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Disjoint Fibring of Non-deterministic Matrices

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Logic, Language, Information, and Computation (WoLLIC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10388))

Abstract

In this paper we give a first definitive step towards endowing the general mechanism for combining logics known as fibring with a meaningful and useful semantics given by non-deterministic logical matrices (Nmatrices). We present and study the properties of two semantical operations: a unary operation of \(\omega \) -power of a given Nmatrix, and a binary operation of strict product of Nmatrices with disjoint similarity types (signatures). We show that, together, these operations can be used to characterize the disjoint fibring of propositional logics, when each of these logics is presented by a single Nmatrix. As an outcome, we also provide a decidability and complexity result about the resulting fibred logic. We illustrate the constructions with a few meaningful examples.

C. Caleiro—Work done under the scope of Project UID/EEA/50008/2013 of Instituto de Telecomunicações, financed by the applicable framework (FCT/MEC through national funds and co-funded by FEDER-PT2020). The first author also acknowledges the FCT postdoctoral grant SFRH/BPD/76513/2011. This research is part of the MoSH initiative of SQIG at Instituto de Telecomunicações.

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Notes

  1. 1.

    \({\langle A,\cdot _{\mathbb {M}}\rangle }\) is a multi-algebra, see [10, 18].

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Authors and Affiliations

  1. SQIG - Instituto de Telecomunicações, Dep. Matemática - Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Sérgio Marcelino & Carlos Caleiro

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  1. Sérgio Marcelino
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  2. Carlos Caleiro
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Correspondence to Sérgio Marcelino .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Juliette Kennedy

  2. Centro de Informática, Recife, Pernambuco, Brazil

    Ruy J.G.B. de Queiroz

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Marcelino, S., Caleiro, C. (2017). Disjoint Fibring of Non-deterministic Matrices. In: Kennedy, J., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2017. Lecture Notes in Computer Science(), vol 10388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55386-2_17

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  • DOI: https://doi.org/10.1007/978-3-662-55386-2_17

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