Classification and representation of types in TDL

TDL is a typed feature-based representation language and inference system, specifically designed to support highly lexicalized constraint-based grammar theories. Type definitions in TDL consist of type and feature constraints over the full Boolean connectives together with coreferences, thus making TDL Turing-complete. TDL provides open- and closed-world reasoning over types. Working with partially as well as with fully expanded types is possible. Efficient reasoning in TDL is accomplished through specialized modules. In this paper, we will highlight the type/inheritance hierarchy module of TDL and show how we represent conjunctively and disjunctively defined types. Negated types and incompatible types are handled by specialized bottom symbols. Redefining a type only leads to the redefinition of the dependent types, and not to the redefinition of the whole grammar/lexicon. Undefined types are nothing special. Reasoning over the type hierarchy is partially realized by a bit vector encoding of types, similar to the one used in Aït-Kaci's LOGIN. However, the underlying semantics does not harmonize with the open-world assumption of TDL. Thus, we have to generalize the GLB/LUB operation to account for this fact. The system, as presented in the paper, has been fully implemented in Common Lisp and is an integrated part of a large NL system. It has been installed and successfully employed at other sites and runs on various platforms