Proof systems for institutional logic

Journal of Logic and Computation

Volumn 16, Issue 3, 2006, Pages 339-357

  Diaconescu, Rǎzvan ^a  

^a INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

Institutions; Proofs systems

Indexed keywords

INSTITUTIONAL REFINEMENT; PROOFS SYSTEMS; THEORETIC QUANTIFICATION;

COMPUTATION THEORY; FORMAL LOGIC; MATHEMATICAL MODELS; PROBLEM SOLVING;

SOCIETIES AND INSTITUTIONS;

EID: 33744730053     PISSN: 0955792X     EISSN: 1465363X     Source Type: Journal    
DOI: 10.1093/logcom/exi082     Document Type: Article

References (34)

1. M. Aiguier, C. Boin, and D.Longuet. On generalized theorems for normalization of proof trees. In preparation.
2. M. Arrais and J.L. Fiadeiro. Unifying theories in different institutions. In Recent Trends in Data Type Specification, M. Haveraaen, O. Owe, and O.-J. Dahl, eds, Lecture Notes in Computer Science, pp. 81-101. Springer, 1996. Proceedings of 11th Workshop on Specification of Abstract Data Types. Oslo, Norway, September 1995.
3. M. Bidoit and R. Hennicker. On the integration of the observability and reachability concepts. In Proc. 5th Int. Conf. Foundations of Software Science and Computation Structures (FOSSACS'2002), Volume 2303 of Lecture Notes in Computer Science, pp. 21-36, 2002.
4. T. Borzyszkowski. Higher-order logic and theorem proving for structured specifications. In Christine Choppy, Didier Bert, and Peter Mosses, eds, Workshop on Algebraic Development Techniques 1999, Volume 1827 of Lecture Notes in Computer Science, pp. 401-418, 2000.
5. P. Burmeister. A Model Theoretic Oriented Approach to Partial Algebras. Akademie-Verlag, Berlin, 1986.
6. C. Cîrstea. Institutionalising many-sorted coalgebraic modal logic. In Coalgebraic Methods in Computer Science 2002, Electronic Notes in Theoretical Computer Science, 2002.
7. I. Claßen, M. Große-Rhode, and U. Wolter. Categorical concepts for parameterized partial specification. Mathematical Structures in Computer Science, 5, 153-188, 1995.
8. R. Diaconescu. Institution-independent ultraproducts. Fundamenta Informatic, 55, 321-348, 2003.
9. R. Diaconescu. Elementary diagrams in institutions. Journal of Logic and Computation, 14, 651-674, 2004.
10. R. Diaconescu. An institution-independent proof of Craig Interpolation Theorem. Studia Logica, 77, 59-79, 2004.
11. R. Diaconescu, J. Goguen, and P. Stefaneas. Logical support for modularisation. In Logical Environments, G. Huet and G. Plotkin, eds, pp. 83-130. Cambridge, 1993. Proceedings of a Workshop held in Edinburgh, Scotland, May 1991.
12. J. L. Fiadeiro and J. F. Costa. Mirror, mirror in my hand: A duality between specifications and models of process behaviour. Mathematical Structures in Computer Science, 6, 353-373, 1996.
13. J. Fiadeiro and A. Sernadas. Structuring theories on consequence. In Recent Trends in Data Type Specification, D. Sannella and A. Tarlecki, eds, pp. 44-72. Volume 332 of Lecture Notes in Computer Science. Springer, 1988.
14. J. Goguen and R. Burstall. Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery, 39, 95-146, January 1992.
15. J. Goguen and R. Diaconescu. Towards an algebraic semantics for the object paradigm. In Harmut Ehrig and Fernando Orejas, eds, Recent Trends in Data Type Specification, Volume 785 of Lecture Notes in Computer Science, pp. 1-34. Springer, 1994.
16. J. Goguen and G. Roşu. Institution morphisms. Formal Aspects of Computing, 13, 274-307, 2002.
17. D. Gǎinǎ and A. Popescu. An institution-independent proof of Robinson consistency theorem. Studia Logica. To appear.
18. J. Lambek and P. Scott. Introduction to Higher Order Categorical Logic. Cambridge, 1986. Cambridge Studies in Advanced Mathematics, Volume 7.
19. F. W. Lawvere. Functorial semantics of elementary theories. Journal of Symbolic Logic, 294-295, 1966.
20. S. MacLane. Categories for the Working Mathematician. Springer, second edition, 1998.
21. J. Meseguer. General logics. In Proceedings, Logic Colloquium., 1987, H.-D. Ebbinghaus et al., eds, pp. 275-329. North-Holland, 1989.
22. J. Meseguer. Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science, 96, 73-155, 1992.
23. T. Mossakowski, J. Goguen, R. Diaconescu, and A. Tarlecki. What is a logic? In Logica Universalis, J.-Y. Beziau, ed., pp. 113-133. Birkhauser, 2005.
24. M. Petria. An institutional generalization of Gödel Completeness Theorem. In preparation.
25. M. Petria and R. Diaconescu. Abstract Beth definability in institutions. Journal of Symbolic Logic, to appear, 2006.
26. H. Reichel. Initial Computability, Algebraic Specifications, and Partial Algebras. Clarendon, 1987.
27. D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Control, 76, 165-210, 1988.
28. Earlier version in Proceedings, International Symposium on the Semantics of Data Types, Lecture Notes in Computer Science, Volume 173, Springer, 1985.
29. L. Schröder, T. Mossakowski, and C. Lüth. Type class polymorphism in an institutional framework. In Recent Trends in Algebraic Development Techniques, 17th Intl. Workshop (WADT 2004), Volume 3423 of Lecture Notes in Computer Science, J. Fiadeiro, ed., pp. 234-248. Springer, Berlin, 2004.
30. A. Tarlecki. On the existence of free models in abstract algebraic institutions. Theoretical Computer Science, 37, 269-304, 1986. Preliminary version, University of Edinburgh, Computer Science Department, Report CSR-165-84, 1984.
31. A. Tarlecki. Quasi-varieties in abstract algebraic institutions. Journal of Computer and System Sciences, 33, 333-360, 1986. Original version, University of Edinburgh, Report CSR-173-84.
32. A. Tarlecki. Moving between logical systems. In Recent Trends in Data Type Specification, M. Haveraaen, O. Owe, and O.-J. Dahl, eds, Lecture Notes in Computer Science, pp. 478-502. Springer, 1996.
33. Proceedings of 11th Workshop on Specification of Abstract Data Types. Oslo, Norway, September 1995.
34. A. Tarlecki. Towards heterogeneous specifications. In Proceedings, International Conference on Frontiers of Combining Systems (FroCoS'98), D. Gabbay and M. van Rijke, eds, pp. 337-360. Research Studies Press, 2000.