Related papers: Deriving laws from ordering relations
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…
What is a question? According to Cox a question can be identified with the set of assertions that constitute possible answers. In this paper we propose a different approach that combines the notion that questions are requests for…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…
Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We…
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
The probabilistic rule that links the formalism of Quantum Mechanics (QM) to the real world was stated by Born in 1926. Since then, there were many attempts to derive the Born postulate as a theorem, Gleason's being the most prominent. The…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
Bell's 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbach's Principle of Common Cause. Despite being a hallmark of scientific thought, dropping the principle has been…
We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of…
The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum…
We establish two new direct product theorems for the randomized query complexity of Boolean functions. The first shows that computing $n$ copies of a function $f$, even with a small success probability of $\gamma^n$, requires $\Theta(n)$…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
In the literature, derivations of exact null distributions of rank-sum statistics is often avoided in cases where one or more ties exist in the data. By deriving the null distribution in the no-ties case with the aid of classical $q$-series…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…