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The development of a “Logic of Argumentation”

  • Logical Methods
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Book cover IPMU '92—Advanced Methods in Artificial Intelligence (IPMU 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 682))

Abstract

A recurring problem with the development of decision support systems in medicine is the difficulty of eliciting precise numerical uncertainty values for large fragments of the domain. A prototype information system for general practitioners, the Oxford System of Medicine (OSM), addressed this problem by using an informal mechanism of argumentation. Arguments supporting and opposing the propositions of interest were identified when numerical uncertainty values where unavailable. We propose, in this paper, a proof theoretic model for reasoning under uncertainty which is motivated by the need to provide a formal underpinning for the OSM inference engine. As well as giving a presentation of a “Logic of Argumentation” (LA) as a labelled deduction system, we also discuss the development of a category theoretic semantics for LA.

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References

  1. S. Ambler: A Categorical Approach to the Semantics of Argumentation. Department of Computer Science Report, Queen Mary College, London (1992)

    Google Scholar 

  2. N. G. de Bruijn: Lambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem. Indagationes Mathematicae 34, 381–392 (1972)

    Google Scholar 

  3. T. Chard: Qualitative probability versus quantitative probability in clinical diagnosis: a study using a computer simulation. Medical Decision Making 11, 38–41 (1991)

    PubMed  Google Scholar 

  4. R.M. Dawes: The robust beauty of improper linear models in decision making. American Psychologist 34, 571–582 (1979)

    Article  Google Scholar 

  5. R. Dyckhoff: Contraction-free Sequent Calculi for Intuitionistic Logic. J. Symbolic Logic (to appear, 1992)

    Google Scholar 

  6. J. Fox, A.J. Glowinski, C. Gordon, S.J. Hajnal, M.J. O'Neil: Logic engineering for knowledge engineering. Artifical Intelligence in Medicine 2, 323–339 (1990)

    Google Scholar 

  7. J. Fox, D. A. Clark, A.J. Glowinski, M.J. O'Neil: Using predicate logic to integrate qualitative reasoning and classical decision theory. IEEE Trans. on Systems, Man, and Cybernetics 20, 347–357 (1990)

    Google Scholar 

  8. J. Fox, M. Clarke: Towards a formalisation of arguments in decision making. Proc. Stanford Spring Symposium on Argumentation and Belief. 92–99 (1991)

    Google Scholar 

  9. D. Gabbay: Labelled Deductive Systems. CIS Technical Report 90-22, University of Munich 1990

    Google Scholar 

  10. J.H. Gallier Logic for Computer Science. Chichester: John Wiley 1987

    Google Scholar 

  11. J. Girard, P. Taylor, Y. Lafont: Proofs and Types. Cambridge: Cambridge University Press 1989

    Google Scholar 

  12. A. Heyting: Intuitionism. An Introduction. Amsterdam: North-Holland Publ. Co 1956

    Google Scholar 

  13. J.R. Hindley, J.P. Seldin: Introduction to Combinators and λ-Calculus. Cambridge: Cambridge University Press 1986

    Google Scholar 

  14. G.M. Kelly: Basic Concepts of Enriched Category Theory. London Math. Soc. Lecture Note Series 64. Cambridge: Cambridge University Press 1982

    Google Scholar 

  15. J. Lambek, P.J. Scott: Introduction to higher order categorical logic. Cambridge: Cambridge University Press 1986

    Google Scholar 

  16. S.L. Lauritzen, D.J. Spiegelhalter: Local computations with probabilities on graphical structures and their application to expert systems. J. R. Statist. Soc. B. 50, 157–224 (1988)

    Google Scholar 

  17. J. Locke (1671). See: R.I. Aaron, J. Gibb (eds): An early draft of Locke's Essay. Oxford: Oxford University Press 1936

    Google Scholar 

  18. M. O'Neil, A.J. Glowinski: Evaluating and validating very large knowledge-based systems. Med. Inform. 15, 237–251 (1990)

    Google Scholar 

  19. G. Shafer: Non-additive Probabilities in the Work of Bernoulli and Lambert. Archive for History of Exact Sciences 19, 309–370 (1978)

    Article  Google Scholar 

  20. P.N. Wilson: Justification, computational efficiency and generalisation of the Dempster Shafer Theory. Research Report no. 15, Dept. of Computing and Math. Sciences, Oxford Polytechnic 1989 (also to appear in Artificial Intelligence)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Imperial Cancer Research Fund, Lincoln's Inn Fields, WC2A 3PX, London

    Paul Krause & John Fox

  2. Department of Computer Science and Statistics, Queen Mary and Westfield College, E1 4NS, London

    Simon Ambler

Authors
  1. Paul Krause
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  2. Simon Ambler
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  3. John Fox
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Editor information

Bernadette Bouchon-Meunier Llorenç Valverde Ronald R. Yager

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© 1993 Springer-Verlag

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Krause, P., Ambler, S., Fox, J. (1993). The development of a “Logic of Argumentation”. In: Bouchon-Meunier, B., Valverde, L., Yager, R.R. (eds) IPMU '92—Advanced Methods in Artificial Intelligence. IPMU 1992. Lecture Notes in Computer Science, vol 682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56735-6_48

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  • DOI: https://doi.org/10.1007/3-540-56735-6_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56735-6

  • Online ISBN: 978-3-540-47643-6

  • eBook Packages: Springer Book Archive

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