eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-11-17
9:1
9:15
10.4230/LIPIcs.CALCO.2017.9
article
The Positivication of Coalgebraic Logics
Dahlqvist, Fredrik
Kurz, Alexander
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol072-calco2017/LIPIcs.CALCO.2017.9/LIPIcs.CALCO.2017.9.pdf
Coalgebraic logic
coalgebras
enriched category theory
boolean algebra
distributive lattice
positive modal logic
monotone modal logic