Combining Fuzziness and Context Sensitivity in Game Based Models of Vague Quantification

On fuzzification mechanisms for unary quantification

“…For our purposes, it suffices to point out that the outlined issue about vagueness-induced range/scope dependencies, by definition, does not arise for strictly unary quantification. A related fact is discussed in [11], where it is pointed out that vague range and scope predicates joined by a binary quantifier may give rise to either dependent or independent standards of precisification, which cannot be fully reflected by membership degrees, which proposes dependent and independent voting models. To understand this phenomenon, consider the following sentences:…”

“…As already indicated, linguists are well aware of this fact when modeling vagueness, e.g., by contextually shifting standards of acceptance or rejection (see, e.g., [2]). For an assessment of this situation that is closer to the concerns of (deductive) fuzzy logic, we refer to [11]. Of course, this does not mean that the standard approach to binary fuzzy quantifiers is not useful.…”

“…In order to express such α-cuts in L we need to be able to express the truth value 0.5, and the product of the truth value of a formula by 0.5. Both are not expressible in Lukasiewicz logic, while this is possible in well-known expansions of it, such as Rational Lukasiewicz logic [4] and the expansion with the the propositional random choice connective π investigated in [11]. Here, however, we prefer to use the more expressive device of propositional quantifiers, since we will need them anyway in the following.…”