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

[34]  Rina Dechter,et al.  Propositional semantics for disjunctive logic programs , 1994, Annals of Mathematics and Artificial Intelligence.

[35]  Taisuke Sato,et al.  Completed Logic Programs and their Consistency , 1990, J. Log. Program..

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

[37]  Alex M. Andrew,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2002 .

[38]  J. Nelson Rushton,et al.  Probabilistic reasoning with answer sets , 2004, Theory and Practice of Logic Programming.

[39]  Donald Michie,et al.  Machine Intelligence 4 , 1970 .

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

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

[42]  Chitta Baral,et al.  A knowledge based approach for representing and reasoning about signaling networks , 2004, ISMB/ECCB.

[43]  David Scott Warren,et al.  Efficient Top-Down Computation of Queries under the Well-Founded Semantics , 1995, J. Log. Program..

[44]  Maurice Bruynooghe,et al.  Well-founded and stable semantics of logic programs with aggregates , 2007, Theory Pract. Log. Program..

[45]  EiterThomas,et al.  The DLV system for knowledge representation and reasoning , 2006 .

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

[47]  V. Wiktor Marek,et al.  Nonmonotonic Logic , 1993, Artificial Intelligence.

[48]  Bernhard Nebel,et al.  Encoding Planning Problems in Nonmonotonic Logic Programs , 1997, ECP.

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

[50]  E. Davis,et al.  Common Sense Reasoning , 2014, Encyclopedia of Social Network Analysis and Mining.

[51]  Jack Minker,et al.  On Indefinite Databases and the Closed World Assumption , 1987, CADE.

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

[53]  Francesco Buccafurri,et al.  Adding Weak Constraints to Disjunctive Datalog , 1997, APPIA-GULP-PRODE.

[54]  Esra Erdem,et al.  Character-Based Cladistics and Answer Set Programming , 2005, PADL.

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

[56]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

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

[58]  Vladimir Lifschitz,et al.  Weight constraints as nested expressions , 2003, Theory and Practice of Logic Programming.

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

[60]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[61]  Tomi Janhunen,et al.  LPEQ and DLPEQ - Translators for Automated Equivalence Testing of Logic Programs , 2004, LPNMR.

[62]  Chitta Baral Knowledge Representation, Reasoning and Declarative Problem Solving: Principles and properties of declarative programming with answer sets , 2003 .

[63]  Hudson Turner,et al.  A Causal Theory of Ramifications and Qualifications , 1995, IJCAI.

[64]  Leon Sterling,et al.  Relating Stable Models and AI Planning Domains , 1995 .

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

[66]  Michael Gelfond,et al.  Logic Programs with Consistency-Restoring Rules , 2003 .

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

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

[69]  Michael Gelfond,et al.  Diagnostic reasoning with A-Prolog , 2003, Theory Pract. Log. Program..

[70]  Tran Cao Son,et al.  Approximation of action theories and its application to conformant planning , 2005, Artif. Intell..

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

[72]  Hudson Turner,et al.  Representing Actions in Logic Programs and Default Theories: A Situation Calculus Approach , 1997, J. Log. Program..

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

[74]  Gerhard Brewka,et al.  Answer Sets: From Constraint Programming Towards Qualitative Optimization , 2004, LPNMR.

[75]  Jack Minker The Workshop on Logic-Based Artificial Intelligence , 1999, AI Mag..

[76]  Marcello Balduccini,et al.  Answer set based design of highly autonomous, rational agents , 2005 .

[77]  Christine Froidevaux,et al.  Negation by Default and Unstratifiable Logic Programs , 1991, Theor. Comput. Sci..

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

[79]  Peter Szolovits,et al.  What Is a Knowledge Representation? , 1993, AI Mag..

[80]  Enrico Pontelli,et al.  A Constructive semantic characterization of aggregates in answer set programming , 2007, Theory Pract. Log. Program..

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

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

[83]  James Harland,et al.  The aditi deductive database system , 1994, The VLDB Journal.

[84]  Thomas Eiter,et al.  Using SAT and Logic Programming to Design Polynomial-Time Algorithms for Planning in Non-Deterministic Domains , 2005, AAAI.

[85]  Yuliya Lierler,et al.  Cmodels-2: SAT-based Answer Set Solver Enhanced to Non-tight Programs , 2004, LPNMR.

[86]  Dino Pedreschi,et al.  Proving Termination of General Prolog Programs , 1991, TACS.

[87]  Chiaki Sakama,et al.  Induction from answer sets in nonmonotonic logic programs , 2005, TOCL.

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

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

[90]  Jack Minker,et al.  Logic and Data Bases , 1978, Springer US.

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

[92]  Victor W. Marek,et al.  The Logic Programming Paradigm: A 25-Year Perspective , 2011 .

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

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

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

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