Informatics Report Series



Related Pages

Report (by Number) Index
Report (by Date) Index
Author Index
Institute Index

Title:Categorical Perspectives
Authors: Michael Fourman
Date:Oct 2007
Publication Title:14th International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR), Yerevan Armenia, October 2007
Publication Type:Conference Paper Publication Status:Pre-print
Quantales provide an abstract algebra of actions equipped with an infinitary operation (sup) of non-deterministic alternation. Formally, they are monoids in the category of complete sup-lattices. Quantales have provided a setting for studying ontic actions and various process equivalences. More recently, they have been used as a semantic setting for discussion of epistemic actions and quantum logics. The archetypical example is given by the monoid of binary relations on a set S. We think of these as non-deterministic actions, acting on states that are elements of S. It is known that every quantale may be represented as a quantale of relations - indeed, Q has a representation as a set of relations on Q. However, these representations use a subset of relations that is not, in general, closed under suprema, so non-determinism is not faithfully represented. We seek to interpret Q faithfully as a quantale of relations over a non-classical set. Given a quantale, Q, we construct the classifying topos for a set equipped with relations reflecting the structure of Q. We represent Q as a quantale of global sections of the generic object in this classifying topos. The site supporting this classifying topos has as objects finitely presented transition systems that represent lax quotients of Q. We interpret these as perspectives, representing a local focus on some aspects of the world - a finitely-observable set of observations of the effects of some actions, compatible with the structure of Q.
2007 by Michael Fourman and The University of Edinburgh. All Rights Reserved
Links To Paper
No links available
Bibtex format
author = { Michael Fourman },
title = {Categorical Perspectives},
book title = {14th International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR), Yerevan Armenia, October 2007},
year = 2007,
month = {Oct},

Home : Publications : Report 

Please mail <> with any changes or corrections.
Unless explicitly stated otherwise, all material is copyright The University of Edinburgh