lntroducing generalized specificity in logic programming

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. Therefore, a criterion for deciding between them is needed. Several extensions of logic programming consider priorities over program (default) rules. However, these priorities must be supplied by the programmer in a more or less arbitrary manner, establishing explicitly relations between rules. The aim of this paper is to investigate beyond explicit comparison between rules, looking for an inherent and autonomous comparison criterion, based on specificity as defined in [22, 25]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion for comparing arguments, namely specificity, is context-sensitive. This means that preference among defeasible rules is determined dynamically during the dialectical analysis. We show how such a specificity criterion can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a more syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in a generic rule-based formalism. We present a theorem which links both characterizations, showing their equivalence. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly, contrasting them with our approach.

[1]  David Poole,et al.  On the Comparison of Theories: Preferring the Most Specific Explanation , 1985, IJCAI.

[2]  Editors , 1986, Brain Research Bulletin.

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

[4]  Donald Nute,et al.  Prolog Programming in Depth , 1988 .

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

[6]  Guillermo Ricardo Simari,et al.  A Mathematical Treatment of Defeasible Reasoning and its Implementation , 1992, Artif. Intell..

[7]  John F. Horty,et al.  Some direct theories of nonmonotonic inheritance , 1994 .

[8]  Guillermo R. Simari,et al.  The Role of Dialectics in Defeasible Argumentation , 1994 .

[9]  Pascal Van Hentenryck.  The Acceptability Semantics for Logic Programs , 1994 .

[10]  John W. Lloyd.  Logic Programming without Negation as Failure , 1995 .

[11]  José Júlio Alferes,et al.  Reasoning with Logic Programming , 1996, Lecture Notes in Computer Science.

[12]  Tran Cao Son,et al.  An Argumentation-theoretic Approach to Reasoning with Specificity , 1996, KR.

[13]  Gerard Vreeswijk,et al.  Abstract Argumentation Systems , 1997, Artif. Intell..

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

[15]  Henry Prakken,et al.  Argument-Based Extended Logic Programming with Defeasible Priorities , 1997, J. Appl. Non Class. Logics.

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

[17]  Jia-Huai You,et al.  Logic programming without default negation revisited , 1997, 1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335).

[18]  Phan Minh Dung,et al.  An Abstract, Argumentation-Theoretic Approach to Default Reasoning , 1997, Artif. Intell..

[19]  Michael J. Maher,et al.  A Study of Provability in Defeasible Logic , 1998, Australian Joint Conference on Artificial Intelligence.

[20]  Oliver Obst,et al.  Spatial Agents Implemented in a Logical Expressible Language , 1999, RoboCup.

[21]  Guillermo Ricardo Simari,et al.  Automating Defeasible Reasoning with Logic Programming (DeReLoP) , 1999 .

[22]  Andreas Winter,et al.  Querying as an enabling technology in software reengineering , 1999, Proceedings of the Third European Conference on Software Maintenance and Reengineering (Cat. No. PR00090).

[23]  Frieder Stolzenburg,et al.  Loop-Detection in Hyper-Tableaux by Powerful Model Generation , 1999, J. Univers. Comput. Sci..

[24]  Jürgen Ebert,et al.  GraX-an interchange format for reengineering tools , 1999, Sixth Working Conference on Reverse Engineering (Cat. No.PR00303).

[25]  Jürgen Ebert,et al.  A Formalization of SOCCA , 1999 .

[26]  Peter Baumgartner,et al.  Abductive Coreference by Model Construction , 1999 .

[27]  Antonis C. Kakas,et al.  Computing Argumentation in Logic Programming , 1999, J. Log. Comput..

[28]  Jens Woch,et al.  Implementation of a Schema-TAG-Parser , 1999 .

[29]  Joseph Douglas Horton,et al.  Merge Path Improvements for Minimal Model Hyper Tableaux , 1999, TABLEAUX.

[30]  Victor W. Marek,et al.  The Logic Programming Paradigm , 1999, Artificial Intelligence.

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

[32]  Andy Schürr,et al.  GXL: toward a standard exchange format , 2000, Proceedings Seventh Working Conference on Reverse Engineering.

[33]  Michael J. Maher,et al.  Defeasible Logic versus Logic Programming without Negation as Failure , 2000, J. Log. Program..

[34]  Manfred Rosendahl,et al.  Specification of Symbols and Implementation of Their Constraints in JKogge , 2000 .

[35]  Peter Baumgartner,et al.  The Taming of the (X)OR , 2000, Computational Logic.

[36]  Ulrich Furbach,et al.  Nonmonotonic Reasoning: Towards Efficient Calculi and Implementations , 2001, Handbook of Automated Reasoning.

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

[38]  Jürgen Dix,et al.  Transformation-based bottom-up computation of the well-founded model , 1996, Theory and Practice of Logic Programming.

[39]  Guillermo Ricardo Simari.  Modeling Defeasibility in an Extended Logic Programming Setting Using an Abstract Argumentation Framework , 2002 .