Bridges Between Contextual Linguistic Models of Vagueness and T-Norm Based Fuzzy Logic

Linguistic models of vagueness usually record contexts of possible precisifications. A link between such models and fuzzy logic is established by extracting fuzzy sets from context based word meanings and by analyzing standard logical connectives in this setting. In this manner the three fundamental t-norms (Łukasiewicz, minimum, and product) highlighted in Petr Hajek’s approach to fuzzy logic reappear as bounds for degrees extracted from contextual models. In a further step, two semantic scenarios for fuzzy logic—similarity based reasoning and Giles’s dialogue game—are adapted to obtain t-norm based truth functions from the point of view of context update semantics.