Combining and representing logical systems
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The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the model-theoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic way of presenting institutions).
We propose a modified notion of parchment together with a notion of parchment morphism and representation, respectively. We lift formal properties of the categories of institutions and their representations to this level: the category of parchments is complete, and parchment representations may be put together using categorical limits as well. However, parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessary invention for proper combination of various logical features may be introduced either on an ad hoc basis (when putting parchments together using limits in the category of parchments) or via representations in a universal logic (when parchment combination is driven by their representations).
- E. Astesiano, M. Cerioli. Relationships between logical frameworks. In M. Bidoit, C. Choppy, eds., Proc. 8th ADT workshop, Lecture Notes in Computer Science 655, 126–143. Springer Verlag, 1992.
- Jon Barwise. Axioms for abstract model theory. Annals of Mathematical Logic 7, 221–265,1974. CrossRef
- P. Burmeister. A model theoretic approach to partial algebras. Akademie Verlag, Berlin, 1986.
- M. Cerioli. Relationships between Logical Formalisms. PhD thesis, TD-4/93, Università di Pisa-Genova-Udine, 1993.
- H. Ehrig, P. Pepper, F. Orejas. On recent trends in algebraic specification. In Proc. ICALP'89, Lecture Notes in Computer Science 372, 263–288. Springer Verlag, 1989.
- J. A. Goguen. A categorical manifesto. Mathematical Structures in Computer Science 1, 49–67, 1991. CrossRef
- J. A. Goguen, R. M. Burstall. A study in the foundations of programming methodology: Specifications, institutions, charters and parchments. In D. Pitt et al., ed., Category Theory and Computer Programming, Lecture Notes in Computer Science 240, 313–333. Springer Verlag, 1985.
- J. A. Goguen, R. M. Burstall. Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery 39, 95–146, 1992. Predecessor in: LNCS 164, 221–256, 1984.
- S.C. Kleene. Introduction to Metamathematics. North Holland, 1952.
- S. Mac Lane. Categories for the working mathematician. Springer, 1972.
- CoFI Task Group on Language Design. CASL-The CoFI Algebraic Specification Language-Summary. CoFI Document: CASL/Summary. WWW7, FTP8, May 1997.
- J. Meseguer. General logics. In Logic Colloquium 87, 275–329. North Holland, 1989.
- T. Mossakowski. Using limits of parchments to systematically construct institutions of partial algebras. In M. Haveraaen, O. Owe, O.-J. Dahl, eds., Recent Trends in Data Type Specifications. 11th Workshop on Specification of Abstract Data Types, Lecture Notes in Computer Science 1130, 379–393. Springer Verlag, 1996.
- Peter D. Mosses. CoFI: The Common Framework Initiative for Algebraic Specification and Development. In M. Bidoit, M. Dauchet, eds., TAPSOFT 97, Lecture Notes in Computer Science 1214, 115–137. Springer Verlag, 1997.
- P. Padawitz. Computing in Horn Clause Theories. Springer Verlag, Heidelberg, 1988.
- W. Pawłowski. Context institutions. In M. Haveraaen, O. Owe, O.-J. Dahl, eds., Recent Trends in Data Type Specifications. 11th Workshop on Specification of Abstract Data Types, Lecture Notes in Computer Science 1130, 436–457. Springer Verlag, 1996.
- G. Priest. Inconsistent arithmetics and non-Euclidean geometries. Invited talk at Logic Colloquium, San Sebasitan, 1996.
- P. Stefaneas. The first order parchment. Report PRG-TR-16-92, Oxford University Computing Laboratory, 1992.
- A. Tarlecki. Bits and pieces of the theory of institutions. In D. Pitt, S. Abramsky, A. Poigné, D. Rydeheard, eds., Proc. Intl. Workshop on Category Theory and Computer Programming, Guildford 1985, Lecture Notes in Computer Science 240, 334–363. Springer-Verlag, 1986.
- A. Tarlecki. Moving between logical systems. In M. Haveraaen, O. Owe, O.-J. Dahl, eds., Recent Trends in Data Type Specifications. 11th Workshop on Specification of Abstract Data Types, Lecture Notes in Computer Science 1130, 478–502. Springer Verlag, 1996.
- Combining and representing logical systems
- Book Title
- Category Theory and Computer Science
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- 7th International Conference, CTCS '97 Santa Margherita Ligure Italy, September 4–6, 1997 Proceedings
- pp 177-196
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- 1. Department of Computer Science, University of Bremen, P.O.Box 33 04 40, D-28334, Bremen, Germany
- 2. Institute of Informatics, Warsaw University and Institute of Computer Science, Polish Academy of Sciences, Warsaw
- 3. Institute of Computer Science, Polish Academy of Sciences, Gdańsk
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