Localic sup-lattices and tropological systems

Authors:
Pedro Resende;Steven Vickers
Affiliations:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England, UK
Venue:
Theoretical Computer Science - Topology in computer science
Year:
2003

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Abstract

The approach to process semantics using quantales and modules is topologized by considering tropological systems whose sets of states are replaced by locales and which satisfy a suitable stability axiom. A corresponding notion of localic sup-lattice (algebra for the lower powerlocale monad) is described, and it is shown that there are contravariant functors from sup-lattices to localic sup-lattices and, for each quantale Q, from left Q-modules to localic right Q-modules. A proof technique for third completeness due to Abramsky and Vickers is reset constructively, and an example of application to failures semantics is given.