Related papers: A Topos Formulation of Consistent Histories

Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…

Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…

A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. One possibility is to find a scheme in which a unique set is selected in some…

The topos approach to the formulation of physical theories includes a new form of quantum logic. We present this topos quantum logic, including some new results, and compare it to standard quantum logic, all with an eye to conceptual…

The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can further the study of quantum logic and give rise to new…

Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Doering, as an alternative mathematical structure within which to formulate physical theories. In particular, it has been used to reformulate standard…

This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…

This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…

Sorkin's coevent interpretation shifts the focus of quantum logic from the structure of a propositional lattice to the nature of truth valuations thereon. We apply this shift in emphasis to a simple formulation of the consistent histories…

Topos theory has been suggested first by Isham and Butterfield, and then by Isham and D\"oring, as an alternative mathematical structure within which to formulate physical theories. In particular it has been used to reformulate standard…

Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving…

An introduction is given to an algebraic formulation and generalisation of the consistent histories approach to quantum theory. The main technical tool in this theory is an orthoalgebra of history propositions that serves as a generalised…

An idealized experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…

This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…

Isham's topos-theoretic perspective on the logic of the consistent-histories theory is extended in two ways. First, the presheaves of consistent sets of history propositions in the topos proposed by Isham are endowed with a Vietoris-type of…

This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a…

All current approaches to quantum gravity employ essentially standard quantum theory including, in particular, continuum quantities such as the real or complex numbers. However, I wish to argue that this may be fundamentally wrong in so far…

An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…

The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object, analogous to the state space of a…

We show how probabilities can be treated as truth values in suitable sheaf topoi. The scheme developed in this paper is very general and applies to both classical and quantum physics. On the quantum side, the results are a natural extension…