DATR Theories and DATR Models

TL;DR

This paper provides a formal mathematical semantics for DATR, a language for representing lexical information, clarifying its non-monotonic features and global context handling.

Contribution

It introduces an explicit, declarative semantics for DATR, modeling it as a language for defining partial functions by cases and explaining its default mechanism.

Findings

Formal semantics for DATR established

Default mechanism explained via indexed value families

Enhanced understanding of DATR's global context

Abstract

Evans and Gazdar introduced DATR as a simple, non-monotonic language for representing natural language lexicons. Although a number of implementations of DATR exist, the full language has until now lacked an explicit, declarative semantics. This paper rectifies the situation by providing a mathematical semantics for DATR. We present a view of DATR as a language for defining certain kinds of partial functions by cases. The formal model provides a transparent treatment of DATR's notion of global context. It is shown that DATR's default mechanism can be accounted for by interpreting value descriptors as families of values indexed by paths.