Abstract
By adopting theories as primitive components of a logic and recognizing that formulae are just presentation details we arrive at the concept of topological institution. In a topological institution, we have, for each signature, a frame of theories, a set of interpretation structures and a satisfaction relation. More precisely, we have, for each signature, a topological system. We show how to extract a topological institution from a given institution and establish an adjunction. Illustrations are given within the context of equational logic. We study the compositionality of theories. Formulae are recovered when we establish a general technique for presenting topological institutions. Topological institutions with finitely observable theories are shown to be useful in temporal monitoring applications where we would like to be able to characterize the properties of the system that can be monitored. Namely, an invariant property (Gϕ) cannot be monitored because it cannot be positively established in finite time. On the contrary, a reactivity property (Fϕ) can be positively established in finite time.
This work was partly supported by CEC under ESPRIT-III BRA WG 6071 IS-CORE (Information Systems — COrrectness and REusability) and BRA WG 6112 COMPASS (COMPrehensive Algebraic approach to System Specification and development) and by ESDI under research contract OBLOG (OBject LOGic).
Preview
Unable to display preview. Download preview PDF.
References
H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification I: Equations and Initial Semantics. Springer-Verlag, 1985.
J. Fiadeiro and A. Sernadas. Structuring theories on consequence. In D. Sannella and A. Tarlecki, editors, Recent Trends in Data Type Specification, pages 44–72. Springer-Verlag, 1988.
J. Fiadeiro, A. Sernadas, and C. Sernadas. Knowledge bases as structured theories. In K. V. Nori, editor, Foundations of Software Technology and Theoretical Computer Science, pages 469–486. Springer-Verlag, 1987.
J. Goguen and R. Burstall. Introducing institutions. In E. Clarke and D. Kozen, editors, Proceedings of the Logics of Programming Workshop, pages 221–256. Springer-Verlag, 1984.
J. Goguen and R. Burstall. Institutions: Abstract model theory for specification and programming. Journal of the ACM, 39(1):95–146, 1992.
P. Johnstone. Stone Spaces. Cambridge University Press, 1982.
M. Kwiatkowska. On topological characterization of behavioural properties. In G. Reed, A. Roscoe, and R. Wachter, editors, Topology and Category Theory in Computer Science, pages 153–177. Oxford University Press, 1991.
U. Lipeck and G. Saake. Monitoring dynamic integrity constraints based on temporal logic. Information Systems, 12:255–269, 1987.
J. Meseguer. General logics. In H.-D. Ebbinghaus et al, editor, Proceedings of the Logic Colloquium, 1987. North-Holland, 1989.
A. Salibra and G. Scollo. A soft starway to institutions. In M. Bidoit and C. Choppy, editors, Recent Trends in Data Type Specification, pages 310–329. Springer-Verlag, 1993.
A. Sernadas and C. Sernadas. Denotational semantics of object specification within an arbitrary temporal logic institution. Research report, Section of Computer Science, Department of Mathematics, Instituto Superior Técnico, 1096 Lisboa, Portugal, 1993. Presented at IS-CORE Workshop 93 — Submitted for publication.
A. Sernadas, C. Sernadas, and J. Valença. A topological view on institutions. Research report, Section of Computer Science, Department of Mathematics, Instituto Superior Técnico, 1096 Lisboa, Portugal, 1994. Available on the ftp server yoda.inesc.pt (146.193.1.5).
M. Smyth. Powerdomains and predicate transformers: A topological view. In J. Diaz, editor, Automata, Languages and Programming, pages 662–675. Springer-Verlag, 1983.
S. Vickers. Topology Via Logic. Cambridge University Press, 1989.
S. Vickers. Geometric logic in computer science. In G. Burn, S. Gay, and M. Ryan, editors, Theory and Formal Methods 1993, pages 37–54. Springer-Verlag, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sernadas, A., Sernadas, C., Valença, J.M. (1995). A theory-based topological notion of institution. In: Astesiano, E., Reggio, G., Tarlecki, A. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1994 1994. Lecture Notes in Computer Science, vol 906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014442
Download citation
DOI: https://doi.org/10.1007/BFb0014442
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59132-0
Online ISBN: 978-3-540-49198-9
eBook Packages: Springer Book Archive