Related papers: Decision under Uncertainty
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
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…
In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure,…
We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability constraints and on a preferred-model…
We introduce a logical framework for reasoning about "uncertain interpretations" and investigate two key applications: a new semantics for implication capturing a kind of "meaning entailment", and a conservative notion of "evidentially…
We propose an integration of possibility theory into non-classical logics. We obtain many formal results that generalize the case where possibility and necessity functions are based on classical logic. We show how useful such an approach is…
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
This paper describes the incorporation of uncertainty in diagnostic reasoning based on the set covering model of Reggia et. al. extended to what in the Artificial Intelligence dichotomy between deep and compiled (shallow, surface) knowledge…
A decision maker's utility depends on her action $a\in A \subset \mathbb{R}^d$ and the payoff relevant state of the world $\theta\in \Theta$. One can define the value of acquiring new information as the difference between the maximum…
This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a…
Reliability (survival analysis, to biostatisticians) is a key ingredient for mak- ing decisions that mitigate the risk of failure. The other key ingredient is utility. A decision theoretic framework harnesses the two, but to invoke this…
When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
During interactions with human consultants, people are used to providing partial and/or inaccurate information, and still be understood and assisted. We attempt to emulate this capability of human consultants; in computer consultation…
Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…
There are multiple proposed interpretations of probability theory: one such interpretation is true-false logic under uncertainty. Cox's Theorem is a representation theorem that states, under a certain set of axioms describing the meaning of…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…