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Automated Abduction

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Book cover Computational Logic: Logic Programming and Beyond

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2408))

Abstract

In this article, I review Peirce’s abduction in the context of Artificial Intelligence. First, I connect abduction from first-order theories with nonmonotonic reasoning. In particular, I consider relationships between abduction, default logic, and circumscription. Then, based on a first-order characterization of abduction, I show a design of abductive procedures that utilize automated deduction. With abductive procedures, proof procedures for nonmonotonic reasoning are also obtained from the relationship between abduction and nonmonotonic reasoning.

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References

  1. Chitta Baral. Abductive reasoning through filtering. Artificial Intelligence, 120:1–28, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  2. Nicole Bidoit and Christine Froidevaux. Minimalism subsumes default logic and circumscription. In: Proceedings of LICS-87, pages 89–97, 1987.

    Google Scholar 

  3. Genevieve Bossu and Pierre Siegel. Saturation, nonmonotonic reasoning, and the closed-world assumption. Artificial Intelligence, 25:13–63, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Bondarenko, P. M. Dung, R. A. Kowalski, and F. Toni. An abstract, argumentation-theoretic approach to default reasoning. Artificial Intelligence, 93:63–101, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  5. Craig Boutilier and Verónica Becher. Abduction as belief revision. Artificial Intelligence, 77:43–94, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  6. Tom Bylander, Dean Allemang, Michael C. Tanner, and John R. Josephson. The computational complexity of abduction. Artificial Intelligence, 49:25–60, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  7. Chin-Liang Chang and Richard Char-Tung Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973.

    MATH  Google Scholar 

  8. Viorica Ciorba. A query answering algorithm for Lukaszewicz’ general open default theory. In: Proceedings of JELIA’ 96, Lecture Notes in Artificial Intelligence, 1126, pages 208–223, Springer, 1996.

    Google Scholar 

  9. Luca Console, Daniele Theseider Dupre, and Pietro Torasso. On the relationship between abduction and deduction. Journal of Logic and Computation, 1:661–690, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  10. P.T. Cox and T. Pietrzykowski. Causes for events: their computation and applications. In: Proceedings of the 8th International Conference on Automated Deduction, Lecture Notes in Computer Science, 230, pages 608–621, Springer, 1986.

    Google Scholar 

  11. Marita Cialdea Mayer and Fiora Pirri. First order abduction via tableau and sequent calculi. Journal of the IGPL, 1(1):99–117, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  12. Marita Cialdea Mayer and Fiora Pirri. Abduction is not deduction-in-reverse. Journal of the IGPL, 4(1):95–108, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  13. Hendrik Decker. An extension of SLD by abduction and integrity maintenance for view updating in deductive databases. In: Proceedings of the 1996 Joint International Conference and Symposium on Logic Programming, pages 157–169, MIT Press, 1996.

    Google Scholar 

  14. Johan de Kleer. An assumption-based TMS. Artificial Intelligence, 28:127–162, 1986.

    Article  Google Scholar 

  15. Alvaro del Val. Approximate knowledge compilation: the first order case. In: Proceedings of AAAI-96, pages 498–503, AAAI Press, 1996.

    Google Scholar 

  16. Alvaro del Val. A new method for consequence finding and compilation in restricted languages. In: Proceedings of AAAI-99, pages 259–264, AAAI Press, 1999.

    Google Scholar 

  17. Alvaro del Val. On some tractable classes in deduction and abduction. Artificial Intelligence, 116:297–313, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  18. Robert Demolombe and Luis Fariñas del Cerro. An inference rule for hypothesis generation. In: Proceedings of IJCAI-91, pages 152–157, 1991.

    Google Scholar 

  19. Marc Denecker and Danny De Schreye. SLDNFA: an abductive procedure for abductive logic programs. Journal of Logic Programming, 34:111–167, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  20. Marc Denecker and Antonis Kakas, editors. Special Issue: Abductive Logic Programming. Journal of Logic Programming, 44(1–3), 2000.

