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Predicate Liftings and Functor Presentations in Coalgebraic Expression Languages

  • Ulrich Dorsch
  • Stefan Milius
  • Lutz Schröder
  • Thorsten Wißmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11202)

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.

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Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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