Related papers: Non-Monotonicity in Probabilistic Reasoning
Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…
Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…
We propose an abductive diagnosis theory that integrates probabilistic, causal and taxonomic knowledge. Probabilistic knowledge allows us to select the most likely explanation; causal knowledge allows us to make reasonable independence…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
The difficulty in manipulating quantum resources deterministically often necessitates the use of probabilistic protocols, but the characterization of their capabilities and limitations has been lacking. We develop a general approach to this…
In broad applications, it is routinely of interest to assess whether there is evidence in the data to refute the assumption of conditional independence of $Y$ and $X$ conditionally on $Z$. Such tests are well developed in parametric models…
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…
Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic…
Defeasible conditionals are a form of non-monotonic inference which enable the expression of statements like "if $\phi$ then normally $\psi$". The KLM framework defines a semantics for the propositional case of defeasible conditionals by…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…
We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions…
Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…