    Google Scholar 

  21. Thomas Eiter and George Gottlob. The complexity of logic-based abduction. Journal of the ACM, 42(1):3–42, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  22. Thomas Eiter, George Gottlob, and Nicola Leone. Semantics and complexity of abduction from default theories. Artificial Intelligence, 90:177–223, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  23. Kave Eshghi. A tractable class of abduction problems. In: Proceedings of IJCAI-93, pages 3–8, 1993.

    Google Scholar 

  24. David W. Etherington. Reasoning with Incomplete Information. Pitman, London, 1988.

    MATH  Google Scholar 

  25. Joseph J. Finger. Exploiting constraints in design synthesis. Ph.D. Dissertation, Technical Report STAN-CS-88-1204, Department of Computer Science, Stanford University, Stanford, CA, 1987.

    Google Scholar 

  26. Peter A. Flach and Antonis C. Kakas, editors. Abduction and Induction—Essays on their Relation and Integration. Kluwer Academic, 2000.

    Google Scholar 

  27. Peter A. Flach and Antonis C. Kakas. Abductive and inductive reasoning: background and issues. In: Antonis C. Kakas, editors. Abduction and Induction—Essays on their Relation and Integration. Kluwer Academic [26], pages 1–27, 2000.

    Google Scholar 

  28. T. H. Fung and R. Kowalski. The iff procedure for abductive logic programming. Journal of Logic Programming, 33:151–165, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  29. Michael Gelfond and Vladimir Lifschitz. Classical negation in logic programs and disjunctive databases. New Generation Computing, 9:365–385, 1991.

    Google Scholar 

  30. Michael Gelfond, Halina Przymusinska, and Teodor Przymusinski. On the relationship between circumscription and negation as failure. Artificial Intelligence, 38:75–94, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  31. Matthew L. Ginsberg. A circumscriptive theorem prover. Artificial Intelligence, 39:209–230, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  32. Nicolas Helft, Katsumi Inoue, and David Poole. Query answering in circumscription. In: Proceedings of IJCAI-91, pages 426–431, 1991.

    Google Scholar 

  33. Carl Gustav Hempel. Philosophy of Natural Science. Prentice-Hall, New Jersey, 1966.

    Google Scholar 

  34. Katsumi Inoue. An abductive procedure for the CMS/ATMS. In: João P. Martins and Michael Reinfrank, editors, Truth Maintenance Systems, Lecture Notes in Artificial Intelligence, 515, pages 34–53, Springer, 1991.

    Google Scholar 

  35. Katsumi Inoue. Linear resolution for consequence finding. Artificial Intelligence, 56:301–353, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  36. Katsumi Inoue. Studies on abductive and nonmonotonic reasoning. Doctoral Dissertation, Kyoto University, Kyoto, 1992.

    Google Scholar 

  37. Katsumi Inoue. Principles of abduction. Journal of Japanese Society for Artificial Intelligence, 7(1):48–59, 1992 (in Japanese).

    Google Scholar 

  38. Katsumi Inoue. Hypothetical reasoning in logic programs. Journal of Logic Programming, 18(3):191–227, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  39. Katsumi Inoue. Induction, abduction, and consequence-finding. In: Céline Rouveirol and Michèle Sebag, editors, Proceedings of the 11th International Conference on Inductive Logic Programming, Lecture Notes in Artificial Intelligence, 2157, pages 65–79, Springer, 2001.

    Google Scholar 

  40. Katsumi Inoue and Hiromasa Haneda. Learning abductive and nonmonotonic logic programs. In: Antonis C. Kakas, editors. Abduction and Induction—Essays on their Relation and Integration. Kluwer Academic [26], pages 213–231, 2000.

    Google Scholar 

  41. Katsumi Inoue and Nicolas Helft. On theorem provers for circumscription. In: Peter F. Patel-Schneider, editor, Proceedings of the 8th Biennial Conference of the Canadian Society for Computational Studies of Intelligence, pages 212–219, Morgan Kaufmann, 1990.

