On fuzzification mechanisms for unary quantification

Abstract

We address a salient issue arising in Glöckner's two-step methodology for modeling vague quantifiers: the design of quantifier fuzzification mechanisms (QFMs). These are mechanisms to turn formal models of vague quantifiers operating only on crisp arguments (semi-fuzzy quantifiers) into vague quantifiers accepting vague arguments as well (fully-fuzzy quantifiers). We critically examine desiderata formulated by Glöckner for QFMs and also point out that previous approaches to quantifier fuzzification largely ignored the question whether the resulting quantifiers can be expressed in suitable extensions of t-norm based fuzzy logics, in particular in Łukasiewicz logic. We also introduce a new family of QFMs, and assess it fares with respect to the mentioned desiderata. We exclusively focus on unary quantifiers, in order to circumvent interference with vagueness related problems arising for all truth functional accounts of quantifiers that refer to more than one argument formula.