Direct Compositionality and Variable-Free Semantics: The Case of Binding into Heads

Abstract

The point of departure for this paper is the hypothesis of “direct compositionality” (see, e.g., Montague 1974): the syntax and the model-theoretic semantics work in tandem. Thus the syntax “builds ” (i.e. proves the well-formedness of) expressions, where each syntactic rule supplies the proof of the well-formedness of an output expression in terms of the well-formedness of one or more input expressions. (These rules might, of course, be stated in highly general and schematic terms as in, e.g., Categorial Grammar.) The semantics works in tandem with this- each output expression is directly assigned a meaning (a model-theoretic interpretation) in terms of the meaning(s) of the input expressions(s). There is thus no need to for any kind of abstract level like LF mediating between the surface syntax and the model-theoretic interpretation, and hence no need for an additional set of rules mapping one “level ” of syntactic representation into another. Within this general program, I will be advocating a sub-program: that of Variable-Free semantics (see, e.g., Jacobson, 1994, 1999; 2000). The claim here is that the semantics makes no use of variables and hence no use of assignment

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