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Methods of Automated Reasoning

A tutorial

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Fundamentals of Artificial Intelligence

Part of the book series: Springer Study Edition ((SSE))

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Abstract

This chapter introduces into various aspects and methods of the formalization and automation of processes involved in performing inferences. It views automated inferencing as a machine-oriented simulation of human reasoning. In this sense classical deductive methods for first-order logic like resolution and the connection method are introduced as a derived form of natural deduction. The wide range of phenomena known as non-monotonic reasoning is represented by a spectrum of technical approaches ranging from the closed-world assumption for data bases to the various forms of circumscription. Meta-reasoning is treated as a particularly important technique for modeling many significant features of reasoning including self-reference. Various techniques of reasoning about uncertainty are presented that have become particularly important in knowledge-based systems applications. Many other methods and techniques (like reasoning with time involved) could only briefly — if at all — be mentioned.

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References

  1. Barr, A.B., Feigenbaum, E.A. (eds.), The Handbook of Artificial Intelligence, 1, W. Kaufmann, Los Altos (1981).

    MATH  Google Scholar 

  2. Beth, E.W., The foundations of mathematics, North-Holland, Amsterdam (1965).

    Google Scholar 

  3. Bibel, W., Programmieren in der Sprache der Prädikatenlogik, Habilitationsarbeit (abgelehnt), Technische Universität München (1975); shortened version: Prädikatives Programmieren, LNCS 33, Springer, Berlin, 274–283 (1975).

    Google Scholar 

  4. Bibel, W., A uniform approach to programming, Report No. 7633, Technische Universität München, Abtlg. Mathematik (1976).

    Google Scholar 

  5. Bibel, W., Automated theorem proving, Vieweg, Braunschweig (1982).

    Book  MATH  Google Scholar 

  6. Bibel, W., Matings in matrices, CACM 26, 844–852 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  7. Bibel, W., Knowledge representation from a deductive point of view, Proc. I IFAC Symposium Artificial Intelligence (V. M. Ponomaryov, ed.), Pergamon Press, Oxford, 37–48 (1984).

    Google Scholar 

  8. Bibel, W., First-order reasoning about knowledge and belief, Proc. Int. Conf. Artificial Intelligence and robotic control systems (I. Plander, ed.), North-Holland, Amsterdam, 9–16 (1984).

    Google Scholar 

  9. Bibel, W., Automated inferencing, J. Symbolic Computation 1, 245–260 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  10. Bibel, W., A deductive solution for plan generation, New Generation Computing 4 (1986).

    Google Scholar 

  11. Bowen, K.A., Kowalski, R., Amalgamating language and meta-language in logic programming, Logic Programming (K.L. Clark, S.-A. Tärnlund, eds.), Academic Press, London, 153–172 (1982).

    Google Scholar 

  12. Bowen, K.A., Weinberg, T., A meta-level extension of PROLOG, Technical Report, CIS-85–1, Syracuse University (1985).

    Google Scholar 

  13. Brown, J.S., de Kleer, J., The origin, form, and logic of qualitative physical laws, IJCAI-83 (A. Bundy, ed.), Kaufmann, Los Altos, 1158–1169 (1984).

    Google Scholar 

  14. Bundy, A., The computer modelling of mathematical reasoning, Academic Press (1983).

    MATH  Google Scholar 

  15. Clark, K.L., Negation as failure, Logic and Data Bases (H. Gallaire et al., eds.), Plenum Press, New York, 293–322 (1978).

    Chapter  Google Scholar 

  16. Clark, K.L., McCabe, F.G., The control facilities of IC-PROLOG, Expert systems in the Microelectronic Age (D. Michie, ed.), Edinburgh University Press (1979).

    Google Scholar 

  17. Cohen, P.R., Heuristic reasoning about uncertainty: an Artificial Intelligence approach, Pitman, Boston (1985).

    Google Scholar 

  18. de Finetti, B., Theory of probability, vol. 1, Wiley, London (1974).

