Abstract
The paper introduces a notion of context parchment. The notion is illustrated by several examples. It is shown, that every logical context parchment generates a context institution. Morphisms between context parchments are introduced, thus yielding a category of context parchments. The use of universal constructions in the category of context parchments, for modular construction of logics is discussed and illustrated by examples.
Preview
Unable to display preview. Download preview PDF.
References
J. Barwise. Axioms for abstract model theory. Annals of Mathematical Logic, vol. 7, 1974, pp. 221–265.
P. Burmeister. A Model Theoretic Oriented Approach to Partial Algebras. Introduction to Theory and Application of Partial Algebras-Part I. Mathematical Research Vol. 32, Akademie-Verlag, Berlin, 1986.
R. Diaconescu, J. Goguen, and P. Stefaneas. Logical Support for Modularisation. In G. Huet and G. Plotkin, editors, Logical Environments, pp. 83–130, Cambridge University Press, 1993.
H.D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical Logic, Springer-Verlag, 1984.
A.A. Fraenkel, Y. Bar-Hillel, and A. Levy. Foundations of Set Theory, second revised edition. Studies in Logic and the Foundations of Mathematics, Vol. 67, North-Holland, 1973.
J.A. Goguen and R.M. Burstall. Introducing Institutions. In Proceedings, Logics of Programming Workshop, LNCS 164, pp. 221–256, Springer-Verlag, 1984.
J.A. Goguen and R.M. Burstall. A study in the foundations of programming methodology: Specifications, institutions, charters and parchments. In D. Pitt, S. Abramsky, A Poigné, and D. Rydeheard, editors, Proceedings, Conference on Category Theory and Computer Programming, LNCS 240, pp. 313-333, Springer-Verlag, 1986.
J.A. Goguen and R.M. Burstall. Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery, vol. 39, pp. 95–146, 1992.
H. Herrlich, G.E. Strecker. Category Theory, second edition. Heldermann Verlag, Berlin, 1979.
T. Mossakowski. Using limits of parchments to systematically construct institutions of partial algebras. In Magne Haveraaen and Olaf Owe and Ole-Johan Dahl, editors, Recent Trends in Data Type Specifications. 11th Workshop on Specification of Ab stract Data Types joint with the 8th general COMPASS workshop. Oslo, Norway, September 1995. Selected papers. LNCS, vol. 1130, pp. 379–393, Springer-Verlag, 1996.
T. Mossakowski, A. Tarlecki, and W. Pawlowski. Combining and representing logical systems. In E. Moggi, editor, Category Theory in Computer Science. LNCS, Springer-Verlag 1997. To appear.
T. Mossakowski, A. Tarlecki, and W. Pawlowski. Combining and representing logical systems using model-theoretic parchments. Presented at 12th Workshop on Algebraic Development Techniques WADT'97, Tasquinia, June 1997.
W. Pawlowski. Context Institutions. In Magne Haveraaen and Olaf Owe and OleJohan Dahl, editors, Recent Trends in Data Type Specifications. 11th Workshop on Specification of Abstract Data Types joint with the 8th general COMPASS workshop. Oslo, Norway, September 1995. Selected papers. LNCS, vol. 1130, pp. 436–457, Springer-Verlag, 1996.
H. Rasiowa, R. Sikorski. The Mathematics of Metamathematics. Państwowe Wydawnictwo Naukowe, Warszawa, 1963.
R. Sikorski. Algebra of Formalized Languages. Colloquium Mathematicum, Vol. IX, 1962, pp. 1–31.
A. Taxlecki, R. Burstall, and J. Goguen. Some fundamental algebraic tools for the semantics of computation, part 3: Indexed categories. Theoretical Computer Science, 91, pp. 239–264, 1991.
U. Wolter, R. Wessdly, M. Klar, and F. Cornelius. Four Institutions: A Unified Presentation of Logical Systems for Specification. Bericht-Nr. 94-24, Technische Universität Berlin, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pawłowski, W. (1998). Context parchments. In: Presicce, F.P. (eds) Recent Trends in Algebraic Development Techniques. WADT 1997. Lecture Notes in Computer Science, vol 1376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64299-4_46
Download citation
DOI: https://doi.org/10.1007/3-540-64299-4_46
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64299-2
Online ISBN: 978-3-540-69719-0
eBook Packages: Springer Book Archive