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An Institution of Modal Logics for Coalgebras

An Institution of Modal Logics for Coalgebras
An Institution of Modal Logics for Coalgebras
This paper presents a modular framework for the specification of certain inductively-defined coalgebraic types. Modal logics for coalgebras of polynomial endofunctors on the category of sets have been studied in [M. Rößiger, Coalgebras and modal logic, in: H. Reichel (Ed.), Coalgebraic Methods in Computer Science, Electronic Notes in Theoretical Computer Science, vol. 33, Elsevier Science, 2000, pp. 299–320; B. Jacobs, Many-sorted coalgebraic modal logic: a model-theoretic study, Theoretical Informatics and Applications 35(1) (2001) 31–59]. These logics are here generalised to endofunctors on categories of sorted sets, in order to allow collections of inter-related types to be specified simultaneously. The inductive nature of the coalgebraic types considered is then used to formalise semantic relationships between different types, and to define translations between the associated logics. The resulting logical framework is shown to be an institution, whose specifications and specification morphisms admit final and respectively cofree models.
Coalgebras, Modal logic, Institutions
87-113
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Orejas, F.
504adad9-f835-4ae9-9e50-6eb1ef26df9a
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Orejas, F.
504adad9-f835-4ae9-9e50-6eb1ef26df9a

Cirstea, Corina, Orejas, F.(ed.) (2006) An Institution of Modal Logics for Coalgebras Journal of Logic and Algebraic Programming, 67, (1-2), pp. 87-113.

Record type: Article

Abstract

This paper presents a modular framework for the specification of certain inductively-defined coalgebraic types. Modal logics for coalgebras of polynomial endofunctors on the category of sets have been studied in [M. Rößiger, Coalgebras and modal logic, in: H. Reichel (Ed.), Coalgebraic Methods in Computer Science, Electronic Notes in Theoretical Computer Science, vol. 33, Elsevier Science, 2000, pp. 299–320; B. Jacobs, Many-sorted coalgebraic modal logic: a model-theoretic study, Theoretical Informatics and Applications 35(1) (2001) 31–59]. These logics are here generalised to endofunctors on categories of sorted sets, in order to allow collections of inter-related types to be specified simultaneously. The inductive nature of the coalgebraic types considered is then used to formalise semantic relationships between different types, and to define translations between the associated logics. The resulting logical framework is shown to be an institution, whose specifications and specification morphisms admit final and respectively cofree models.

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Published date: 2006
Keywords: Coalgebras, Modal logic, Institutions
Organisations: Electronic & Software Systems

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Local EPrints ID: 261662
URI: http://eprints.soton.ac.uk/id/eprint/261662
PURE UUID: f175799f-134b-48c2-a64e-d3f2faa35310

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Date deposited: 14 Dec 2005
Last modified: 10 Nov 2017 20:04

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Contributors

Author: Corina Cirstea
Editor: F. Orejas

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