72 research outputs found
Quantale Modules and their Operators, with Applications
The central topic of this work is the categories of modules over unital
quantales. The main categorical properties are established and a special class
of operators, called Q-module transforms, is defined. Such operators - that
turn out to be precisely the homomorphisms between free objects in those
categories - find concrete applications in two different branches of image
processing, namely fuzzy image compression and mathematical morphology
A Unified Algebraic Framework for Fuzzy Image Compression and Mathematical Morphology
In this paper we show how certain techniques of image processing, having
different scopes, can be joined together under a common "algebraic roof"
Sup-lattice 2-forms and quantales
A 2-form between two sup-lattices L and R is defined to be a sup-lattice
bimorphism L x R -> 2. Such 2-forms are equivalent to Galois connections, and
we study them and their relation to quantales, involutive quantales and
quantale modules. As examples we describe applications to C*-algebras.Comment: 30 pages. Contains more detailed background section and corrections
of several typos and mistake
An order-theoretic analysis of interpretations among propositional deductive systems
In this paper we study interpretations and equivalences of propositional
deductive systems by using a quantale-theoretic approach introduced by Galatos
and Tsinakis. Our aim is to provide a general order-theoretic framework which
is able to describe and characterize both strong and weak forms of
interpretations among propositional deductive systems also in the cases where
the systems have different underlying languages
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