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An argumentation framework in default logic

  • Henry Prakken
Article

Abstract

This article presents a formal theory about nontrivial reasoning with inconsistent information, applicable, among other things, to defeasible reasoning. The theory, which is inspired by a formal analysis of legal argument, is based on the idea that inconsistency tolerant reasoning is more than revising an unstructural set of premises; rather it should be regarded as constructing and comparing arguments for incompatible conclusions. This point of view gives rise to two important observations, both pointing at some flaws of other theories. The first is that arguments should be compared as they are constructed, viz. step-by-step, while the second observation is that a knowledge representation language is needed with a defeasible conditional, since the material implication gives rise to arguments which are not constructed in actual reasoning. Accordingly, a nonmonotonic logic, default logic, is chosen as the formalism underlying the argumentation framework. The general structure of the framework allows for any standard for comparing pairs of arguments; in this study two such standards are investigated, based on specificity and on orderings of the premises.

Keywords

Neural Network General Structure Formal Analysis Important Observation Formal Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    C.E. Alchourrón and D. Makinson, Hierarchies of regulations and their logic, in:New Studies in Deontic Logic, ed. R. Hilpinen (Reidel, Dordrecht, 1981) pp. 125–148.Google Scholar
  2. [2]
    K.D. Ashley and E.L. Rissland, A case-based system for trade secrets law,Proc. 1st Int. Conf. on Artificial Intelligence and Law, Boston (1987) pp. 60–66.Google Scholar
  3. [3]
    G. Brewka, Preferred subtheories: an extended logical framework for default reasoning,Proc. IJCAI-1989, pp. 1043–1048.Google Scholar
  4. [4]
    G. Brewka,Nonmonotonic Reasoning: Logical Foundations of Commonsense, (Cambridge Univ. Press, 1991).Google Scholar
  5. [5]
    J. Delgrande, An approach to default reasoning based on a first-order conditional logic: revised report, Artificial Intelligence 36(1988)63–90.Google Scholar
  6. [6]
    A. v.d. Lieth Gardner,An Artificial Intelligence Approach to Legal Reasoning (MIT Press, 1987).Google Scholar
  7. [7]
    P. Gärdenfors,Knowledge in Flux. Modeling the Dynamics of Epistemic States (MIT Press, 1988).Google Scholar
  8. [8]
    K. Konolige, Hierarchic autoepistemic theories for nonmonotonic reasoning,Proc. AAAI-88, (1988).Google Scholar
  9. [9]
    F. Lin and Y. Shoham, Argument systems. A uniform basis for nonmonotonic reasoning,Proc. 1st Int. Conf. on Principles of Knowledge Representation and Reasoning (Morgan Kaufmann, 1989) pp. 245–255.Google Scholar
  10. [10]
    R. Loui and K. Stiefvater, Corrigenda to Poole's rules and a lemma of Simari-Loui, Department of Computer Science, Washington University, St. Louis (1992).Google Scholar
  11. [11]
    D. Nute, Defeasible reasoning: a philosophical analysis in Prolog, in:Aspects of Artificial Intelligence, ed. J.H. Fetzer (Kluwer, 1988) pp. 251–288.Google Scholar
  12. [12]
    J.L. Pollock, Defeasible reasoning, Cognitive Sco. 11(1987)481–518.Google Scholar
  13. [13]
    D.L. Poole, On the comparison of theories: Preferring the most specific explanation,Proc. IJCAI-1985, pp. 144–147.Google Scholar
  14. [14]
    D.L. Poole, A logical framework for default reasoning, Artificial Intelligence 36(1988)27–47.Google Scholar
  15. [15]
    H, Prakken, A tool in modelling disagreement in law: preferring the most specific argument,Proc. 3rd Int. Conf. on Artificial Intelligence and Law, Oxford, 1991 (ACM Press, 1991) pp. 165–174.Google Scholar
  16. [16]
    H. Prakken, Reasoning with normative hierarchies (extended abstract).Proc. 1st Int. Workshop on Deontic Logic and Computer Science, Amsterdam (1991) pp. 315–334.Google Scholar
  17. [17]
    H. Prakken, Logical tools for modelling legal argument, Doctoral Dissertation, Free University Amsterdam (1993).Google Scholar
  18. [18]
    R. Reiter, A logic for default reasoning, Artificial Intelligence 13(1980)81–132.Google Scholar
  19. [19]
    N. Rescher,Hypothetical Reasoning (North-Holland, Amsterdam, 1964).Google Scholar
  20. [20]
    N. Roos, What is on the machine's mind? Models for reasoning with incomplete and uncertain knowledge, Doctoral Dissertation, Technical University Delft (1991).Google Scholar
  21. [21]
    G. Sartor, Reasoning with hierarchies of premises: derivation versus assumption based approaches, Draft, University of Bologna (1992).Google Scholar
  22. [22]
    G.R. Simari and R.P Loui, A mathematical treatment of defeasible reasoning and its implementation, Artificial Intelligence 2(1992)125–157.Google Scholar
  23. [23]
    G.A.W. Vreeswijk, Abstract argumentation systems, to appear in Studia Logica.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Henry Prakken
    • 1
  1. 1.Computer/Law InstituteFree UniversityAmsterdamThe Netherlands

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