The University of Southampton
University of Southampton Institutional Repository

Enriched coalgebraic modal logic

Enriched coalgebraic modal logic
Enriched coalgebraic modal logic
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, ?) 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, ?).

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.
Wilkinson, Toby
c711a6aa-a538-4b99-9048-3812a14d27a4
Wilkinson, Toby
c711a6aa-a538-4b99-9048-3812a14d27a4
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea

Wilkinson, Toby (2013) Enriched coalgebraic modal logic. University of Southampton, faculty of Physical Sciences and Engineering, Doctoral Thesis, 228pp.

Record type: Thesis (Doctoral)

Abstract

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, ?) 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, ?).

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.

Text
Wilkinson.pdf - Other
Download (1MB)

More information

Published date: May 2013
Organisations: University of Southampton, Electronic & Software Systems

Identifiers

Local EPrints ID: 354112
URI: http://eprints.soton.ac.uk/id/eprint/354112
PURE UUID: 0cedb4d4-aea5-43e2-972c-e8073aac86bf
ORCID for Corina Cirstea: ORCID iD orcid.org/0000-0003-3165-5678

Catalogue record

Date deposited: 02 Jul 2013 11:38
Last modified: 15 Mar 2024 03:18

Export record

Contributors

Author: Toby Wilkinson
Thesis advisor: Corina Cirstea ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×