The Positivication of Coalgebraic Logics

Authors

Fredrik Dahlqvist, University College London
Alexander Kurz, Chapman UniversityFollow

Document Type

Conference Proceeding

Publication Date

2017

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.

Comments

This paper was originally presented at the Conference on Algebra and Coalgebra in Computer Science (CALCO) in 2017. DOI: 10.4230/LIPIcs.CALCO.2017.9

Recommended Citation

F. Dahlqvist and A. Kurz, “The Positivication of Coalgebraic Logics,” Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany, 2017. doi: 10.4230/LIPIcs.CALCO.2017.9

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.