Related papers: Measuring on Lattices
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.
The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…
We apply the algebraic theory of infinite classical lattices from Part I to write an axiomatic theory of measurements, based on Mackey's axioms for quantum mechanics. The axioms give a complete theory of measurements in the sense of Haag…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra…
This is the third in a series of papers dealing with the algebraic theory of infinite classical lattices. This paper presents a theory of single measurements on a lattice which we represent as comprising a finite subvolume--the system of…
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…
In decision theory an act is a function from a set of conditions to the set of real numbers. The set of conditions is a partition in some algebra of events. The expected value of an act can be calculated when a probability measure is given.…
I provide a simple derivation of the Born rule as giving a classical probability, that is, the ratio of the measure of favorable states of the system to the measure of its total possible states. In classical systems, the probability is due…
In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a…
The problem of relating the mathematics of probability theory to the empirical world of experiments has been debated for centuries. One of the oldest solutions proposed for this problem is a principle that states that an event with…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
There has not been an established mathematical measure of evidence. Some Bayesians have argued that probability can be an objectively correct measure of ``rational degrees of belief,'' which we do not distinguish from evidence. However,…
We study the origin of quantum probabilities as arising from non-boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorvian…
The theory of influences in product measures has profound applications in theoretical computer science, combinatorics, and discrete probability. This deep theory is intimately connected to functional inequalities and to the Fourier analysis…
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…