Skip to main content
Springer Nature Link
Log in

A soft stairway to institutions

  • Contributed Papers
  • Conference paper
  • First Online:
Recent Trends in Data Type Specification (ADT 1991, COMPASS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 655))

Abstract

The notion of institution is dissected into somewhat weaker notions. We introduce a novel notion of institution morphism, and characterize preservation of institution properties by corresponding properties of such morphisms. Target of this work is the stepwise construction of a general framework for translating logics, and algebraic specifications using logical systems. Earlier translations of order-sorted conditional equational logic and of conditional equational logics for partial algebras into equational type logic are revisited in this light. Model-theoretic results relating to compactness are presented as well.

on temporary leave at: LIENS/DMI, École Normale Supérieure, 45 Rue d'Ulm, F-75230 Paris, France

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.

Similar content being viewed by others

References

  1. Andréka, H., Burmeister, P., Németi, I.: Quasivarieties of Partial Algebras — A Unifying Approach towards a Two-Valued Model Theory for Partial Algebras. Studia Sci. Math. Hungar. 16 (1981) 325–372

    Google Scholar 

  2. Andréka, H., Németi, I.: Generalization of Variety and Quasivariety Concepts to Partial Algebras through Category Theory. Dissertationes Mathematicæ (Rozprawy Mathematyczne) 204 (Warsaw, 1983)

    Google Scholar 

  3. Astesiano E., Cerioli, M.: On the Existence of Initial Models for Partial (Higher-Order) Conditional Specifications, In: Diaz, J., Orejas, F. (Eds.) TAPSOFT'89, LNCS 351 (Springer-Verlag, Berlin, 1989) 74–88

    Google Scholar 

  4. Astesiano E., Cerioli, M.: Commuting between Institutions via Simulation. University of Genova, Formal Methods Group, Technical Report n. 2 (1990)

    Google Scholar 

  5. Barwise, K. J.: Axioms for Abstract Model Theory. Ann. Math. Logic 7 (1974) 221–265

    Google Scholar 

  6. Bernot, G., Bidoit, M.: Proving the Correctness of Algebraically Specified Software: Modularity and Observability Issues. Proc. 2nd Int. Conf. Algebraic Methodology And Software Technology, Iowa City, (Iowa, USA, May 22–25, 1991) 139–161

    Google Scholar 

  7. Broy, M., Wirsing, M.: Partial Abstract Types. Acta Informatica, 18, 3 (1982) 47–64

    Article  Google Scholar 

  8. Burmeister, P.: A Model-Theoretic Oriented Approach to Partial Algebras. Mathematical Research, Volume 31, (Akademie-Verlag, Berlin, 1986)

    Google Scholar 

  9. Chang, C.C., Keisler, H.J.: Model Theory. Third Edition (North-Holland, Amsterdam, 1990)

    Google Scholar 

  10. Ebbinghaus, H.-D.: Extended logics: the general framework. In: Barwise, J., Feferman, S. (Eds.) Model-Theoretic Logics (Springer-Verlag, Berlin, 1985) 25–76

    Google Scholar 

  11. Ebbinghaus, H.-D., Flum, J., Thomas, W.: Mathematical Logic. (Springer-Verlag, New York, 1984)

    Google Scholar 

  12. Ehrig, H., Baldamus, M., Cornelius, F., Orejas, F.: Theory of Algebraic Module Specification Including Behavioural Semantics, Constraints and Aspects of Generalized Morphisms. Proc. 2nd Int. Conf. Algebraic Methodology And Software Technology, Iowa City, (Iowa, USA, May 22–25, 1991) 101–125

    Google Scholar 

  13. Goguen, J.A., Burstall, R.: Introducing Institutions. In: Clarke, E., Kozen, D. (Eds.), Logics of Programs, LNCS 164 (Springer-Verlag, Berlin, 1984) 221–256

    Google Scholar 

  14. Goguen, J.A., Meseguer, J.: Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations. Report SRI-CSL-89-10, SRI International, Computer Science Laboratory (Menlo Park, California, July 1989)

    Google Scholar 

  15. Mac Lane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics, Volume 5 (Springer-Verlag, New-York, 1971)

    Google Scholar 

  16. Makowski, J.-A.: Compactness, Embeddings an Definability. In: Barwise, J., Feferman, S. (Eds.) Model-Theoretic Logics (Springer-Verlag, Berlin, 1985) 645–716

    Google Scholar 

  17. Manca, V., Salibra, A., Scollo, G.: Equational Type Logic. Theoret. Comput. Sci. 77 (1990) 131–159

    Google Scholar 

  18. Manca, V., Salibra, A., Scollo, G.: On the Expressiveness of Equational Type Logic. In: Rattray, C.M.I., Clark R.G. (Eds.) The Unified Computation Laboratory, Proc. IMA Conf., Stirling, Scotland, July 3–6, 1990; to appear (Oxford University Press, 1992)

    Google Scholar 

  19. Meseguer, J.: General Logics. In: Ebbinghaus, H.-D. et al. (Eds.) Logic Colloquium'87 (North-Holland, Amsterdam, 1989) 275–329

    Google Scholar 

  20. Nivela, M.P., Orejas, F.: Initial Behaviour Semantics for Algebraic Specifications. In: Sannella, D.T., Tarlecki, A. (Eds.) Recent Trends in Data Type Specification, LNCS 332 (Springer-Verlag, Berlin, 1988) 184–207

    Google Scholar 

  21. Orejas, F., Nivela, M.P., Ehrig, H.: Semantical Constructions for Categories of Behavioural Specifications. In: Ehrig, H., Herrlich, H., Kreowski, H.-J., Preuß, G. (Eds.) Categorical Methods in Computer Science — with Aspects from Topology, LNCS 393 (Springer-Verlag, Berlin, 1989) 220–243

    Google Scholar 

  22. Reichel, H.: Initial Computability, Algebraic Specifications, and Partial Algebras. The International Series of Monographs on Computer Science, Volume 2 (Oxford University Press, Oxford, 1987)

    Google Scholar 

  23. Salibra, A., Scollo, G.: Compactness and Löwenheim-Skolem Properties in Pre-Institution Categories. Memoranda Informatica 92-27, TIOS 92/12, University of Twente, March 1992; submitted for publication.

    Google Scholar 

  24. Sannella, D.T., Tarlecki, A.: Specifications in an Arbitrary Institution. Information and Computation 76 (1988) 165–210

    Google Scholar 

  25. Tarlecki, A.: On the Existence of Free Models in Abstract Algebraic Institutions. Theoret. Comput. Sci. 37 (1985) 269–304

    Google Scholar 

  26. Tarlecki, A.: Quasi-Varieties in Abstract Algebraic Institutions, J. of Computer and System Sciences 33 (1986) 333–360

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dip. Informatica, University of Pisa, C.so Italia 40, I-56125, Pisa, Italy

    Antonino Salibra

  2. Fac. Informatica, University of Twente, P.O. Box 217, NL-7500, AE Enschede, The Netherlands

    Giuseppe Scollo

Authors
  1. Antonino Salibra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giuseppe Scollo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michel Bidoit Christine Choppy

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Salibra, A., Scollo, G. (1993). A soft stairway to institutions. In: Bidoit, M., Choppy, C. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1991 1991. Lecture Notes in Computer Science, vol 655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56379-2_47

Download citation

  • DOI: https://doi.org/10.1007/3-540-56379-2_47

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56379-2

  • Online ISBN: 978-3-540-47545-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics