M-fuzzifying basic inquisitive semantics.

The basic system of inquisitive semantics (InqB) established by Groenendijk et al. is a general inquisitive semantic theory which doesn't concern fuzziness. To explain the fuzzy phenomena in natural languages, this paper extends InqB into the framework of M-fuzzifying setting and establishes a basic system of M-fuzzifying inquisitive semantics. To begin with, the notion of M-fuzzifying supporting mapping is defined, where M is a completely distributive lattice with an involution operator and each subset of the universal set of all possible worlds can be regarded as a support of any well-formed formula to some degree. Then the notions of M-fuzzifying entailment order, M-fuzzifying truth mappings, M-fuzzifying informative content mappings and M-fuzzifying inquisitive content mappings are introduced and their properties are discussed. Further, the degrees of assertiveness, informativeness, inquisitiveness and questioning of a well-formed formula are defined, by which the M-fuzzifying assertive projection operator and the M-fuzzifying questioning projection operator are introduced and characterized. Finally, a necessary and sufficient condition is obtained, where a well-formed formula is exactly the disjunction of its unique M-fuzzifying assertive projection and unique M-fuzzifying questioning projection. [ABSTRACT FROM AUTHOR]