    Google Scholar 

  42. Katsumi Inoue, Yoshihiko Ohta, Ryuzo Hasegawa, and Makoto Nakashima. Bottom-up abduction by model generation. In: Proceedings of IJCAI-93, pages 102–108, Morgan Kaufmann, 1993.

    Google Scholar 

  43. Katsumi Inoue and Chiaki Sakama. Abductive framework for nonmonotonic theory change. In: Proceedings of IJCAI-95, pages 204–210, Morgan Kaufmann, 1995.

    Google Scholar 

  44. Katsumi Inoue and Chiaki Sakama. A fixpoint characterization of abductive logic programs. Journal of Logic Programming, 27(2):107–136, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  45. Katsumi Inoue and Chiaki Sakama. Negation as failure in the head. Journal of Logic Programming, 35(1):39–78, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  46. Katsumi Inoue and Chiaki Sakama. Abducing priorities to derive intended conclusions. In: Proceedings of IJCAI-99, pages 44–49, Morgan Kaufmann, 1999.

    Google Scholar 

  47. Katsumi Inoue and Chiaki Sakama. Computing extended abduction through transaction programs. Annals of Mathematics and Artificial Intelligence, 25(3,4):339–367, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  48. Koji Iwanuma and Katsumi Inoue. Minimal conditional answer computation and SOL. To appear, 2002.

    Google Scholar 

  49. Koji Iwanuma, Katsumi Inoue, and Ken Satoh. Completeness of pruning methods for consequence finding procedure SOL. In: Peter Baumgartner and Hantao Zhang, editors, Proceedings of the 3rd International Workshop on First-Order Theorem Proving, pages 89–100, Research Report 5-2000, Institute for Computer Science, University of Koblenz, Germany, 2000.

    Google Scholar 

  50. John R. Jpsephson and Susan G. Josephson. Abductive Inference: Computation, Philosophy, Technology. Cambridge University Press, 1994.

    Google Scholar 

  51. Antonis Kakas and Marc Denecker. Abductive logic programming. In this volume, 2002.

    Google Scholar 

  52. A.C. Kakas and P. Mancarella. Generalized stable models: a semantics for abduction. In: Proceedings of ECAI-90, pages 385–391, 1990.

    Google Scholar 

  53. A. C. Kakas, R. A. Kowalski, and F. Toni. Abductive logic programming. Journal of Logic and Computation, 2:719–770, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  54. A. C. Kakas, R. A. Kowalski, and F. Toni. The role of abduction in logic programming. In: Dov M. Gabbay, C. J. Hogger, and J. A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 5, pages 235–324, Oxford University Press, 1998.

    Google Scholar 

  55. Kurt Konolige. Abduction versus closure in causal theories. Artificial Intelligence, 53:255–272, 1992.

    Article  MathSciNet  Google Scholar 

  56. Kurt Konolige. Abductive theories in artificial intelligence. In: Gerhard Brewka, editor, Principles of Knowledge Representation, pages 129–152, CSLI Publications & FoLLI, 1996.

    Google Scholar 

  57. R. Kowalski. The case for using equality axioms in automated demonstration. In: Proceedings of the IRIA Symposium on Automatic Demonstration, Lecture Notes in Mathematics, 125, pages 112–127, Springer, 1970.

    Google Scholar 

  58. Robert A. Kowalski. Logic for Problem Solving. Elsevier, New York, 1979.

    MATH  Google Scholar 

  59. Robert Kowalski and Donald G. Kuehner. Linear resolution with selection function. Artificial Intelligence, 2:227–260, 1971.

    Article  MATH  MathSciNet  Google Scholar 

  60. Robert A. Kowalski and Francesca Toni. Abstract argumentation. Artificial Intelligence and Law, 4:275–296, 1996.

    Article  Google Scholar 

  61. Char-Tung Lee. A completeness theorem and computer program for finding theorems derivable from given axioms. Ph.D. thesis, Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA, 1967.

