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Abstract

When reasoning with implicitly defined contexts or theories, a general notion of proof in context is more appropriate than classical uses of reflection rules. Proofs in a multicontext framework can still be carried out by switching to a context, reasoning within it, and exporting the result. Context switching however does not correspond to reflection or reification but involves changing the level of nesting of theory within another theory. We introduce a generalised rule for proof in context and a convenient notation to express nesting of contexts, which allows us to carry out reasoning in and across contexts in a safe and natural way.

Keywords

Inference Rule Implicit Theory Natural Deduction Context Switching Referential Statement 
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.
    P. Aczel (1988). Non-well-founded sets, CSLI lecture notes, 12, Center for the Study of Language and Information, Stanford, California.Google Scholar
  2. 2.
    L. C. Aiello, d. Nardi, M. Schaerf (1988). Reasoning about Knowledge and Ignorance, in International Conference of 5th generation Computer System, pages 618–627, Tokyo.Google Scholar
  3. 3.
    G. Attardi and M. Simi (1984). Metalanguage and reasoning across viewpoints, in ECAI84: Advances in Artificial Intelligence, T. O'Shea (ed.), Elsevier Science Publishers, Amsterdam.Google Scholar
  4. 4.
    G. Attardi and M. Simi (1991). Reflections about reflection, in Allen, J. A., Fikes, R., and Sandewall, E. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference. Morgan Kaufmann, San Mateo, California.Google Scholar
  5. 5.
    G. Attardi and M. Simi (1993). A formalisation of viewpoints, TR-93-062, International Computer Science Institute, Berkeley.Google Scholar
  6. 6.
    G. Attardi and M. Simi (1994). Proofs in context, in Doyle, J. and Torasso, P. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference. Morgan Kaufmann, San Mateo, California.Google Scholar
  7. 7.
    K.A. Bowen and R.A. Kowalski (1982). Amalgamating language and metalanguage in logic programming, in Logic Programming, K. Clark and S. Tarnlund (eds.), Academic Press, 153–172.Google Scholar
  8. 8.
    S. Buvač and I.A. Mason (1993). Propositional Logic in Context, Proc. of the Eleventh AAAI Conference, Washington DC, 412–419.Google Scholar
  9. 9.
    A. Cimatti and L. Serafini (1994). Multi Agent Reasoning with Belief Contexts: the Approach and a Case Study”, proceedings of ECAI-94, Workshop on Agent Theories, Architectures, and Languages.Google Scholar
  10. 10.
    F. Giunchiglia, L. Serafini, Multilanguage hierarchical logics (or: how we can do without modal logics), Artificial Intelligence, 65:29–70, 1994.Google Scholar
  11. 11.
    R.V. Guha (1991). Contexts: a formalization and some applications, MCC Tech. Rep. ACT-CYC-42391.Google Scholar
  12. 12.
    K. Konolige (1982). A first order formalization of knowledge and action for a multiagent planning system, Machine Intelligence 10.Google Scholar
  13. 13.
    R. Kowalski and Kim J.S. (1991). A metalogic programming approach to multi-agent knowledge and belief, in Vladimir Lifschitz (ed.), Artificial Intelligence and the Mathematical Theory of Computation: Papers in Honor of John McCarthy, Academic Press, 1991, Academic Press, 231–246.Google Scholar
  14. 14.
    J. McCarthy, Generality in Artificial Intelligence, Communications of the ACM, 30(12), 1987, 1030–1035.Google Scholar
  15. 15.
    J. McCarthy (1993). Notes on Formalizing Context, Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, Chambery.Google Scholar
  16. 16.
    D. Kalish and R. Montague (1964). Logic: techniques of formal reasoning, New York, Harcourt, Brace & World.Google Scholar
  17. 17.
    R. Montague (1963). Syntactical treatment of modalities, with corollaries on reflexion principles and finite axiomatizability, Acta Philosoph. Fennica, 16, 153–167.Google Scholar
  18. 18.
    R. C. Moore (1977). Reasoning about knowledge and action, Proc. of IJCAI77, Cambridge, MA, 223–227.Google Scholar
  19. 19.
    D. Perlis (1985). Languages with self-reference I: foundations, Artificial Intelligence, 25:301–322.Google Scholar
  20. 20.
    Y. Shoham (1991). Varieties of contexts, in Vladimir Lifschitz (ed.), Artificial Intelligence and the Mathematical Theory of Computation: Papers in Honor of John McCarthy, Academic Press, 393–407.Google Scholar
  21. 21.
    M. Simi (1991). Viewpoints subsume belief, truth and situations, in Trends in Artificial Intelligence, Proc. of 2nd Congress of the Italian Association for Artificial Intelligence, Ardizzone, Gaglio, Sorbello (Eds), Lecture Notes in Artificial Intelligence 549, Springer Verlag, 38–47.Google Scholar
  22. 22.
    R.W. Weyhrauch (1980). Prolegomena to a theory of mechanized formal reasoning, Artificial Intelligence, 13(1,2):133–170.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Giuseppe Attardi
    • 1
  • Maria Simi
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly

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