Vagueness is a ubiquitous feature that we know from many expressions in natural languages. It can invite a serious problem: the Sorites Paradox. The aim of this paper is to propose a new version of complete logic for vague predicates - JND-based vague predicate logic (
) which can avoid the Sorites Paradox and give answers to all of the Semantic Question, the Epistemological Question and the Psychological Question given by Graff. To accomplish this aim, we provide
with a probabilistic model by means of measurement theory.
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