Semantic Composition for Partial Proof Trees

Abstract

We address the problem of semantic composition in a categorial system based on a hybrid logic. One logic is used for unfolding a categorial type, resulting in a partial derivation. The second logic computes the semantic representation from those partial derivations. We encode the history of the derivation from the first logic by using bound variables to represent the missing assumptions. Since the application of the partial derivations can take place in either direction in the second logic, this allows for a semantic representation with ,\-terms embedded inside ,\-terms. We show that by allowing such terms to be moved to the outermost position, compositionality can be maintained in the hybrid logic.