A semantic framework for preference handling in answer set programming

We provide a semantic framework for preference handling in answer set programming. To this end, we introduce preference preserving consequence operators. The resulting fixpoint characterizations provide us with a uniform semantic framework for characterizing preference handling in existing approaches. Although our approach is extensible to other semantics by means of an alternating fixpoint theory, we focus here on the elaboration of preferences under answer set semantics. Alternatively, we show how these approaches can be characterized by the concept of order preservation. These uniform semantic characterizations provide us with new insights about inter-relationships and moreover about ways of implementation.

[1]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[2]  Henry Prakken,et al.  Logical Tools for Modelling Legal Argument , 1997 .

[3]  Gerhard Brewka.  On the Relationship between Defeasible Logic and Well-Founded Semantics , 2001, LPNMR.

[4]  Hans Tompits,et al.  Logic Programs with Compiled Preferences , 2000, ECAI.

[5]  Chiaki Sakama,et al.  Representing Priorities in Logic Programs , 1996, JICSLP.

[6]  Torsten Schaub,et al.  Preferredwell-foundedsemanticsfor logic programming by alternating fixpoints , 2002 .

[7]  Thomas Eiter,et al.  Prioritizing Default Logic , 2000, Intellectics and Computational Logic.

[8]  Theresa Swift,et al.  Preference Logic Grammars: Fixed point semantics and application to data standardization , 2002, Artif. Intell..

[9]  Wolfgang Faber,et al.  Disjunctive Logic Programs with Inheritance , 1999, ICLP.

[10]  Benjamin N. Grosof.  Prioritized Conflict Handling for Logic Programs , 1997, ILPS.

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

[12]  Fangzhen Lin,et al.  Alternating Fixpoint Theory for Logic Programs with Priority , 2000, Computational Logic.

[13]  Gerhard Brewka,et al.  Adding Priorities and Specificity to Default Logic , 1994, JELIA.

[14]  Torsten Schaub,et al.  The role of default logic in knowledge representation , 2000 .

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

[16]  Donald Nute,et al.  Defeasible Logic , 1994, INAP.

[17]  E. Groves.  A Dissertation ON , 1928 .

[18]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

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

[20]  Jussi Rintanen.  On Specificity in Default Logic , 1995, IJCAI.

[21]  Jack Minker,et al.  Using Priorities to Combine Knowledge Bases , 1996, Int. J. Cooperative Inf. Syst..

[22]  Kurt Konolige,et al.  On the Relation Between Default and Autoepistemic Logic , 1987, Artif. Intell..

[23]  Dov M. Gabbay,et al.  Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning , 1994 .

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

[25]  Franz Baader,et al.  How to Prefer More Specific Defaults in Terminological Default Logic , 1993, IJCAI.

[26]  Hans Tompits,et al.  A Compilation of Brewka and Eiter's Approach to Prioritization , 2000, JELIA.

[27]  KonoligeKurt.  On the relation between default and autoepistemic logic , 1988 .

[28]  José Júlio Alferes,et al.  Dynamic Logic Programming , 1998, APPIA-GULP-PRODE.

[29]  Gerhard Brewka.  Well-Founded Semantics for Extended Logic Programs with Dynamic Preferences , 1996, J. Artif. Intell. Res..

[30]  Norman Y. Foo,et al.  Answer Sets for Prioritized Logic Programs , 1997, ILPS.

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

[32]  Benjamin N. Grosof.  Prioritized conflict handing for logic programs , 1997, International Conference on Logic Programming.

[33]  Antonis C. Kakas,et al.  Logic Programming without Negation as Failure , 1995, ILPS.

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

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

[36]  Van GelderAllen.  The alternating fixpoint of logic programs with negation , 1993 .

[37]  John L. Pollock,et al.  Defeasible Reasoning , 2020, Synthese Library.

[38]  Tran Cao Son,et al.  Reasoning with Prioritized Defaults , 1997, LPKR.

[39]  Thomas F. Gordon,et al.  Pleadings game - an artificial intelligence model of procedural justice , 1995 .

[40]  Hans Tompits,et al.  Considerations on Updates of Logic Programs , 2000, JELIA.

[41]  Li-Yan Yuan,et al.  Nonmonotonic Reasoning as Prioritized Argumentation , 2001, IEEE Trans. Knowl. Data Eng..