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On rules of abduction

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Abstract

We present a logical theory of abduction based on the idea of recognizing explanation, or abduction, as a separate reasoning activity. We describe a formalism for writing rules of abduction; furthermore, we define a validity criterion for such rules. The criterion is based on the concept of invariants. This idea allows us to link abduction with induction and deduction. We believe that the three types of inference rules can best be understood in terms of symmetry, i.e. types of relations they preserve, namely: explainability, falsifiability and truth. We also formulate a model theory of abduction and link it with a proof theory. We discuss a variety of rules of abduction and argue that logical forms of abduction do not have to be restricted to the reversemodus ponens. These rules are used to describe such tasks as word-sense disambiguation and anaphora resolution in natural language processing, as well as abduction-based diagnosis.

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References

  1. A. Anderson and N. Belnap,Entailment, The Logic of Relevance and Necessity (Princeton University Press, Princeton, NJ, 1975).

    Google Scholar 

  2. L. Braden-Harder and W. Zadrozny, Lexicons for broad coverage semantics, in:Lexical Acquisition: Using On-Line Resources to Build a Lexicon, ed. U. Zernik (Lawrence Erlbaum Associates, Hillsdale, NJ, 1991) pp. 369–388.

    Google Scholar 

  3. P. Brezillon,Proc. ECAI'92 Workshop W15 on Improving the Use of Knowledge-Based Systems with Explanations, Report No. 92/21, Institute Blaise Pascal, 4, Place Jussies, Paris (1992).

    Google Scholar 

  4. A. Brogi, E. Lamma, P. Mancarella and P. Mello, Abductive reasoning in a multi-theory framework, in:Trends in Artificial Intelligence, ed. E. Ardizzone, S. Galio and F. Sorbello, Lecture Notes in Computer Science, Vol. 549 (Springer, New York, 1991) pp. 137–146.

    Google Scholar 

  5. A. Chandra and D. Harel, Computable queries for relational data bases, J. Comp. Syst. Sci. 21(1980)156–178.

    Google Scholar 

  6. E. Charniak and R. Goldman, A logic for semantic interpretation,Proc. 26th Annual Meeting of the ACL, Buffalo, NY (1988) pp. 87–94.

  7. J. de Kleer and J. Brown, A qualitative physics based on confluences, Artificial Intelligence 24(1984)7–83.

    Google Scholar 

  8. J. de Kleer, A.K. Mackworth and R Reiter, Characterizing diagnoses and systems. Artificial Intelligence 56(1992)197–222.

    Google Scholar 

  9. J. de Kleer and B.C. Williams, Focusing the diagnostic engine, presented at1st Int. Workshop on Principles of Diagnosis, Standford, CA (1990).

  10. J. de Kleer and B. Williams, Diagnosing multiple faults, Artificial Intelligence 32(1987)97–130.

    Google Scholar 

  11. H. Geffner, Causal theories for nonmonotonic reasoning, in:Proc. AAAI-90 (AAAI Press/MIT Press, Cambridge, MA, 1990) pp. 524–530.

    Google Scholar 

  12. M. Genesereth, The use of design descriptions in automated diagnosis, Artificial Intelligence 24(1984)411–436.

    Google Scholar 

  13. J.J. Gibson,The Senses Considered as Perceptual Systems (Houghton Mifflin, Boston, MA, 1966).

    Google Scholar 

  14. G. Hirst,Semantic Interpretation and the Resolution of Ambiguity (Cambridge University Press, Cambridge, UK, 1987).

    Google Scholar 

  15. J. Hobbs, M. Stickel, P. Martin and D. Edwards, Interpretation as abduction,Proc. 26th Annual Meeting of the Association for Computational Linguistics, ACL (ACL, Buffalo, NY, 1988) pp. 95–103.

    Google Scholar 

  16. J. Jaffar and J.L. Lassez, Constraint logic programming,14th Annual Symp. on Prin. Progr. Langu. (POPL), ACM (1987).

  17. A. Kakas and P. Mancarella, Generalized stable models: a semantic for abduction,Proc. 9th Eur. Conf. on Artificial Intelligence (Pitman, 1990).

  18. H. Levesque, A logic of implicit and explicit beliefs,AAAI-84, Austin, TX (1984) pp. 198–202.

  19. H. Levesque, A knowledge level account of abduction,Proc. IJCAI-89, Detroit, MI (1989) pp. 1061–1067.

  20. D. Marr,Vision (Freeman, San Francisco, 1982).

    Google Scholar 

  21. R. Michalski, J. Carbonell and T. Mitchell,Machine Learning: An Artificial Intelligence Approach (Tioga, Palo Alto, CA, 1983).

