On a generalized modularization theorem

Information Processing Letters

Volumn 74, Issue 1, 2000, Pages 65-71

  Dimitrakos, Theodosis ^a   Maibaum, Tom ^b  

^a RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^b KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DATA STRUCTURES; FORMAL LOGIC; MATHEMATICAL MORPHOLOGY; THEOREM PROVING;

GENERALIZED MODULARIZATION THEOREM;

INTERPOLATION;

EID: 0033745315     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-0190(00)00037-5     Document Type: Article

References (26)

1. J.A. Bergstra, J. Heering, P. Klint, Module algebra, J. ACM 37 (2) (1990) 335-372.
2. W. Craig, Three uses of the Herbrand-Getzen theorem in relating model theory and proof theory, J. Symbolic Logic 22 (1957) 269-285.
3. R. Diaconnescu, J. Goguen, P. Stefaneas, Logical support for modularisation, in: Logical Environments, Cambridge University Press, Cambridge, 1993, pp. 83-130.
4. T. Dimitrakos, Parameterising (algebraic) specifications on diagrams, in: Automated Software Engineering - ASE'98, IEEE Press, New York, 1998, pp. 221-224.
5. T. Dimitrakos, T.S.E. Maibaum, Notes on refinement, interpolation and uniformity, in: Automated Software Engineering - ASE'97, IEEE Press, New York, 1997.
6. H.D. Ehrich, On the theory of specification, implementation and parametrization of abstract data types, J. ACM 29 (1) (1982).
7. J.L. Fiadeiro, A. Sernadas, Structuring theories on consequence, in: Recent Trends in Data Type Specification, 1988, pp. 44-72.
8. J.L. Fiadeiro, T.S.E. Maibaum, Generalising interpretations between Theories in the Context of (π-)institutions, in: Theory and Formal Methods, Springer, Berlin, 1993, pp. 126-147.
9. D.M. Gabbay, Semantic proof of the Craig interpolation theorem for intuitionistic logic and extensions, in: Logic Colloquium'69, North-Holland, Amsterdam, 1971.
10. G. Kreisel, Survey of proof theory, J. Symbolic Logic (1968).
11. S. Maehara, Craig's interpolation theorem, Sugaku (1961) 235-237.
12. T.S.E. Maibaum, M.R. Sadler, Axiomatising specification theory, in: Recent Trends in Data Type Specification, Springer, Bremen, 1985, pp. 171-177.
13. L.L. Maksimova, Craig's interpolation theorem and amalgamable varieties, Soviet Math. Dokl. 18 (6) (1977) 1550-1553.
14. M. Marx, Interpolation, modularization and knowledge representation, in: Proc. Dutch Conference on AI (NAIC'95), June 1995.
15. J. Meseguer, General logics, in: Logic Colloquium'87, 1989, pp. 275-329.
16. G. Mints, Modularisaton and interpolation, Kestrel Institute, Dec. 1998 (Available at ftp : //www.kestrel.edu/pub/papers/mints/mod.ps).
17. A.M. Pitts, Amalgamation and interpolation in the category of Heyting algebras, J. Pure Appl. Algebra 29 (1983) 155-165.
18. G. Roşu, J. Goguen, On equational Craig interpolation, J. Univ. Comput. Sci. (2000), to appear.
19. P.H. Rodenburg, R.J. van Glabbeek, An interpolation theorem in equational logic, Technical Report CS-R8838, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, 1988.
20. J.R. Shoenfield, Mathematical Logic, Addison-Wesley, Reading, MA, 1967.
21. G. Tǎkeuti, Proof Theory, North-Holland, Amsterdam, 1976.
22. A. Tarlecki, Bits and pieces of the theory of institutions, in: Workshop on Category Theory and Computer Science, Lecture Notes in Comput. Sci., Vol. 240, Springer, Berlin, 1986.
23. A. Tarski, A. Mostowski, R.M. Robinson, Undecidable Theories, North-Holland, Amsterdam, 1953.
24. W.M. Turski, T.S.E. Maibaum, The Specification of Computer Programs, Addison-Wesley, Reading, MA, 1987.
25. P.A.S. Veloso, On pushout consistency, modularity and interpolation for logical specifications, Inform. Process. Lett. 60 (2) (1996) 59-66.
26. F.A.S. Veloso, T.S.E. Maibaum, On the modularisation theorem for logical specifications, Inform. Process. Lett. 53 (1995) 287-293.