    Google Scholar 

  19. Doyle, J., A truth maintenance system, Artificial Intelligence 12, 231–272 (1979).

    Article  MathSciNet  Google Scholar 

  20. Doyle, J., Circumscription and implicit definability, Non-monotonic Reasoning Workshop, AAAI, 57–67 (1984).

    Google Scholar 

  21. Duda, R.O., Hart, P.E., Nilsson, N.J., Subjective Bayesian methods for rule-based inference systems, Techn. Note 124, SRI International, AI Center, Menlo Park; also: Proc. NCC, AFIPS Press (1976).

    Google Scholar 

  22. Etherton, D.W., Mercer, R.E., Reiter, R., On the adequacy of predicate circumscription for closed-world reasoning, Proc. Non-monotonic Reasoning Workshop, AAAI, 70–81 (1984).

    Google Scholar 

  23. Feferman, S., Toward useful type-free theories I, JSL 49, 75–111 (1984).

    MATH  MathSciNet  Google Scholar 

  24. Gallagher, J., Transforming logic programs by specialising interpreters, Report, Dept. Computer Science, University of Dublin (1984).

    Google Scholar 

  25. Gallaire, H., Lasserre, C, Meta-level control for logic programming, Logic Programming (K.L. Clark, S.-A. Tärnlund, eds.), Academic Press, London (1982).

    Google Scholar 

  26. Genesereth, M.R., Ginsberg, M.L., Logic Programming, CACM 28, 933–941 (1985).

    Article  MathSciNet  Google Scholar 

  27. Gentzen, G., Untersuchungen über das logische Schliessen, Mathem. Zeitschr. 39, 176–210, (1935).

    Article  MathSciNet  Google Scholar 

  28. Gentzen, G., Untersuchungen über das logische Schliessen, Mathem. Zeitschr. 39, 405–431 (1935).

    Article  MathSciNet  Google Scholar 

  29. Glymour, C, Independence assumptions and Bayesian updating, Artificial Intelligence 25, 95–99 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  30. Gordon, J., Shortliffe, E.H., The Dempster-Shafer theory of evidence and its relevance to expert systems, Rule-based Expert Systems (B.G. Buchanan, E.H. Shortliffe, eds.), Addison-Wesley, Readings, ch. 13 (1984).

    Google Scholar 

  31. Green, C.C., Theorem proving by resolution as a basis for question-answering systems, Machine Intelligence 4, Elsevier, New York, 183 – 205 (1969).

    Google Scholar 

  32. Grosof, B., Default reasoning as circumscription, Proc. Non-monotonic Reasoning Workshop, AAAI, 115–124 (1984).

    Google Scholar 

  33. Haas, A.R., A syntactic theory of belief and action, Artificial Intelligence 28 (1986).

    Google Scholar 

  34. Hayes, P.J., Naive physics 1 — Ontology for liquids, Formal Theories of the Common-sense World (Hobbs, J.R., Moore, R.C., eds.), Ablex (1984).

    Google Scholar 

  35. Hintikka, J., Knowledge and belief: An introduction to the logic of the two notions, Cornell University Press (1962).

    Google Scholar 

  36. Jaffar, J., Lassez, J.-L., Lloyd, J., Completeness of the negation as failure rule, IJCAI-83 (A. Bundy, ed.), Kaufmann, Los Altos, 500–506 (1983).

    Google Scholar 

  37. Kadesch, R.R., Subjective inference with multiple evidence, Artificial Intelligence 28 (1986).

    Google Scholar 

  38. Kowalski, R.A., Sergot, M., A logic-based calculus of events, New Generation Computing 4, 67–95 (1986).

    Article  Google Scholar 

  39. Kripke, S., Semantical analysis of modal logic, Zeitschrift f. Mathem. Logik u. Grundlagen der Mathem. 9, 67–96 (1962).

    Article  MathSciNet  Google Scholar 

  40. Levesque, H., A logic of knowledge and active belief, Proc. AAAI-84 (1984).

    Google Scholar 

  41. Lifschitz, V., Computing circumscription, Proc. IJCAI-85, Kaufmann, Los Altos, 121–127 (1985).

    Google Scholar 

  42. Lifschitz, V., On the satisfiability of circumscription, Artificial Intelligence 28, 17–27 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  43. Lloyd, J.W., Foundations of logic programming, Springer, Berlin (1984).

