A standard view in cognitive psychology is that people estimate probabilities using heuristics that do not follow probability theory. We describe a model of probability estimation where people do follow probability theory in estimation, but are subject to random error or noise. This model predicts that people’s conditional probability estimates will agree closely with probability theory for cer...

In the probabilistic approach tb uncertainty management the input knowledge is usually represented by means of some probability distributions. In this paper we assume that the input knowledge is given by two discrete conditional probability distributions, represented by two stochastic matrices P and Q. The consistency of the knowledge base is analyzed. Coherence conditions and explicit formulas...

Since Störring’s [63] pioneering experiments on syllogistic reasoning at the beginning of last century, experimental psychology has investigated deductive reasoning in the framework of classical logic. The most prominent examples are the theories of mental models [27] and mental rules [8, 59]. A fragment of the model theory of classical logic is central to mental models. Likewise, a fragment of...

The purpose of this note is to take a few steps toward a first order logic of incomplete information, based on the idea that such a logic may be obtained by importing an essential ingredient of probability theory, conditional expectation, into the logic. The reason that we focus on conditional expectation is that it is often used to model a kind of incomplete knowledge that is of interest in it...

We study the problem of computing conditional probabilities, a fundamental operation in statistics and machine learning. In the elementary discrete setting, a ratio of probabilities defines conditional probability. In the abstract setting, conditional probability is defined axiomatically and the search for more constructive definitions is the subject of a rich literature in probability theory a...

Conditional statements, including subjunctive and counterfactual conditionals, are the source of many enduring challenges in formal reasoning. The language of probability can distinguish among several different kinds of conditionals, thereby strengthening our methods of analysis. Here we shall use probability to define four principal types of conditional statements: SUBJUNCTIVE, MATERIAL, EXIST...

This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain “triangle-fill-in” condition, connecting marginal and joint probabilities, in the Kleisli category of the distribution monad. The conditional probabilities are induced by a map together with a predicate (the condit...

Probability theory first reached its modern form in the work of Kolmogorov.1 Along with his famous axioms for unconditional probability, he gave a formula for calculating conditional probabilities. “If P (A) > 0, then the quotient PA(B) = P (AB) P (A) is defined to be the conditional probability of the event B under the condition A.”2 (Throughout this paper, I will use the more standard notatio...

breast cancer is a major public health problem for women in the iran and many other parts of the world. dynamic contrast-enhanced magnetic resonance imaging (dce-mri) plays a pivotal role in breast cancer care, including detection, diagnosis, and treatment monitoring. but segmentation of these images which is seriously affected by intensity inhomogeneities created by radio-frequency coils, is a...