Non-iterative Modal Logics are Coalgebraic

Forster J, Schröder L (2020)

Publication Language: English

Publication Type: Conference contribution

Publication year: 2020

Publisher: College Publications

Series: Advances in Modal Logic

Book Volume: 13

Pages Range: 229-248

Event location: Virtual, Helsinki FI

ISBN: 978-1-84890-341-8

URI: http://www.aiml.net/volumes/volume13/Forster-Schroeder.pdf

Abstract

A modal logic is non-iterative if it can be defined by axioms that do not nest modal operators, and rank-1 if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every syntactically defined rank-1 modal logic can be equipped with a canonical coalgebraic semantics, ensuring soundness and strong completeness. In the present work, we extend this result to non-iterative modal logics, showing that every non-iterative modal logic can be equipped with a canonical coalgebraic semantics defined in terms of a copointed functor, again ensuring soundness and strong completeness via a canonical model construction. Like in the rank-1 case, the coalgebraic semantics is equivalent to a neighbourhood semantics with suitable frame conditions, so that our main result may be phrased as saying that every non-iterative modal logic is complete over its neighbourhood semantics. As an example application of these results, we establish strong completeness of deontic logics with factual detachment, strengthening previous weak completeness results.

Authors with CRIS profile

Jonas Forster Lehrstuhl für Informatik 8 (Theoretische Informatik) Lutz Schröder Lehrstuhl für Informatik 8 (Theoretische Informatik)

How to cite

APA:

Forster, J., & Schröder, L. (2020). Non-iterative Modal Logics are Coalgebraic. In Nicola Olivetti, Rineke Verbrugge, Sara Negri, Sara Negri, Gabriel Sandu (Eds.), Proceedings of the 13th Conference on Advances in Modal Logic, AiML 2020 (pp. 229-248). Virtual, Helsinki, FI: College Publications.

MLA:

Forster, Jonas, and Lutz Schröder. "Non-iterative Modal Logics are Coalgebraic." Proceedings of the 13th Conference on Advances in Modal Logic, AiML 2020, Virtual, Helsinki Ed. Nicola Olivetti, Rineke Verbrugge, Sara Negri, Sara Negri, Gabriel Sandu, College Publications, 2020. 229-248.

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