Predicate Liftings and Functor Presentations in Coalgebraic Expression Languages
Abstract
We introduce a generic expression language describing behaviours of finite coalgebras over sets; besides relational systems, this covers, e.g., weighted, probabilistic, and neighbourhood-based system types. We prove a generic Kleene-type theorem establishing a correspondence between our expressions and finite systems. Our expression language is similar to one introduced in previous work by Myers but has a semantics defined in terms of a particular form of predicate liftings as used in coalgebraic modal logic; in fact, our expressions can be regarded as a particular type of modal fixed point formulas. The predicate liftings in question are required to satisfy a natural preservation property; we show that this property holds in particular for the Moss liftings introduced by Marti and Venema in work on lax extensions.
Keywords
Cite
@article{arxiv.1805.07211,
title = {Predicate Liftings and Functor Presentations in Coalgebraic Expression Languages},
author = {Ulrich Dorsch and Stefan Milius and Lutz Schröder and Thorsten Wißmann},
journal= {arXiv preprint arXiv:1805.07211},
year = {2018}
}