    Google Scholar 

  62. R. Letz, K. Mayer, and C. Goller. Controlled integration of the cut rule into connection tableau calculi. Journal of Automated Reasoning, 13(3):297–337, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  63. Hector J. Levesque. A knowledge-level account of abduction (preliminary version). In: Proceedings of IJCAI-89, pages 1061–1067, 1989.

    Google Scholar 

  64. Vladimir Lifschitz. Computing circumscription. In: Proceedings of IJCAI-85, pages 121–127, 1985.

    Google Scholar 

  65. Jorge Lobo and Carlos Uzcátegui. Abductive consequence relations. Artificial Intelligence, 89:149–171, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  66. Donald W. Loveland. Automated Theorem Proving: A Logical Basis. North-Holland, Amsterdam, 1978.

    MATH  Google Scholar 

  67. Lorenzo Magnani. Abduction, Reason, and Science—Processes of Discovery and Explanation. Kluwer Academic, 2001.

    Google Scholar 

  68. Pierre Marquis. Consequence finding algorithms. In: Dov M. Gabbay and Philippe Smets, editors, Handbook for Defeasible Reasoning and Uncertain Management Systems, Volume 5, pages 41–145, Kluwer Academic, 2000.

    Google Scholar 

  69. Philippe Mathieu and Jean-Paul Delahaye. A kind of logical compilation for knowledge bases. Theoretical Computer Science, 131:197–218, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  70. John McCarthy. Circumscription—a form of non-monotonic reasoning. Artificial Intelligence, 13:27–39, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  71. John McCarthy. Applications of circumscription to formalizing common-sense knowledge. Artificial Intelligence, 28:89–116, 1986.

    Article  MathSciNet  Google Scholar 

  72. Eliana Minicozzi and Raymond Reiter. A note on linear resolution strategies in consequence-finding. Artificial Intelligence, 3:175–180, 1972.

    Article  MATH  MathSciNet  Google Scholar 

  73. Jack Minker. On indefinite databases and the closed world assumption. In: Proceedings of the 6th International Conference on Automated Deduction, Lecture Notes in Computer Science, 138, pages 292–308, Springer, 1982.

    Chapter  Google Scholar 

  74. Robert C. Moore. Semantical considerations on nonmonotonic logic. Artificial Intelligence, 25:75–94, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  75. Stephen Muggleton. Inverse entailment and Progol. New Generation Computing, 13:245–286, 1995.

    Google Scholar 

  76. Shan-Hwei Nienhuys-Cheng and Ronald de Wolf. Foundations of Inductive Logic Programming. Lecture Notes in Artificial Intelligence, 1228, Springer, 1997.

    Google Scholar 

  77. Yoshihiko Ohta and Katsumi Inoue. Incorporating top-down information into bottom-up hypothetical reasoning. New Generation Computing, 11:401–421, 1993.

    MATH  Google Scholar 

  78. Gabriele Paul. AI approaches to abduction. In: Dov M. Gabbay and Philippe Smets, editors, Handbook for Defeasible Reasoning and Uncertain Management Systems, Volume 4, pages 35–98, Kluwer Academic, 2000.

    Google Scholar 

  79. Charles Sanders Peirce. Elements of Logic. In: Charles Hartshorne and Paul Weiss, editors, Collected Papers of Charles Sanders Peirce, Volume II, Harvard University Press, Cambridge, MA, 1932.

    Google Scholar 

  80. Ramón Pino-Pérez and Carlos Uzcátegui. Jumping to explanations versus jumping to conclusions. Artificial Intelligence, 111:131–169, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  81. David Poole. A logical framework for default reasoning. Artificial Intelligence, 36:27–47, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  82. David Poole. Explanation and prediction: an architecture for default and abductive reasoning. Computational Intelligence, 5:97–110, 1989.

    Article  Google Scholar 

  83. David Poole. Compiling a default reasoning system into Prolog. New Generation Computing, 9:3–38, 1991.

    Article  MATH  Google Scholar 

  84. David Poole, Randy Goebel, and Romas Aleliunas. Theorist: a logical reasoning system for defaults and diagnosis. In: Nick Cercone and Gordon McCalla, editors, The Knowledge Frontier: Essays in the Representation of Knowledge, pages 331–352, Springer, New York, 1987.

