PP-2009-16: Equational Coalgebraic Logic

PP-2009-16: Leal, Raul and Kurz, Alexander (2009) Equational Coalgebraic Logic. [Report]

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Abstract

Coalgebra develops a general theory of transition systems, parametric in a functor $T$; the functor $T$ specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor $T$, a logic for $T$-coalgebras. We compare two existing proposals, Moss's coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in \cite{leal:cmcs08} by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatization of Moss's logic. The three logics are equivalent for a natural but restricted class of functors. We give examples showing that the logics fall apart in general. Finally, we argue that the quest for a generic logic for $T$-coalgebras is still open in the general case.

Item Type: Report
Report Nr: PP-2009-16
Series Name: Prepublication (PP) Series
Year: 2009
Uncontrolled Keywords: Coalgebra; Caolgebraic Logic; Stone Duality; Predicate liftings; Moss' modality
Depositing User: raulleal
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/346

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