Next: Lexicon as an injective Up: Computational Lexicography Previous: DATR
Next: Lexicon as an injective
Up: Computational Lexicography
Previous: DATR
In the past section and generally in introductions to structures of
lexica lexicon was a more or less concrete item, a book with
lexical information or another representation of lexical information,
e.g. a lexicon on a computer. Nevertheless, it might be possible to
find a way to describe a lexicon purely formal, with any form of
lexical categories forming separate sets of information that are
related by certain maps or even more general by a form of algebraic
relation
. This section is a
first attempt to formalise lexical relations by means of algebraic
relations.
With the language of Mathematicians a formal description of a lexicon could be:
Let X be the set of forms (the words),
Y be the set of meanings (definitions). Figure 2.1 illustrates these sets.
Figure 2.1: Two sets are mapped onto each other by the map f X is the set of terms/words, Y is the set of concepts/properties
A map in itself does not help solving problems existing in lexicography (such as polysemy, synonymy, etc). If certain restrictions apply to the maps more valuable information can be gained from mathematics. Having a distinct map mathematicians test if the map is
If these relations can be found in lexical maps a more thorough description of existing lexicographic theories resulting from procedural approaches might be possible:
: f is an injective map. In procedural nomenclature this kind of lexicon would be called semasiological. This relation is illustrated by figure 2.2.
is a surjective map. Again, classical nomenclature resulting from a procedural approach to lexicography calls such an lexicon onomasiological (see figure 2.3).
is an injective and surjective map, it is a bijective map; in such a case a lexicon could be called onomasiological and semasiological which results in a higher value of the available information.
Thorsten Trippel Tue Nov 16 15:01:58 MET 1999