Related papers: Topos Quantum Logic and Mixed States
To each quantum system, described by a von Neumann algebra of physical quantities, we associate a complete bi-Heyting algebra. The elements of this algebra represent contextualised propositions about the values of the physical quantities of…
Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units.…
In a recent paper [12], we discussed the serious inconsistency present within the operational and mathematical definition(s) of the notion of pure state. Continuing this analysis, in this work we attempt to address the role of 'purity' and…
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…
This is a series of lecture notes explaining topos theory and its application in physics.
We discuss some conceptual issues that any approach to quantum gravity has to confront. In particular, it is argued that one has to find a theory that can be interpreted in a realist manner, because theories with an instrumentalist…
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive,…
In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…
In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such 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…
The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due…
The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems.…
Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by 'superposition' in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the…
If one takes seriously the postulate of quantum mechanics in which physical states are rays in the standard Hilbert space of the theory, one is naturally lead to a geometric formulation of the theory. Within this formulation of quantum…
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…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a…