Statistics Seminars: Borderlines and Probabilities of Borderlines
11 May 2015 14:05 in CM221
In this talk I will describe an integrated approach to vagueness and uncertainty based on a combination of three valued logic and probability. In a propositional logic setting, three valued valuations are employed in order to model explicitly borderline cases, and by defining probabilities over such valuations we can also quantify both epistemic and linguistic uncertainty. In particular, I consider probability defined over two well known three valued models; Kleene valuations and supervaluations. This approach naturally generates belief pairs of lower and upper measures on the sentences of the language, where the lower measure of a sentence corresponds to the probability that it is true and the upper measure to the probability that it is not false. I will discuss links between these measures and other uncertainty theories and in particular I will show that compositional fuzzy truth degrees are completely characterised by a special case of Kleene belief pairs. Furthermore, supervaluation belief pairs are Dempster-Shafer belief and plausibility measures on the sentences of the language and I show that there is a close relationship between Kleene belief pairs and a sub-class of the former. Finally, I will consider the justification for using Kleene or supervaluations to model borderline cases in this context.
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