Discourse Consistency and Many-Sorted Logic

We propose the use of a many-sorted logic based on a boolean lattice of sorts, with polymorphic functions and predicates, for natural language understanding. This type of logic provides a unified framework for various problems such as discourse consistency verification, polysemy and "abuses" of terms, syntactic ambiguity solving and anaphora resolution. In addition, this logic enables intelligent diagnosis of categorial constraint violations between predicates and arguments.