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Title: Enriched coalgebraic modal logic
Author: Wilkinson, Toby
ISNI:       0000 0004 2743 4570
Awarding Body: University of Southampton
Current Institution: University of Southampton
Date of Award: 2013
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We formalise the notion of enriched coalgebraic modal logic, and determine conditions on the category V (over which we enrich), that allow an enriched logical connection to be extended to a framework for enriched coalgebraic modal logic. Our framework uses V-functors L: A → A and T: X → X, where L determines the modalities of the resulting modal logics, and T determines the coalgebras that provide the semantics. We introduce the V-category Mod(A, α) of models for an L-algebra (A, α), and show that the forgetful V-functor from Mod(A, α) to X creates conical colimits. The concepts of bisimulation, simulation, and behavioural metrics (behavioural approximations),are generalised to a notion of behavioural questions that can be asked of pairs of states in a model. These behavioural questions are shown to arise through choosing the category V to be constructed through enrichment over a commutative unital quantale (Q, Ⓧ, I) in the style of Lawvere (1973). Corresponding generalisations of logical equivalence and expressivity are also introduced,and expressivity of an L-algebra (A, α) is shown to have an abstract category theoretic characterisation in terms of the existence of a so-called behavioural skeleton in the category Mod(A, α). In the resulting framework every model carries the means to compare the behaviour of its states, and we argue that this implies a class of systems is not fully defined until it is specified how states are to be compared or related.
Supervisor: Cirstea, Corina Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA75 Electronic computers. Computer science