Jonathan Lawry

Uncertainty in AI explores different theories of uncertainty as studied in the context of artificial intelligence. By adopting a common representation framework based on sets of possible worlds, it explores the relationships between different theories of uncertainty, taking note of the different properties that they satisfy, their expressiveness, and their computational complexity. It distinguishes between uncertainty about the true state of the world, ignorance about the correct level of uncertainty, and fuzziness in the propositions being evaluated. Concepts are introduced using simple illustrative examples, prioritising intuitive understanding before reviewing key mathematical results. This makes it ideal for undergraduate students wanting a sense of the strengths and weaknesses of different uncertainty formalisms, providing them with sufficient technical detail to begin to apply them in practice while requiring only foundation level mathematics — as taught in the first year of most science and engineering undergraduate programmes.This book is based on material from 'Uncertainty Modelling for Intelligent Systems', a course taught to 3rd and 4th year undergraduate engineers and computer scientists at the University of Bristol for more than a decade. Instead of promoting a particular approach to or philosophy of uncertainty, this book maps the landscape of uncertainty theories, explicitly highlighting the connections and relationships between them that often remain implicit. It provides students with a broad overview, allowing them to better assess which uncertainty formalisms are most appropriate within the context of a particular application.

Uncertainty in AI explores different theories of uncertainty as studied in the context of artificial intelligence. By adopting a common representation framework based on sets of possible worlds, it explores the relationships between different theories of uncertainty, taking note of the different properties that they satisfy, their expressiveness, and their computational complexity. It distinguishes between uncertainty about the true state of the world, ignorance about the correct level of uncertainty, and fuzziness in the propositions being evaluated. Concepts are introduced using simple illustrative examples, prioritising intuitive understanding before reviewing key mathematical results. This makes it ideal for undergraduate students wanting a sense of the strengths and weaknesses of different uncertainty formalisms, providing them with sufficient technical detail to begin to apply them in practice while requiring only foundation level mathematics — as taught in the first year of most science and engineering undergraduate programmes.This book is based on material from 'Uncertainty Modelling for Intelligent Systems', a course taught to 3rd and 4th year undergraduate engineers and computer scientists at the University of Bristol for more than a decade. Instead of promoting a particular approach to or philosophy of uncertainty, this book maps the landscape of uncertainty theories, explicitly highlighting the connections and relationships between them that often remain implicit. It provides students with a broad overview, allowing them to better assess which uncertainty formalisms are most appropriate within the context of a particular application.

Vague concepts are intrinsic to human communication. Somehow it would seems that vagueness is central to the flexibility and robustness of natural l- guage descriptions. If we were to insist on precise concept definitions then we would be able to assert very little with any degree of confidence. In many cases our perceptions simply do not provide sufficient information to allow us to verify that a set of formal conditions are met. Our decision to describe an individual as 'tall' is not generally based on any kind of accurate measurement of their height. Indeed it is part of the power of human concepts that they do not require us to make such fine judgements. They are robust to the imprecision of our perceptions, while still allowing us to convey useful, and sometimes vital, information. The study of vagueness in Artificial Intelligence (AI) is therefore motivated by the desire to incorporate this robustness and flexibility into int- ligent computer systems. This goal, however, requires a formal model of vague concepts that will allow us to quantify and manipulate the uncertainty resulting from their use as a means of passing information between autonomous agents. I first became interested in these issues while working with Jim Baldwin to develop a theory of the probability of fuzzy events based on mass assi- ments.

Vague concepts are intrinsic to human communication. Somehow it would seems that vagueness is central to the flexibility and robustness of natural l- guage descriptions. If we were to insist on precise concept definitions then we would be able to assert very little with any degree of confidence. In many cases our perceptions simply do not provide sufficient information to allow us to verify that a set of formal conditions are met. Our decision to describe an individual as 'tall' is not generally based on any kind of accurate measurement of their height. Indeed it is part of the power of human concepts that they do not require us to make such fine judgements. They are robust to the imprecision of our perceptions, while still allowing us to convey useful, and sometimes vital, information. The study of vagueness in Artificial Intelligence (AI) is therefore motivated by the desire to incorporate this robustness and flexibility into int- ligent computer systems. This goal, however, requires a formal model of vague concepts that will allow us to quantify and manipulate the uncertainty resulting from their use as a means of passing information between autonomous agents. I first became interested in these issues while working with Jim Baldwin to develop a theory of the probability of fuzzy events based on mass assi- ments.

The analysis of experimental data resulting from some underlying random process is a fundamental part of most scientific research. Probability Theory and Statistics have been developed as flexible tools for this analyis, and have been applied successfully in various fields such as Biology, Economics, Engineering, Medicine or Psychology. However, traditional techniques in Probability and Statistics were devised to model only a singe source of uncertainty, namely randomness. In many real-life problems randomness arises in conjunction with other sources, making the development of additional "softening" approaches essential. This book is a collection of papers presented at the 2nd International Conference on Soft Methods in Probability and Statistics (SMPS’2004) held in Oviedo, providing a comprehensive overview of the innovative new research taking place within this emerging field.