Proofs and types
Type-theoretical grammar
A Modal Logic for Non-Deterministic Discourse Processing
Journal of Logic, Language and Information
EACL '93 Proceedings of the sixth conference on European chapter of the Association for Computational Linguistics
Monotonic semantic interpretation
ACL '92 Proceedings of the 30th annual meeting on Association for Computational Linguistics
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Ambiguous propositions are analyzed in a type system where disambiguation is effected during assembly (i.e. by coercion). Ambiguity is introduced through a layer of types that are underspecified relative to a pre-existing collection of dependent types, construed as unambiguous propositions. A simple system of reasoning directly with such underspecification is described, and shown to be sound and complete for the full range of disambiguations. Beyond erasing types, the system supports constraints on disambiguations, including co-variation.