# On a purely categorical framework for coalgebraic modal logic

Chen, Liang-Ting (2014). On a purely categorical framework for coalgebraic modal logic. University of Birmingham. Ph.D.

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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: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Jung , AchimUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Computer Science
Funders: None/not applicable
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
URI: http://etheses.bham.ac.uk/id/eprint/4882

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