Skip to main content
SpringerLink
Log in

Definable naming relations in meta-level systems

  • Conference paper
  • First Online:
Meta-Programming in Logic (META 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 649))

Included in the following conference series:

Abstract

Meta-level architectures are always, implicitly or explicitly, equipped with a component that establishes a relation between their object- and meta-level layers. This so-called naming relation has been a neglected part of the architecture of meta-level systems. This paper argues that the naming relation can be employed to increase the expressiveness and efficiency of meta-level architectures, while preserving known logical properties. We argue that the naming relation should not be a fixed part of a meta-level architecture, but that it should be definable to allow suitable encoding of syntactic information. Once the naming relation is definable, we can also make it meaningful. That is, it can also be used to encode pragmatic and semantic information, allowing for more compact and efficient meta-theories. We explore the formal constraints that such a definable naming relation must satisfy, and we describe a definition mechanism for naming relations which is based on term rewriting systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K.A. Bowen and R.A. Kowalski. Amalgamating language and metalanguage in logic programming. In K. Clark and S. Tarnlund, editors, Logic Programming, pages 152–172. Academic Press, 1982.

    Google Scholar 

  2. A. Bundy and B. Welham. Using meta-level inference for selective application of multiple rewrite rule sets in algebraic manipulation. Artificial Intelligence, 16:189–212, 1981.

    Google Scholar 

  3. S. Costantini and G. A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proceedings of the Sixth International Conference on Logic Programming, pages 218–233, Lisbon, 1989. The MIT Press.

    Google Scholar 

  4. L. Erman, A. Scott, and P. London. Separating and integrating control in a rulebased tool. In Proceedings of the IEEE Workshop on Principles of Knowledge Based Systems, pages 37–43, Denver, Colorado, December 1984.

    Google Scholar 

  5. K. Gödel. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatsh. Math. Phys., 38:173–98, 1931. English translation in From Frege to Gödel: a source book in Mathematical Logic, 1879–1931, J. van Heijenoort (ed.), Harvard University Press, 1967, Cambridge, Mass.

    Google Scholar 

  6. P.M. Hill and J.W. Lloyd. The Gödel report (preliminary version). Technical Report TR-91-02, Computer Science Department, University of Bristol, March (Revised September '91) 1991.

    Google Scholar 

  7. G. Huet and D.C. Oppen. Equations and rewrite rules: a survey. In R. Book, editor, Formal languages: perspectives and open problems. Academic Press, 1978. Presented at the conference on formal language theory, Santa Barbara, 1979. Also: technical report CSL-111, SRI International, Menlo Park, California.

    Google Scholar 

  8. P. Jackson, H. Reichgelt, and F. van Harmelen. Logic-Based Knowledge Representation. The MIT Press, Cambridge, MA, 1989.

    Google Scholar 

  9. P. Maes. Reflection in an object-oriented language. In P. Maes and D. Nardi, editors, Meta-Level Architectures and Reflection, Amsterdam, 1988. North-Holland. Also: AI-Laboratory Memon 86-8, Vrije Universiteit Brüssel.

    Google Scholar 

  10. J. McDermott. Preliminary steps towards a taxonomy of problem-solving methods. In S. Marcus, editor, Automating Knowledge Acquisition for Expert Systems, pages 225–255. Kluwer Academic Publishers, The Netherlands, 1988.

    Google Scholar 

  11. B. Smith. Reflection and semantics in a procedural language. Technical Report TR-272, MIT, Computer Science Lab., Cambridge, Massachusetts, 1982.

    Google Scholar 

  12. B. Smith. Reflection and semantics in Lisp. In Proc. 11th ACM Symposium on Principles of Programming Languages, pages 23–35, Salt Lake City, Utah, 1984. also: Xerox PARC Intelligent Systems Laboratory Technical Report ISL-5.

    Google Scholar 

  13. A. Tarski. Der Wahrheitsbegriff in den formalisierten Sprachen. Studia Philosophica, 1:261–405, 1936. English translation in Logic, Semantics, Metamathematics, A. Tarski, Oxford University Press, 1956.

    Google Scholar 

  14. C. Walther. A mechanical solution of Schuberts steamroller by many-sorted resolution. Artificial Intelligence, 26(2):217–224, 1985.

    Google Scholar 

  15. R. Weyhrauch. Prolegomena to a theory of mechanized formal reasoning. Artificial Intelligence, 13, 1980. Also in: Readings in Artificial Intelligence, Webber, B.L. and Nilsson, N.J. (eds.), Tioga publishing, Palo Alto, CA, 1981, pp. 173–191. Also in: Readings in Knowledge Representation, Brachman, R.J. and Levesque, H.J. (eds.), Morgan Kaufman, California, 1985, pp. 309–328.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S.W.I., University of Amsterdam, Germany

    Frank van Harmelen

Authors
  1. Frank van Harmelen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

A. Pettorossi

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van Harmelen, F. (1992). Definable naming relations in meta-level systems. In: Pettorossi, A. (eds) Meta-Programming in Logic. META 1992. Lecture Notes in Computer Science, vol 649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56282-6_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-56282-6_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56282-5

  • Online ISBN: 978-3-540-47505-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation