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The Positivication of Coalgebraic Logics

Dahlqvist, FPH; Kurz, A; (2017) The Positivication of Coalgebraic Logics. In: Aceto, L and Alberts, S and Hankin, C and Kapur, D and Mitzenmacher, M and Mukund, M and Muscholl, A and Palamidessi, C and Schwentick, T and Wilhelm, R, (eds.) Proceedings of the 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). (pp. pp. 1-15). Leibniz-Zentrum für Informatik: Wadern, Germany. Green open access

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Abstract

We present positive coalgebraic logic in full generality, and show how to obtain a positive coalgebraic logic from a boolean one. On the model side this involves canonically computing a endofunctor T': Pos->Pos from an endofunctor T: Set->Set, in a procedure previously defined by the second author et alii called posetification. On the syntax side, it involves canonically computing a syntax-building functor L': DL->DL from a syntax-building functor L: BA->BA, in a dual procedure which we call positivication. These operations are interesting in their own right and we explicitly compute posetifications and positivications in the case of several modal logics. We show how the semantics of a boolean coalgebraic logic can be canonically lifted to define a semantics for its positive fragment, and that weak completeness transfers from the boolean case to the positive case.

Type: Proceedings paper
Title: The Positivication of Coalgebraic Logics
Event: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Location: Ljubljana, Slovenia
Dates: 12th-16th June 2017
ISBN-13: 978-3-95977-033-0
Open access status: An open access version is available from UCL Discovery
DOI: 10.4230/LIPIcs.CALCO.2017.9
Publisher version: http://dx.doi.org/10.4230/LIPIcs.CALCO.2017.0
Language: English
Additional information: © 2017 F. Dahlqvist and A. Kurz; licensed under Creative Commons License CC-BY (http://creativecommons.org/licenses/by/3.0/legalcode).
Keywords: Coalgebraic logic, coalgebras, enriched category theory, boolean algebra, distributive lattice, positive modal logic, monotone modal logic
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/10064489
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