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Combining Logics: Parchments Revisited

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Recent Trends in Algebraic Development Techniques (WADT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2267))

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Abstract

In the general context of the theory of institutions, several notions of parchment and parchment morphism have been proposed as the adequate setting for combining logics. However, so far, they seem to lack one of the main advantages of the combination mechanism known as fibring: general results of transference of important logical properties from the logics being combined to the resulting fibred logic. Herein, in order to bring fibring to the institutional setting, we propose to work with the novel notion of c-parchment. We show how both free and constrained fibring can be characterized as colimits of c-parchments, and illustrate both the construction and its preservation capabilities by exploring the idea of obtaining partial equational logic by fibring equational logic with a suitable logic of partiality. Last but not least, in the restricted context of propositional based, we state and prove a collection of meaningful soundness and completeness preservation results for fibring, with respect to Hilbert-like proof-calculi.

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Authors and Affiliations

  1. CMA/CLC - Dep. de Matemática, IST, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    C. Caleiro, P. Mateus, J. Ramos & A. Sernadas

Authors
  1. C. Caleiro
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  2. P. Mateus
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  3. J. Ramos
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  4. A. Sernadas
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Editor information

Editors and Affiliations

  1. DISI -Dipartimento e Informatica di Scienze dell’Informazione, Università di Genova, Via Dodecaneso,35, 16146, Genova, Italy

    Maura Cerioli  & Gianna Reggio  & 

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Caleiro, C., Mateus, P., Ramos, J., Sernadas, A. (2002). Combining Logics: Parchments Revisited. In: Cerioli, M., Reggio, G. (eds) Recent Trends in Algebraic Development Techniques. WADT 2001. Lecture Notes in Computer Science, vol 2267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45645-7_3

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  • DOI: https://doi.org/10.1007/3-540-45645-7_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43159-6

  • Online ISBN: 978-3-540-45645-2

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