Abstract
Adopting the concept of institution to represent logical frames, we have introduced in a previous paper the concept of simulation of an institution by another. Here we first show how simulations can be used to investigate the relationships between frames, distinguishing three levels, corresponding to different kinds of simulations: “set-theoretic”, where the individual models of different frames are related disregarding their categorical and logical interconnection, “categorical”, where the relation is between the categories of models, and “logical”, where the relation is between specifications. Then we propose a concept of translation of inference systems along simulations such that soundness and completeness are preserved.
This work has been partially supported by Esprit-BRA W.G. n.3264 Compass, Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of C.N.R. (Italy), MURST-40% Modelli e Specifiche di Sistemi Concorrenti
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
E. Astesiano and M. Cerioli. On the existence of initial models for partial (higher-order) conditional specifications. In TAPSOFT'89, number 351 in Lecture Notes in Computer Science, pages 74–88, Berlin, 1989. Springer Verlag.
E. Astesiano and M. Cerioli. Commuting between institutions via simulation. Technical report, University of Genova, 1990.
E. Astesiano and M. Cerioli. Free objects and equational deduction for partial conditional specifications. Technical report, University of Genova, 1990.
E. Astesiano and M. Cerioli. Partial higher-order specifications. In Math. Found. of Comp. Sci. '91, number 520 in Lecture Notes in Computer Science, pages 74–84, Berlin, 1991. Springer Verlag.
E. Astesiano and M. Cerioli. Partial higher-order specifications. Fundamenta Informaticae, 16(2), 1992. To appear.
M. Broy and M. Wirsing. Partial abstract types. Acta Information, (18):47–64, 1982.
P. Burmeister. Partial algebras — survey of an unifying approach towards a two-valued model theory for partial algebras. Algebra Universalis, 15, 1982.
R. Burstall and J. Goguen. Introducing institutions. In E. Clarke and D. Kozen, editors, Logics of Programming Workshop, number 164 in Lecture Notes in Computer Science, pages 221–255, Berlin, 1984. Springer Verlag.
R. Burstall and J. Goguen. Institutions: Abstract model theory for specification and programming. Technical report. Computer Science Lab., SRI International, 1990.
V. Manca and A. Salibra. Equational calculi for many-sorted algebras with empty carriers. In Math. Found. of Comp. Sci. '90, number 452 in Lecture Notes in Computer Science. 1990.
V. Manca, A. Salibra, and G. Scollo. On the expressiveness of equational type logic. In C. Rattray and R. Clark, editors, The Unified Computation Laboratory. Oxford University Press, 1992.
K. Meinke. Universal algebra in higher types. Theoretical Computer Science, 1992.
J. Meseguer. General logics. In Logic Colloquium '87. North Holland, 1989.
J. Meseguer and J. Goguen. Initiality, Induction and Computability, pages 459–540. Cambridge University Press, Cambridge, 1985.
B. Möller. Algebraic specifications with higher-order operations. In IFJP TC 2 Working Conference on Program Specification and Transformation. North Holland, 1987.
P. Mosses. Unified algebras and modules. Technical Report DAIMI PB-266, CS Dept., Aarhus University, 1988.
M. Navarro, P. Nivela, F. Orejas, and A. Sanchez. On translating partial to total specifications with applications to theorem proving for partial specifications. Technical Report LSI-89-21, Universitat Politecnica de Catalunya, 1990.
P. Padawitz and M. Wirsing. Completeness of many-sorted equational logic revisited. Bulletin EATCS, (24), 1984.
Z. Qian. Higher-order order-sorted algebras. In 2nd International Conference on Algebraic and Logic Programming, Lecture Notes in Computer Science, Berlin, 1990.
H. Reichel. Initial Computability, Algebraic Specifications, and Partial Algebras. Oxford University Press, 1987.
A. Salibra and G. Scollo. A soft stairway to institutions. In this volume, August 1991.
D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, (76):165–210, 1988.
D. Sannella and M. Wirsing. Implementations of parameterized specifications. In 9th Colloquium on Automata, Languages and Programming, number 140 in Lecture Notes in Computer Science, Berlin, 1982. Springer Verlag.
A. Tarlecki. Quasi-varieties in abstract algebraic institutions. Journal of Computer and System Science, (33):333–360, 1986.
A. Tarlecki. Institution representation. draft note, November 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Astesiano, E., Cerioli, M. (1993). Relationships between logical frameworks. In: Bidoit, M., Choppy, C. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1991 1991. Lecture Notes in Computer Science, vol 655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56379-2_37
Download citation
DOI: https://doi.org/10.1007/3-540-56379-2_37
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56379-2
Online ISBN: 978-3-540-47545-3
eBook Packages: Springer Book Archive