    Google Scholar 

  85. Harry E. Pople, Jr. On the mechanization of abductive logic. In: Proceedings of IJCAI-73, pages 147–152, 1973.

    Google Scholar 

  86. Teodor C. Przymusinski. An algorithm to compute circumscription. Artificial Intelligence, 38:49–73, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  87. Raymond Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  88. Raymond Reiter and Johan de Kleer. Foundations of assumption-based truth maintenance systems: preliminary report. In: Proceedings of AAAI-87, pages 183–187, 1987.

    Google Scholar 

  89. J.A. Robinson. A machine-oriented logic based on the resolution principle. Journal of the ACM, 12:23–41, 1965.

    Article  MATH  Google Scholar 

  90. Olivier Roussel and Philippe Mathieu. Exact knowledge compilation in predicate calculus: the partial achievement case. In: Proceedings of the 14th International Conference on Automated Deduction, Lecture Notes in Artificial Intelligence, 1249, pages 161–175, Springer, 1997.

    Google Scholar 

  91. Murray Shanahan. Prediction is deduction but explanation is abduction. In: Proceedings of IJCAI-89, pages 1055–1060, Morgan Kaufmann, 1989.

    Google Scholar 

  92. Bart Selman and Hector J. Levesque. Support set selection for abductive and default reasoning. Artificial Intelligence, 82:259–272, 1996.

    Article  MathSciNet  Google Scholar 

  93. Pierre Siegel, Représentation et utilization de la connaissance en calcul propo-sitionnel. Thèse d’État, Université d’Aix-Marseille II, Luminy, France, 1987 (in French).

    Google Scholar 

  94. Pierre Siegel and Camilla Schwind. Hypothesis theory for nonmonotonic reasoning. In: Proceedings of the Workshop on Nonstandard Queries and Nonstandard Answers, pages 189–210, 1991.

    Google Scholar 

  95. J.R. Slagle, C.L. Chang, and R.C.T. Lee, Completeness theorems for semantic resolution in consequence-finding. In: Proceedings of IJCAI-69, pages 281–285, Morgan Kaufmann, 1969.

    Google Scholar 

  96. Mark E. Stickel. Rationale and methods for abductive reasoning in natural-language interpretation. In: R. Studer, editor, Natural Language and Logic, Proceedings of the International Scientific Symposium, Lecture Notes in Artificial Intelligence, 459, pages 233–252, Springer, 1990.

    Google Scholar 

  97. Mark E. Stickel. Upside-down meta-interpretation of the model elimination theorem-proving procedure for deduction and abduction. Journal of Automated Reasoning, 13(2):189–210, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  98. Akihiro Yamamoto. Using abduction for induction based on bottom generalization. In: Antonis C. Kakas, editors. Abduction and Induction—Essays on their Relation and Integration. Kluwer Academic [26], pages 267–280, 2000.

    Google Scholar 

  99. Eiko Yamamoto and Katsumi Inoue. Implementation of SOL resolution based on model elimination. Transactions of Information Processing Society of Japan, 38(11):2112–2121, 1997 (in Japanese).

    MathSciNet  Google Scholar 

  100. Wlodek Zadrozny. On rules of abduction. Annals of Mathematics and Artificial Intelligence, 9:387–419, 1993.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Kobe University, Rokkodai, Nada, Kobe, 657-8501, Japan

    Katsumi Inoue

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  1. Katsumi Inoue
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Editors and Affiliations

  1. Department of Computer Science, University of Cyprus, 75 Kallipoleos St., 1678, Nicosia, Cyprus

    Antonis C. Kakas

  2. Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen’s Gate, London, SW7 2BZ, UK

    Fariba Sadri

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Inoue, K. (2002). Automated Abduction. In: Kakas, A.C., Sadri, F. (eds) Computational Logic: Logic Programming and Beyond. Lecture Notes in Computer Science(), vol 2408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45632-5_13

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