Label Semantics for Reasoning with Uncertainty

This article gives a tutorial introduction on label semantics framework on reasoning with uncertainty. Modelling real world problems typically involves processing uncertainty of two distinct types. These are uncertainty arising from a lack of knowledge relating to concepts which, in the sense of classical logic, may be well defined and uncertainty due to inherent vagueness in concepts themselves. Traditionally, these two types of uncertainties are modelled in terms of probability theory and fuzzy set theory, respectively. Furthermore, there are many situations where we have insufficient information regarding vague or fuzzy concepts. That is where both types of uncertainty are present. Fuzzy logic is an extension of traditional Boolean logic. In a wider sense, which is in predominant use today, fuzzy logic is almost synonymous with the theory of fuzzy sets; a theory which relates to classes of objects with blurred boundaries in which membership is a matter of degree. In this chapter, we will introduce an alternate approach for modelling uncertainties by using random set and probability theory. This framework is referred to as label semantics where the labels could be discrete or fuzzy labels.