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Unified domains and abstract computational structures

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Artificial Intelligence and Symbolic Mathematical Computing (AISMC 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 737))

Abstract

This paper introduces a formalism to specify abstract computational structures (ACS) of mathematical domains of computation. This is a basic step of a project aiming at designing an environment for symbolic computing based upon knowledge representation and relying, when needed, on AI methods.

We present a method for the specification of these ACS's which is embedded in the framework of algebraic specifications and of unified domains. The first part of this paper deals with the theoretical solution of this specification problem. The second part reports on the implementation in the hybrid knowledge representation system MANTRA.

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References

  1. Bauer, F.L. and Woessner, H., Algorithmische Sprache und Programmentwicklung(2nd Edition), Springer-Verlag Berlin Heidelberg New York Tokyo, 1984.

    Google Scholar 

  2. Brachman, R. J., Gilbert, V.P., Levesque,H.J., An Essential Hybrid Reasoning System: Knowledge and Symbol Level Accounts of KRYPTON, Proceedings of IJCAI 9, pp. 532–539, 1985.

    Google Scholar 

  3. Calmet,J., Tjandra, I.A., Learning Complete Computational Structures, in Emrich et al (Eds), 5th International Symposium on Methodologies for Intelligent Systems (Selected Papers), Knoxville — USA, October 24–27, 1990, pp. 63–71, ICAIT.

    Google Scholar 

  4. Calmet, J., Tjandra, I.A, Representation of Mathematical Knowledge, Z. W. Ras et al.. (Eds.) Proceedings of the 6th International Symposium on Methodologies for Intelligent Systems, Charlotte USA, October 16–19, 1991, Springer-Verlag.

    Google Scholar 

  5. Calmet, J., Bittencourt.G., Tjandra, I.A., MANTRA: A Shell for Hybrid Knowledge Representation, Proceedings of the third International conference on Tools for Artificial Intelligence, San Jose USA, November 5–8, 1991, IEEE Computer Society Press.

    Google Scholar 

  6. Etherington,D.W., On Inheritance Hierarchies with Exceptions, Proceedings of AAAI-83, pp. 104–108, 1986.

    Google Scholar 

  7. Frisch,A.M., Knowledge Retrieval as Specialized Inference, Report No.214, Department of Computer Science, University of Rochester, May 1987.

    Google Scholar 

  8. Goguen, J.A. and Burstall, R.M., Introducing Institutions, in Clarke, E. and Kozen, D. (Eds.), Proceedings Logics of Programming Workshop, Springer-Verlag, 1984.

    Google Scholar 

  9. Goguen, J.A., Thatcher, J.W. and Wagner, E., An Initial Algebra Approach to the Specification Correctness and Implementation of Abstract Data Types, in Yeh, R.T. (Ed.), Current Trends in Programming Methodology IV, Prentice Hall, 1978.

    Google Scholar 

  10. Guttag, J.: The Specification and Application to Programming of Abstract Data Types, University of Toronto, Department of Computer Science, Ph. D. Thesis, Report CSRG-59; 1975.

    Google Scholar 

  11. Guttag,J.V., The Algebraic Specification of Abstract Data Types, Acta Informatica 10, 27–52, Springer-Verlag, 1978.

    Google Scholar 

  12. Huet, G., Oppen D.: Equations and Rewrite Rules: a survey; in Book R., editor, Formal Language Theory: Perspective and Open Problems, Academic Press, 1980.

    Google Scholar 

  13. Lenat, D.B., McDermott,J., Less Than General Production Systems Architectures, Proceedings of IJCAI 5, pp. 928–932, 1977.

    Google Scholar 

  14. Mosses, P.D., Unified Algebras and Action Semantics, in Monien, B. and Cori, R. (Eds.), Proceedings of 6th Annual Symposium on Theoretical Aspects of Computet Science, Springer-Verlag, 1986.

    Google Scholar 

  15. Mosses, P.D., Unified Algebras and Institutions, in Proceedings IEEE-Logics in Computer Science, IEEE-Press, 1989.

    Google Scholar 

  16. Patel-Schneider, P.F., A Decidable First-Order Logic for Knowledge Representation, Proceedings of IJCAI 9, pp. 455–458, 1985.

    Google Scholar 

  17. Stoy, J.E., Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory, the MIT Press, 1977.

    Google Scholar 

  18. Thomason, R.H, Horty, J.F. and Touretzky, D.S., A Calculus for Inheritance in Monotonic Semantic Nets, Technical Report CMU-CS-86-138, Computer Science Department, Carnegie mellon University, Pittsburgh, PA, 1986.

    Google Scholar 

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Jacques Calmet John A. Campbell

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© 1993 Springer-Verlag Berlin Heidelberg

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Calmet, J., Homann, K., Tjandra, I.A. (1993). Unified domains and abstract computational structures. In: Calmet, J., Campbell, J.A. (eds) Artificial Intelligence and Symbolic Mathematical Computing. AISMC 1992. Lecture Notes in Computer Science, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57322-4_11

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  • DOI: https://doi.org/10.1007/3-540-57322-4_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57322-7

  • Online ISBN: 978-3-540-48063-1

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