Readings in nonmonotonic reasoning
Readings in nonmonotonic reasoning
What does a conditional knowledge base entail?
Artificial Intelligence
The uncertain reasoner's companion: a mathematical perspective
The uncertain reasoner's companion: a mathematical perspective
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Belief Revision
Reasoning about Uncertainty
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
A counterexample to theorems of Cox and fine
Journal of Artificial Intelligence Research
Possibility theory and statistical reasoning
Computational Statistics & Data Analysis
Making solomonoff induction effective: or: you can learn what you can bound
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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The question of how to represent and process uncertainty is of fundamental importance to the scientific process, but also in everyday life. Currently there exist a lot of different calculi for managing uncertainty, each having its own advantages and disadvantages. Especially, almost all are defining the domain and structure of uncertainty values a priori, e.g., one real number, two real numbers, a finite domain, and so on, but maybe uncertainty is best measured by complex numbers, matrices or still another mathematical structure. Here we investigate the notion of uncertainty from a foundational point of view, provide an ontology and axiomatic core system for uncertainty, derive and not define the structure of uncertainty, and review the historical development of approaches to uncertainty which have led to the results presented here.