Open Access. Powered by Scholars. Published by Universities.®

Other Computer Engineering Commons

Open Access. Powered by Scholars. Published by Universities.®

Chapman University

Positive modal logic

Publication Year

Articles 1 - 2 of 2

Full-Text Articles in Other Computer Engineering

The Positivication Of Coalgebraic Logics, Fredrik Dahlqvist, Alexander Kurz Jan 2017

The Positivication Of Coalgebraic Logics, Fredrik Dahlqvist, Alexander Kurz

Engineering Faculty Articles and Research

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 ...


Positive Fragments Of Coalgebraic Logics, Adriana Balan, Alexander Kurz, Jirí Velebil Jan 2015

Positive Fragments Of Coalgebraic Logics, Adriana Balan, Alexander Kurz, Jirí Velebil

Engineering Faculty Articles and Research

Positive modal logic was introduced in an influential 1995 paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization that derives all modal formulas that are valid on all Kripke frames and are built only from atomic propositions, conjunction, disjunction, box and diamond. In this paper, we provide a coalgebraic analysis of this theorem, which not only gives a conceptual proof based on duality theory, but also generalizes Dunn's result from Kripke frames to coalgebras for weak-pullback preserving functors. To facilitate this analysis we prove a number of category theoretic results ...