On properties of update sequences based on causal rejection

In this paper, we consider an approach to update nonmonotonic knowledge bases represented as extended logic programs under the answer set semantics. In this approach, new information is incorporated into the current knowledge base subject to a causal rejection principle, which enforces that, in case of conflicts between rules, more recent rules are preferred and older rules are overridden. Such a rejection principle is also exploited in other approaches to update logic programs, notably in the method of dynamic logic programming, due to Alferes et al.One of the central issues of this paper is a thorough analysis of various properties of the current approach, in order to get a better understanding of the inherent causal rejection principle. For this purpose, we review postulates and principles for update and revision operators which have been proposed in the area of theory change and nonmonotonic reasoning. Moreover, some new properties for approaches to updating logic programs are considered as well. Like related update approaches, the current semantics does not incorporate a notion of minimality of change, so we consider refinements of the semantics in this direction. We also investigate the relationship of our approach to others in more detail. In particular, we show that the current approach is semantically equivalent to inheritance programs, which have been independently defined by Buccafurri et al., and that it coincides with certain classes of dynamic logic programs. In view of this analysis, most of our results about properties of the causal rejection principle apply to each of these approaches as well. Finally, we also deal with computational issues. Besides a discussion on the computational complexity of our approach, we outline how the update semantics and its refinements can be directly implemented on top of existing logic programming systems. In the present case, we implemented the update approach using the logic programming system DLV.

[1]  Georg Gottlob,et al.  Complexity and expressive power of logic programming , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[2]  Norman Y. Foo,et al.  Updating Logic Programs , 1998, ECAI.

[3]  J. Pearl,et al.  On the Logic of Iterated Belief Revision , 1994, Artif. Intell..

[4]  Hans Tompits,et al.  ON UPDATES OF LOGIC PROGRAMS: SEMANTICS AND PROPERTIES , 2000 .

[5]  José Júlio Alferes,et al.  Update-Programs Can Update Programs , 1996, NMELP.

[6]  José Júlio Alferes,et al.  Updates plus Preferences , 2000, JELIA.

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

[8]  Victor W. Marek,et al.  Autoepistemic logic , 1991, JACM.

[9]  Francesca Toni,et al.  Abstract argumentation , 1996, Artificial Intelligence and Law.

[10]  Norman Y. Foo,et al.  Towards Generalized Rule-based Updates , 1997, IJCAI.

[11]  Hirofumi Katsuno,et al.  On the Difference between Updating a Knowledge Base and Revising It , 1991, KR.

[12]  Peter Gärdenfors,et al.  Nonmonotonic Inference Based on Expectations , 1994, Artif. Intell..

[13]  V. Marek Revision Speciications by Means of Programs , 1994 .

[14]  Daniel Lehmann,et al.  What does a Conditional Knowledge Base Entail? , 1989, Artif. Intell..

[15]  Gerald Pfeifer,et al.  A Deductive System for Non-Monotonic Reasoning , 1997, LPNMR.

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

[17]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

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

[19]  Marianne Winslett,et al.  Reasoning about Action Using a Possible Models Approach , 1988, AAAI.

[20]  Bernhard Nebel,et al.  Belief Revision and Default Reasoning: Syntax-Based Approaches , 1991, KR.

[21]  Dov M. Gabbay,et al.  Handbook of logic in artificial intelligence and logic programming (vol. 1) , 1993 .

[22]  David S. Johnson,et al.  A Catalog of Complexity Classes , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

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

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

[25]  Peter Gärdenfors,et al.  Belief Revision , 1995 .

[26]  Paolo Mancarella,et al.  Database Updates through Abduction , 1990, VLDB.

[27]  Daniel Lehmann Belief Revision, Revised , 1995, IJCAI.

[28]  José Júlio Alferes,et al.  Dynamic updates of non-monotonic knowledge bases , 2000, J. Log. Program..

[29]  Christos H. Papadimitriou,et al.  Computational complexity , 1993 .

[30]  Peter Gärdenfors,et al.  Relations between the logic of theory change and nonmonotonic logic , 1989, The Logic of Theory Change.

[31]  Victor W. Marek,et al.  Default Reasoning System DeReS , 1996, KR.

[32]  Ilkka Niemelä,et al.  Efficient Implementation of the Well-founded and Stable Model Semantics , 1996, JICSLP.

[33]  Francesco Buccafurri,et al.  Stable Models and Their Computation for Logic Programming with Inheritance and True Negation , 1996, J. Log. Program..

[34]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[35]  Dov M. Gabbay,et al.  Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems , 1989, Logics and Models of Concurrent Systems.

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

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

[38]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[39]  Gerhard Brewka,et al.  Nonmonotonic Reasoning: Logical Foundations of Commonsense By Gerhard Brewka (Cambridge University Press, 1991) , 1991, SGAR.

[40]  Didier Dubois,et al.  Inconsistency Management and Prioritized Syntax-Based Entailment , 1993, IJCAI.

[41]  Georg Gottlob,et al.  On the complexity of propositional knowledge base revision, updates, and counterfactuals , 1992, Artif. Intell..

[42]  Torsten Schaub On Commitment and Cumulativity in Default Logics , 1991, ECSQARU.

[43]  Victor W. Marek,et al.  Revision Specifications by Means of Programs , 1994, JELIA.

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

[45]  Katsumi Inoue,et al.  A Simple Characterization of Extended Abduction , 2000, Computational Logic.

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

[47]  Juliana Freire,et al.  XSB: A System for Effciently Computing WFS , 1997, LPNMR.

[48]  John S. Schlipf A Survey of Complexity and Undecidability Results in Logic Programming , 1992, Structural Complexity and Recursion-theoretic methods in Logic-Programming.

[49]  D. Warren,et al.  Xsb -a System for Eeciently Computing Well Founded Semantics , 1997 .

[50]  José Júlio Alferes,et al.  LUPS - A Language for Updating Logic Programs , 1999, LPNMR.

[51]  José Júlio Alferes,et al.  Multi-dimensional Dynamic Logic Programming , 2000, CL-2000 Workshop on Computational Logic in Multi-Agent Systems.

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

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

[54]  Peter Gärdenfors Nonmonotonic Inferences Based on Expectations: A Preliminary Report , 1991, KR.

[55]  Gerald Pfeifer,et al.  The KR System dlv: Progress Report, Comparisons and Benchmarks , 1998, KR.

[56]  Luís Moniz Pereira,et al.  Generalizing Updates: From Models to Programs , 1997, LPKR.

[57]  Gerhard Brewka,et al.  Declarative Representation of Revision Strategies* , 2000, J. Appl. Non Class. Logics.

[58]  Domenico Saccà,et al.  Extending logic programming , 1990, SIGMOD '90.

[59]  Gerhard Brewka Cumulative Default Logic: In Defense of Nonmonotonic Inference Rules , 1991, Artif. Intell..

[60]  Chiaki Sakama,et al.  Abductive Framework for Nonmonotonic Theory Change , 1995, IJCAI.