Related papers: Bayesian Probabilities and the Histories Algebra
In this paper we study the interaction between logic and probability. In particular, we show that the convex hull of evaluations of a broad class of logics is always effectively axiomatizable. We define a Birkhoff-style calculus for…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
This paper is a comparison of two theories of the probability of a history in quantum mechanics. One is derived from Copenhagen quantum mechanics using the projection postulate and is the basis of the "consistent histories" interpretation;…
In a recent paper Kent has pointed out that in consistent histories quantum theory it is possible, given initial and final states, to construct two different consistent families of histories, in each of which there is a proposition that can…
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
The consistent histories approach to quantum mechanics is traditionally based on linearly ordered sequences of events. We extend the histories formalism to sets of events whose causal ordering is described by directed acyclic graphs. The…
Generalised Bayesian learning algorithms are increasingly popular in machine learning, due to their PAC generalisation properties and flexibility. The present paper aims at providing a self-contained survey on the resulting PAC-Bayes…
We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. A quantum theory of closed systems requires two elements; 1) a condition specifying which sets of histories may…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
The formalism for histories-based generalized quantum mechanics developed in two earlier papers is applied to the treatment of histories (of particles or fields or more general objects) in curved spacetimes (which need not admit foliation…
In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and…
We introduce the idea of a {\it beable-guided quantum theory}. Beable-guided quantum theories (BGQT) are generalisations of quantum theory, inspired by Bell's concept of beables. They modify the quantum probabilities for some specified set…
Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical…
We present here a set of lecture notes on quantum thermodynamics and canonical typicality. Entanglement can be constructively used in the foundations of statistical mechanics. An alternative version of the postulate of equal a priori…
We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for…