In this paper, I will focus on the event quantification and free variable problems in semantics for Minimalist Grammar formalism, with which both Montagovian compositional semantics and neo-Davidsonian event semantics are compatible. In the literature, two operations of the formalism, MERGE and MOVE, are considered to correspond to semantic operations. MERGE corresponds to functional application or predicate conjunction, whereas MOVE determines a quantifier scope. In these semantic frameworks for Minimalist Grammar, however, the event quantification and free variable problems remain unsolved. Here I first propose a compositional event semantics for a subset of the formalism without MOVE and show that compositional event semantics is a key to solving the event quantification problem. Then, I extend the result to the formalism enriched with MOVE, and show that it is unnecessary to add any free variables or assignment functions.
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