Towards "dynamic domains" : totally continuous cocomplete Q-categoriesTowards "dynamic domains" : totally continuous cocomplete Q-categories
Faculty of Sciences. Mathematics and Computer Science

Fundamental Mathematics

article

2007Amsterdam, 2007

Computer. Automation

Theoretical computer science. - Amsterdam

21st Annual Conference on Mathematical Foundations of Programming, Semantics (MFPS XXI), MAY 17-21, 2005, Univ Birmingham, Birmingham, ENGLAND

373(2007):1-2, p. 142-160

0304-3975

000245499700007

E

English (eng)

University of Antwerp

It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system organize themselves quite naturally in a quantale, or more generally, a quantaloid. In fact, we are led to consider cocomplete quantaloid-enriched categories as a fundamental mathematical structure for a dynamic logic common to both computer science and physics. Here we explain the theory of totally continuous cocomplete categories as a generalization of the well-known theory of totally continuous suplattices. That is to say, we undertake some first steps towards a theory of "dynamic domains". (c) 2007 Elsevier B.V. All rights reserved.

https://repository.uantwerpen.be/docman/iruaauth/8cd495/d0c4542.pdf

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