M -fuzzifying basic inquisitive semantics
Lili Xie, Xiu-Yun Wu · Journal of Intelligent & Fuzzy Systems · 2019
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.