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

Abstract

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 analyzing standard logical connectives in this setting. In a further step Lawry's voting semantics for fuzzy logics is used to re-interpret standard t-norm based truth functions from the point of view of context update semantics.

On the Context Dependence of Many

“…This is still a plausible reading of many. Since (3) is just the relative version of (1), it it obvious how the interpret the two ( absolute and relative) weakenings (4) and (5), as well as the two (absolute and relative) strengthenings (6) and (7). Clearly, (8) and (9) are the truly new intensional readings of many.…”

“…One is carried out by linguists, like Fernando and Kamp [6], Keenan and Stavi [9], Barwise and Cooper [1], or Westerståhl [13,14], and Lappin [10,11,12], and they all share the feature of twovalued interpretation, that is, the expressions, involving many, are either true or false. Then, there is the other community, namely the fuzzy logicians, like Zadeh [15], Glöckner [8], or Hájek [2], and Fermüller [3,4,5]. They, accept the need of graded interpretations, while the use of contexts, that is in particular also the acceptance of intensional aspects of the matter, is still best observed in [12], where extensionality and intensionality get fit into one unifying frame.…”