(i) For all x, man(x) ==> exits(y), woman(y) and love(x, y)
(ii) Exist y, woman(y) and for all x, man(x) ==> love(x, y)The difference between these 2 interpretations comes from the relative scoping of the quantifiers (introduced by the determiner every and a). A simple compositional interpretation approach fails to capture this systematic ambiguity in quantifier scope. Cooper proposed a mechanism known as Cooper Quantifier Storage to allow a compositional treatment of quantifier scope ambiguity. (See Cooper, R., Quantification and Syntactic Theory, 1983, D. Reidel, Dordrecht, Netherlands.)
Such structures can be recursively embedded - but there exist syntactic constraints on the location of gaps:
(1) * A woman who saw every man disliked him.
(1) is not syntactically correct, while the following examples do have a possible interpretation:
(2) Every man saw a friend of his.
(3) Every admirer of a picture of himself is vain.
(4) Every man who owns a donkey beats him.
See Categorial Semantics and Scoping, F.C.N. Pereira, Computational Linguistics, 6:1, 1990.
The accessibility of certain NPs as arguments in various syntactic locations is determined by properties of the NP (whether it is a pronoun, reflexive, proper name, definite or indefinite reference) and of the syntactic context. Similar constraints also explain different scoping possibilities.
;; binding ;; / \ ;; referential expletive ;; / \ / \ ;; npro pro it there ;; / \ ;; ppro anaphor ;; / \ ;; reflexive reciprocal ;;