What techniques exist for parsing sentences based on logical connectives and quantifiers? That is, for parsing sentences that are structured "around" logical connectives and quantifiers.
[A] fish is [any] [member of] a paraphyletic [group of] organism[s] that [consist of] [all] gill- bearing aquatic craniate animal[s] that lack limb[s] [with] digit[s].
Here brackets [ ] are used to denote the semantics (quantifiers and connectives) that I'm interested in being able to parse.
Can e.g. the context-free grammar express all sorts of connectives and quantifiers?