Related papers: A Logic for Arguing About Probabilities in Measure…
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays the important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of…
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…
The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
Three basic postulates for Quantum Theory are proposed, namely the Probability, Maximum-Speed and Hilbert-Space postulates. Subsequently we show how these postulates give rise to well-known and widely used quantum results, as the…
This note generalizes the notion of conditional probability to Riesz spaces using the order-theoretic approach. With the aid of this concept, we establish the law of total probability and Bayes' theorem in Riesz spaces; we also prove an…
Complex classifiers may exhibit "embarassing" failures in cases where humans can easily provide a justified classification. Avoiding such failures is obviously of key importance. In this work, we focus on one such setting, where a label is…
Combining measurements which have "theoretical uncertainties" is a delicate matter, due to an unclear statistical basis. We present an algorithm based on the notion that a theoretical uncertainty represents an estimate of bias.
We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations…
For a symmetric hyperbolic system of the first order, we prove a Carleman estimate under some positivity condition concerning the coefficient matrices. Next, applying the Carleman estimate, we prove an observability $L^2$-estimate for…
Some exact formulae of the expectation values and probability densities in a weak measurement for an operator ${\bf A}$ which satisfies the property ${\bf A}^{2}=1$ are derived. These formulae include all-order effects of the unitary…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…