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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.

@article{XieWu:19, abstract = {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.}, author = {Xie, Li-Li and Wu, Xiu-Yun}, date-added = {2021-08-17 00:00:00 +0000}, date-modified = {2021-08-17 00:00:00 +0000}, doi = {10.3233/JIFS-182500}, journal = {Journal of Intelligent & Fuzzy Systems}, keywords = {inquisitive logic}, pages = {7711-7723}, title = {M-fuzzifying basic inquisitive semantics}, url = {https://content.iospress.com/articles/journal-of-intelligent-and-fuzzy-systems/ifs182500}, year = {2019}, Bdsk-Url-1 = {https://content.iospress.com/articles/journal-of-intelligent-and-fuzzy-systems/ifs182500}}

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