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On the Algebraization of Many-Sorted Logics

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Recent Trends in Algebraic Development Techniques (WADT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4409))

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Abstract

The theory of abstract algebraic logic aims at drawing a strong bridge between logic and universal algebra, namely by generalizing the well known connection between classical propositional logic and Boolean algebras. Despite of its successfulness, the current scope of application of the theory is rather limited. Namely, logics with a many-sorted language simply fall out from its scope. Herein, we propose a way to extend the existing theory in order to deal also with many-sorted logics, by capitalizing on the theory of many-sorted equational logic. Besides showing that a number of relevant concepts and results extend to this generalized setting, we also analyze in detail the examples of first-order logic and the paraconsistent logic \(\mathcal{C}_1\) of da Costa.

This work was partially supported by FCT and FEDER through POCI, namely via the QuantLog POCI/MAT/55796/2004 Project of CLC and the recent KLog initiative of SQIG-IT. The second author was also supported by FCT under the PhD grant SFRH/BD/18345/2004/SV7T and a PGEI research grant from Fundaçäo Calouste Gulbenkian.

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Authors and Affiliations

  1. CLC and SQIG-IT, Department of Mathematics, IST, TU Lisbon, Portugal

    Carlos Caleiro & Ricardo Gonçalves

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  1. Carlos Caleiro
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  2. Ricardo Gonçalves
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José Luiz Fiadeiro Pierre-Yves Schobbens

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Caleiro, C., Gonçalves, R. (2007). On the Algebraization of Many-Sorted Logics. In: Fiadeiro, J.L., Schobbens, PY. (eds) Recent Trends in Algebraic Development Techniques. WADT 2006. Lecture Notes in Computer Science, vol 4409. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71998-4_2

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  • DOI: https://doi.org/10.1007/978-3-540-71998-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71997-7

  • Online ISBN: 978-3-540-71998-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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