Generalised distributivity and the logic of metric spaces

The aim of the thesis is to work towards a many-valued logic over a commutative unital quantale and, at the same time, towards a generalisation of coalgebraic logic enriched over a commutative unital quantale Ω. This is done by noticing that the contravariant powerset adjunction can be generalised t...

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Main Author:	Babus, Octavian Vladut
Other Authors:	Kurz, Alexander ; de Vries, Fer-Jan
Published:	University of Leicester 2016
Subjects:	514
Online Access:	http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.686597

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spelling	ndltd-bl.uk-oai-ethos.bl.uk-6865972017-10-04T03:31:04ZGeneralised distributivity and the logic of metric spacesBabus, Octavian VladutKurz, Alexander ; de Vries, Fer-Jan2016The aim of the thesis is to work towards a many-valued logic over a commutative unital quantale and, at the same time, towards a generalisation of coalgebraic logic enriched over a commutative unital quantale Ω. This is done by noticing that the contravariant powerset adjunction can be generalised to categories enriched over a commutative unital quantale. From here we define categorical algebras for the monad generated by this adjunction. We finish by showing that these categorical algebras are algebras over Set with operations and equations, and show that in some cases we can restrict the arity of those operations to be finite.514University of Leicesterhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.686597http://hdl.handle.net/2381/37701Electronic Thesis or Dissertation
collection	NDLTD
sources	NDLTD
topic	514
spellingShingle	514 Babus, Octavian Vladut Generalised distributivity and the logic of metric spaces
description	The aim of the thesis is to work towards a many-valued logic over a commutative unital quantale and, at the same time, towards a generalisation of coalgebraic logic enriched over a commutative unital quantale Ω. This is done by noticing that the contravariant powerset adjunction can be generalised to categories enriched over a commutative unital quantale. From here we define categorical algebras for the monad generated by this adjunction. We finish by showing that these categorical algebras are algebras over Set with operations and equations, and show that in some cases we can restrict the arity of those operations to be finite.
author2	Kurz, Alexander ; de Vries, Fer-Jan
author_facet	Kurz, Alexander ; de Vries, Fer-Jan Babus, Octavian Vladut
author	Babus, Octavian Vladut
author_sort	Babus, Octavian Vladut
title	Generalised distributivity and the logic of metric spaces
title_short	Generalised distributivity and the logic of metric spaces
title_full	Generalised distributivity and the logic of metric spaces
title_fullStr	Generalised distributivity and the logic of metric spaces
title_full_unstemmed	Generalised distributivity and the logic of metric spaces
title_sort	generalised distributivity and the logic of metric spaces
publisher	University of Leicester
publishDate	2016
url	http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.686597
work_keys_str_mv	AT babusoctavianvladut generaliseddistributivityandthelogicofmetricspaces
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Generalised distributivity and the logic of metric spaces

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