Localic sup-lattices and tropological systems

✍ Scribed by Pedro Resende; Steven Vickers

• Book ID: 104325672
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 401 KB
• Volume: 305
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(02)00702-8

✦ Synopsis

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.