相关论文: Generalized Qualitative Probability: Savage revisi…

We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel and others. Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws…

Opacity is a general language-theoretic framework in which several security properties of a system can be expressed. Its parameters are a predicate, given as a subset of runs of the system, and an observation function, from the set of runs…

The systematic biases seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory, but instead use heuristics which sometimes yield reasonable…

The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…

For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows to construct new distributions with support (0,1), and to obtain a…

This paper proposes a decision theory for a symbolic generalization of probability theory (SP). Darwiche and Ginsberg [2,3] proposed SP to relax the requirement of using numbers for uncertainty while preserving desirable patterns of…

Generalized sorting problem, also known as sorting with forbidden comparisons, was first introduced by Huang et al. together with a randomized algorithm which requires $\tilde O(n^{3/2})$ probes. We study this problem with additional…

Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry,…

The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…

We describe a very general abstract form of sieve based on a large sieve inequality which generalizes both the classical sieve inequality of Montgomery (and its higher-dimensional variants), and our recent sieve for Frobenius over function…

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.

There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…

The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong…

A nonmonotonic logic of thresholded generalizations is presented. Given propositions A and B from a language L and a positive integer k, the thresholded generalization A=>B{k} means that the conditional probability P(B|A) falls short of one…

We give here a constructive account of the frequentist approach to probability, by means of natural density. Using this notion of natural density, we introduce some probabilistic versions of the Limited Principle of Omniscience. Finally we…

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…

Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social…

The 'expected utility hypothesis' is one of the foundations of classical approaches to economics and decision theory and Savage's 'Sure-Thing Principle' is a fundamental element of it. It has been put forward that real-life situations…

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…

This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…