Our main objective will be to construct a fully compositional representation of nominal anaphora in discourse. The proposed representation is not dependent on the remote ascription (i.e. done outside the formal representation) of syntactic indexes, which identify anaphoric links. A formal language of variable free logic is introduced. It is based on dynamic semantics paradigm and is a variant of many-sorted type logic. We will also present the scope free treatment of quantification in multiple quantifier sentences. The interpretation of multiple quantifiers is defined by means of a construction of the polyadic Generalised Quantifier (GQ). The polyadic GQ is a constraint that should be satisfied by the denotation of a ?clausal? predicate.
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