    Book  MATH  Google Scholar 

  44. McCarthy, J., First-order theories of individual concepts and propositions, Expert Systems in the Micro-electronic Age (D. Michie, ed.), Edinburgh University Press, 271–287 (1979).

    Google Scholar 

  45. McCarthy, J., Circumscription — a form of non-monotonic reasoning, Artificial Intelligence 13, 27–39 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  46. McCarthy, J., Applications of circumscription to formalizing common sense knowledge, Proc. Non-monotonic Reasoning Workshop, AAAI, 295–324 (1984).

    Google Scholar 

  47. Minker, J., Perlis, D., Completeness results for circumscription, Artificial Intelligence 28, 29–42 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  48. Moore, R.C., Semantical considerations on non-monotonic logic, IJCAI-83 (A. Bundy, ed.), Kaufmann, Los Altos, 272–279 (1983).

    Google Scholar 

  49. Pearl, J., On evidential reasoning in a hierarchy of hypothesis, Artificial Intelligence 28, 9–16 (1986).

    Article  Google Scholar 

  50. Perlis, D., Languages with self-reference, Artificial Intelligence 25, 301–322 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  51. Quinlan, J.R., Internal consistency in plausible reasoning systems, New Generation Computing 3, 157–180 (1985).

    Article  Google Scholar 

  52. Reiter, R., A logic for default reasoning, Artificial Intelligence 13, 81–132 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  53. Reiter, R., Circumscription implies predicate completion (sometimes), Proc. AAAI-82, 418–420 (1982).

    Google Scholar 

  54. Reiter, R., Towards a logical reconstruction of relational database theory, On Conceptual Modelling: perspectives from Artificial Intelligence, databases, and programming languages (M.L. Brodie et al., eds.), Springer, Berlin, 191–238 (1983).

    Google Scholar 

  55. Schütte, K., Proof theory, Springer, Berlin (1977).

    Book  MATH  Google Scholar 

  56. Shafer, G., A mathematical theory of evidence, Princeton University Press, Princeton (1976).

    MATH  Google Scholar 

  57. Shepherdson, J.C., Negation as failure: A comparison of Clark’s completed data base and Reiter’s closed-world assumption, Report PM-84–01, School of Mathematics, University of Bristol (1984).

    Google Scholar 

  58. Shoham, Y., Ten requirements for a theory of change, New Generation Computing 3, 467–477 (1985).

    Article  Google Scholar 

  59. Turner, R., Logics for Artificial Intelligence, E. Horwood, Chichester (1984).

    Google Scholar 

  60. Weyrauch, R., Prolegomena to a theory of mechanized formal reasoning, Artificial Intelligence 13, 133–197 (1980).

    Article  MathSciNet  Google Scholar 

  61. Winston, P.H., Learning and reasoning by analogy, CACM 23, 689–703 (1979).

    Article  Google Scholar 

  62. Zadeh, L.A., A computational approach to fuzzy quantifiers in natural languages, Comp. & Maths. with Appls. 9, 149–184 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  63. Zadeh, L.A., The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems 11, 199–227 (1983).

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Technische Universität München, Germany

    Wolfgang Bibel

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  1. Wolfgang Bibel
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Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Postfach 202420, D-8000, München 2, Germany

    W. Bibel

  2. LIFIA-IMAG, BP 68, F-38402, St. Martin d’Hères Cédex, France

    Ph. Jorrand

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© 1987 Springer-Verlag Berlin Heidelberg

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Bibel, W. (1987). Methods of Automated Reasoning. In: Bibel, W., Jorrand, P. (eds) Fundamentals of Artificial Intelligence. Springer Study Edition. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-40145-3_5

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  • DOI: https://doi.org/10.1007/978-3-662-40145-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-39157-0

  • Online ISBN: 978-3-662-40145-3

  • eBook Packages: Springer Book Archive

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