We develop a formal system to reason about knowledge properties of quantum security protocols. The formalism is obtained via a marriage of measurement calculus [3], an algebraic framework for measurementbased quantum computing [7], with the algebra of epistemic actions and their appearance maps [1, 8]. Measurement calculus has also proven to be a proper language to describe and to analyse distr...

Let κQnt be the category of of κ-quantales, quantales closed under κ-joins in which the monoid identity is the largest element. (κ is an infinite regular cardinal.) Although the lack of lattice completeness in this setting would seem to mitigate against the techniques which lend themselves so readily to the calculation of frame quotients, we show how to easily compute κQnt quotients by applying...

The development of operational quantum logic points out that classical boolean structures are too rigid to describe the actual and potential properties of quantum systems. Operational quantum logic bears upon basic axioms which are motivated by empirical facts and as such supports the dynamic shift from classical to non-classical logic resulting into a dynamics of logic. On the other hand, a dy...

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 lead to consider cocomplete quantaloid-enriched categories as fu...

Some uniform categorical theoretical treatment of automata and lattice-valued fuzzy automata using quantale theory is studied in this paper. First, L-relational sheaves on a monoidM andQ-enriched categories are introduced for quantales L andQ, the equivalence of the corresponding categories are proved next. Then lattice-valued (fuzzy) automata are described by Q-enriched categories. In fact, la...

Abstract Behavioural distances measure the deviation between states in quantitative systems, such as probabilistic or weighted systems. There is growing interest generic approaches to behavioural distances. In particular, coalgebraic methods capture variations system type (nondeterministic, probabilistic, game-based etc.), and notion of quantale abstracts over actual values take, thus covering,...

Recently, I. Stubbe constructed an isomorphism between the categories of right Q-modules and cocomplete skeletal Q-categories for a given unital quantale Q. Employing his results, we obtain an isomorphism between the categories of Q-algebras and Q-quantales, where Q is additionally assumed to be commutative. As a consequence, we provide a common framework for two concepts of lattice-valued fram...

A principled approach to the design of program verification and construction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts resource monoids to assertion and predicate transformer quantales. The data flow is captured by concrete store/heap models. These are linked to the separation algeb...

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.