    Google Scholar 

  22. R. Michalski, J. Carbonell and T. Mitchell,Machine Learning: An Artificial Intelligence Approach, Vol II (Kaufmann, Los Altos, 1986).

    Google Scholar 

  23. H.T. Ng and R.J. Mooney, The role of coherence in adbductive explanation, in:Proc. AAAI-90 (AAAI Press/MIT Press, Cambridge, MA, 1990) pp. 337–342.

    Google Scholar 

  24. P. Patel-Schneider, A decidable first order logic for knowledge representation,Proc. IJCAI-85 (AAAI, 1985) pp. 455–458.

  25. J. Pearl, Embracing causality in formal reasoning, Artificial Intelligence 35(1988)259–271.

    Google Scholar 

  26. D. Poole, Representing knowledge for logic-based diagnosis,Proc. Int. Conf. on Fifth Generation Computer Systems, Tokyo (1988).

  27. D. Poole, A logical framework for default reasoning, Artificial Intelligence 36(1988)27–47.

    Google Scholar 

  28. D. Poole, Explanation and prediction: an architecture for default and abductive reasoning, Computational Intelligence 5(1989)97–110.

    Google Scholar 

  29. D. Poole, Normality and faults in logic-based diagnosis,Proc. IJCAI-89, Detroit, MI (1989) pp. 1304–1310.

  30. J. Reggia, Abductive inference, in:Expert Systems in Government Symposium, ed. K.N. Karma (IEEE, 1985) pp. 484–489.

  31. J. Reggia, D. Nau and Y. Wang, Diagnostic expert systems based on a set covering model, Int. J. Man-Mach. Stud. 19(1983)437–460.

    Google Scholar 

  32. R. Reiter, A theory of diagnosis from first principles, Artificial Intelligence 32(1987)57–95.

    Google Scholar 

  33. R. Reiter and J. de Kleer, Foundations of assumption-based truth maintenance systems,Proc. AAAI-87, Seattle, Washington (1987) pp. 183–188.

  34. B.C. Van Fraassen,Laws and Symmetry (Clarendon Press, Oxford, 1989).

    Google Scholar 

  35. H. Weyl,Symmetry (Princeton University Press, Princeton, NJ, 1952).

    Google Scholar 

  36. M.R. Wick and W.B. Thompson, Reconstructive expert system explanations, Artificial Intelligence 54(1992)33–70.

    Google Scholar 

  37. E.P. Wigner,Symmetries and Reflections (Indiana University Press, Bloomington, IN, 1967).

    Google Scholar 

  38. W. Zadrozny, A theory of default reasoning,Proc. AAAI-87, Seattle, Washington, 1987) pp. 385–390.

  39. W. Zadrozny, The logic od abduction (Preliminary Report), presented at1st Int. Workshop on Principles of Diagnosis, Stanford, CA (1990).

  40. W. Zadrozny, Abductive rules for natural language understanding,Proc. Int. Conf. on Current Issues in Computational Linguistics, Penang, Malaysia (1991) pp. 248–261.

  41. W. Zadrozny, Explanations at the knowledge level, in:Proc. 10th Eur. Conf. on Artificial Intelligence ECAI'92, ed. B. Neumann (Wiley, Chichester, UK, 1992) pp. 344–348.

    Google Scholar 

  42. W. Zadrozny, Reasoning with background knowledge — a three-level theory, Computational Intelligence (1994), to appear.

  43. W. Zadrozny, Is there a prototypical rule of abduction?, J. Exp. Theor. Artificial Intelligence 5(1993), to appear.

  44. W. Zadrozny and K. Jensen, Semantics of paragraphs, Computational Linguistics 17(1991)171–210.

    Google Scholar 

  45. W. Zadrozny and M.M. Kokar, A logical model of machine learning: A study of vague predicates, in:Change of Representation and Inductive Bias, ed. D.P. Benjamin (Kluwer, Boston, MA, 1990).

    Google Scholar 

  46. A. Zee,Fearful Symmetry (Collier Books, Macmillan, New York, NY, 1986).

    Google Scholar 

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  1. T.J. Watson Research Center, IBM Research, P.O. Box 704, 10598, Yorktown Heights, NY, USA

    Wlodek Zadrozny

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  1. Wlodek Zadrozny
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Zadrozny, W. On rules of abduction. Ann Math Artif Intell 9, 387–419 (1993). https://doi.org/10.1007/BF01530940

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