DATR Theories and DATR Models

DATR Theories and DATR Models Bill Keller School of Cognitive and Computing Sciences The University of Sussex Brighton, UK email: billk@cogs.susx.ac.uk Abstract Evans and Gazdar (Evans and Gazdar, 1989a; Evans and Gazdar, 1989b) intro- duced DATR as a simple, non-monotonic language for representing natural language lexicons. Although a number of implemen- tations of DATR exist, the full language has until now lacked an explicit, declarative se- mantics. This paper rectifies the situation by providing a mathematical semantics for DATR. We present a view of DATR as a lan- guage for defining certain kinds of partial functions by cases. The formal model pro- vides a transparent treatment of DATR's notion of global context. It is shown that DA-I'R's default mechanism can be accoun- ted for by interpreting value descriptors as families of values indexed by paths. 1 Introduction DATR was introduced by Evans and Gazdar (1989a; 1989b) as a simple, declarative language for repre- senting lexical knowledge in terms of path/value equations. The language lacks many of the con- structs found in general purpose, knowledge repre- sentation formalisms, yet it has sufficient expressive power to capture concisely the structure of lexical information at a variety of levels of linguistic des- cription. At the present time, DATR is probably the most widely-used formalism for representing natu- ral language lexicons in the natural language pro- cessing (NLP) community. There are around a do- zen different implementations of the language and large DATR lexicons have been constructed for use in a variety of applications (Cahill and Evans, 1990; Andry et al., 1992; Cahill, 1994). DATR has been applied to problems in inflectional and derivational morphology (Gazdar, 1992; Kilbury, 1992; Corbett and Fraser, 1993), lexical semantics (Kilgariff, 1993), morphonology (Cahill, 1993), prosody (Gibbon and Bleiching, 1991) and speech (Andry et al., 1992). In more recent work, the language has been used to provide a concise encoding of Lexicalised Tree Ad- joining Grammar (Evans et al., 1994; Evans et al., 1995). A primary objective in the development of DATR has been the provision of an explicit, mathematically rigorous semantics. This goal was addressed in one of the first publications on the language (Evans and Gazdar, 1989b). The definitions given there deal with a subset of DATR that includes core features of the language such as the notions of local and global inheritance and DATR's default mechanism. Howe- ver, they exclude some important and widely-used constructs, most notably string (or 'list') values and evaluable paths. Moreover, it is by no means clear that the approach can be generalized appropriately to cover these features. In particular, the formal ap- paratus introduced by Evans and Gazdar in (1989b) provides no explicit model of DATR's notion of glo- bal contexL Rather, local and global inheritance are represented by distinct semantic functions £: and G. This approach is possible only on the (overly restric- tive) assumption that DArR statements involve eit- her local or global inheritance relations, but never both. The purpose of the present paper is to remedy the deficiencies …

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