Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Logical Foundations of Computer Science

LFCS 1992: Logical Foundations of Computer Science — Tver '92 pp 314–325Cite as

Partial algebra + order-sorted algebra = galactic algebra

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 620))

Abstract

Galactic algebra is a clean superset of universal algebra, which suits this intention: to consider semi-functions (partial functions) and subsets of some universe, then to reason in a uniform way about identity (equality of terms), membership, and inclusion. The logic of galactic algebra is expressed as a first-order Hilbert-style system, which has all the desired qualities. — This text means an announcement and a description of my thesis [9]. Only the proof technique is explained.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bidoit, M.; Kreowski, H.-J.; Lescanne, P.; Orejas, F.; Sannella, D.; eds. Algebraic system specification and development — A survey and annotated bibliography. Springer-Verlag; 1991. (Lecture notes in computer science; 501).

    Google Scholar 

  2. Burmeister, P. A model-theoretic oriented approach to partial algebras. Berlin: Akademie-Verlag; 1986. (Mathematical research; 31).

    Google Scholar 

  3. Burstall, R. M.; Goguen, J. A. Algebras, theories and freeness — An introduction for computer scientists. Theoretical foundation of programming methodology — Lecture notes of an international summer school. Dordrecht, Holland, the Netherlands: D. Reidel; 1982. (NATO Advanced Study Institutes series).

    Google Scholar 

  4. Goguen, Joseph A.; Meseguer, José. Order-sorted algebra-I-Partial and overloaded operators, errors and inheritance. Menlo Park, California: S.R.I. International; 1986, March 25; technical report, draft.

    Google Scholar 

  5. Goguen, J.; Kirchner, C.; Kirchner, H.; Mégrelis, A.; Meseguer, J.; Winkler, T. An introduction to OBJ 3. Jouannaud, J.-P.; Kaplan, S.; eds. Proceedings of the first international workshop on conditional term-rewriting systems; 1987, July 8–10; Orsay, France. Springer-Verlag; 1988. (Lecture notes in computer science; 308).

    Google Scholar 

  6. Grätzer, George. Universal algebra. D. van Nostrand; 1968. (The university series in higher mathematics).

    Google Scholar 

  7. Isakowitz, Tomás; Gallier, Jean H. Congruence closure in order-sorted algebra. Philadelphia, Pennsylvania, U.S.A.: University of Pennsylvania; 1988, June 24; technical report.

    Google Scholar 

  8. Manca, V.; Salibra, A.; Scollo, G. Equational type logic. Conference on algebraic methodology and software technology (AMAST); 1989, May; Iowa City, Iowa, U.S.A. Theoretical Computer Science. 77(1 & 2); 1990, December 7.

    Google Scholar 

  9. Mégrelis, Aristide. Algèbre galactique — Un procédé de calcul formel, relatif aux semi-fonctions, à l'inclusion et à l'égalité. Nancy, France: Université Nancy I; 1990, septembre; thèse [thesis].

    Google Scholar 

  10. Poigné, Axel. Partial algebras, subsorting, and dependent types — Prerequisites of error handling in algebraic specifications. Proceedings of a workshop on abstract data types. Springer-Verlag; 1988. (Lecture notes on computer science; 332).

    Google Scholar 

  11. Reichel, Horst. Initial computability, algebraic specifications, and partial algebras. Berlin: Akademie-Verlag; 1987. (The international series of monographs on computer science; 2).

    Google Scholar 

  12. Schmidt-Schauß, Manfred. Computational aspects of an order-sorted logic with term declarations. Springer-Verlag; 1989. (Lecture notes in artificial intelligence; 395).

    Google Scholar 

  13. Smolka, Gert; Nutt, Werner; Goguen, Joseph A.; Meseguer José. Order-sorted equational computation. Ait-Kaci, H.; Nivat, M.; eds. Resolution of equations in algebraic structures-Vol. 2-Rewriting techniques. Academic Press; 1989.

    Google Scholar 

  14. Thomas, Christophe. VEGA — Système de vérification formelle de preuve. Nancy, France: Université Nancy I; 1991, juin [June] [; report, written in French].

    Google Scholar 

  15. Waldmann, Uwe. Semantics of order-sorted specifications. Dortmund, Deutschland: Universität Dortmund, Abteilung Informatik; 1989; Forschungsbericht Nr. 297 [research report].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INRIA-Lorraine-C.N.R.S.-CRIN, B.P. 101, F-54602, Villers-lès-Nancy Cedex, France

    Aristide Mégrelis

Authors
  1. Aristide Mégrelis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Anil Nerode Mikhail Taitslin

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mégrelis, A. (1992). Partial algebra + order-sorted algebra = galactic algebra. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023885

Download citation

  • DOI: https://doi.org/10.1007/BFb0023885

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55707-4

  • Online ISBN: 978-3-540-47276-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation