Modelling and Reasoning with Vague Concepts

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.

Gives a "semantic" treatment of vague concepts in AI emphasizing the operational interpretation of the measures proposed

List of FiguresPrefaceAcknowledgmentsForeword1: Introduction2: Vague Concepts And Fuzzy Sets2.1 Fuzzy Set Theory2.2 Functionality and Truth-Functionality2.3 Operational Semantics for Membership Functions3: Label Semantics3.1 Introduction and Motivation3.2 Appropriateness Measures and Mass Assignments on Labels3.3 Label Expressions and lambda-Sets3.4 A Voting Model for Label Semantics3.5 Properties of Appropriateness Measures3.6 Functional Label Semantics3.7 Relating Appropriateness Measures to Dempster-Shafer Theory3.8 Mass Selection Functions based on t-norms3.9 Alternative Mass Selection Functions3.10 An Axiomatic Approach to Appropriateness Measures3.11 Label Semantics as a Model of Assertions3.12 Relating Label Semantics to Existing Theories of Vagueness4: Multi-Dimensional And Multi-Instance Label Semantics4.1 Descriptions Based on Many Attributes4.2 Multi-dimensional Label Expressions and A-Sets4.3 Properties of Multi-dimensional Appropriateness Measures4.4 Describing Multiple Objects5: Information From Vague Concepts5.1 Possibility Theory5.2 The Probability of Fuzzy Sets5.3 Bayesian Conditioning in Label Semantics5.4 Possibilistic Conditioning in Label Semantics5.5 Matching Concepts5.6 Conditioning From Mass Assignments in Label Semantics6: Learning Linguistic Models From Data6.1 Defining Labels for Data Modelling6.2 Bayesian Classification using Mass Relations6.3 Prediction using Mass Relations6.4 Qualitative Information from Mass Relations6.5 Learning Linguistic Decision Trees6.6 Prediction using Decision Trees6.7 Query evaluation and Inference from Linguistic Decision Trees7: Fusing Knowledge And Data7.1 From Label Expressions to Informative Priors7.2 Combining Label Expressions with Data8: Non-Additive Appropriateness Measures8.1 Properties of Generalised Appropriateness Measures8.2 Possibilstic Appropriateness Measures8.3 An Axiomatic Approach to Generalised Appropriateness Measures8.4 The Law of Excluded MiddleReferencesIndex