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On a purely categorical framework for coalgebraic modal logic

Chen, Liang-Ting (2014)
Ph.D. thesis, University of Birmingham.

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Abstract

A category CoLog of distributive laws is introduced to unify different approaches to modal logic for coalgebras, based merely on the presence of a contravariant functor P
that maps a state space to its collection of predicates. We show that categorical constructions, including colimits, limits, and compositions of distributive laws as a tensor product, in CoLog generalise and extend existing constructions given for Set coalgebraic logics and that the framework does not depend on any particular propositional logic or state space.

In the case that P establishes a dual adjunction with its dual functor S, we show that a canonically defined coalgebraic logic exists for any type of coalgebras. We further restrict our discussion to finitary algebraic logics and study equational coalgebraic logics. Objects of predicate liftings are used to characterise equational coalgebraic logics.

The expressiveness problem is studied via the mate correspondence, which gives an isomorphism between CoLog and the comma category from the pre-composition to the post-composition with S. Then, the modularity of the expressiveness is studied in the comma category via the notion of factorisation system.

Type of Work:Ph.D. thesis.
Supervisor(s):Jung , Achim
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Computer Science
Subjects:QA75 Electronic computers. Computer science
Institution:University of Birmingham
ID Code:4882
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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