The view that a lexicon is a theory may seem odd when used in the practical context of lexicography. But the use of computer implementations of lexica, and of computational tools for building lexica, is leading to greater and greater convergence of lexical theory and lexicographic practice. Some relations between theoretical and practical aspects of lexical representation are shown in Figure 3. The formalism, with its component parts of syntax and procedural semantics, which together define well-formed formulae, is represented in the top of the large box. The lexicon is regarded as a theory, with its structure adhering to the syntactic rules of the formalism, and its inference or access rules dependent on the procedural semantics of the formalism. The mapping of the lexicon theory to the modelling conventions of a lexical database or other kind of implementation are shown by the large downward arrows; conversely, the lexical acquisition function is shown as a large upward arrow from the model to the theory.
The relation between theoretical and practical lexica can be usefully illustrated with two examples, seen here as `ideal types': the framework of HPSG (Head Driven Phrase Structure Grammar), and the classical paper dictionary.
The lexicon in HPSG [Pollard & Sag 1987, ], for example, is a theory which has:
A complex of theoretical assumptions of this kind is referred to as a framework or approach.
A classical paper dictionary may have the following representation features during the lexicographic development process:
With the classical dictionary type there are obvious parallels to the theoretically motivated kind of lexicon, but often there is no obvious logic or algebra behind its metasyntax, and the modelling conventions often have to be kept fuzzy around the edges in order to cope with real-world variety.