Lexicon as an injective map

In a lexical map that is injective any word has exactly one meaning; every word has a meaning and two different words have different meanings.

Obviously, as soon as real synonyms exist an injective map is not possible any more because two words share the same meaning. However, the problem of synonymy can not be solved easily because the existence of synonymy is not clear; most so called synonyms are only partial synonyms, they belong to different registers or are used in different contexts; they differ at least in this sense --maybe marginally -- in the inherited information. As long as all of these marginal differences are recorded (and included as part of the meaning) we can hope that all different words have different meanings.

In terminology resulting form procedural approaches to lexicography this is not a necessary restriction to semasiological lexica, for this sort of lexicon it is only necessary that all words have a meaning. However the additional restriction of one meaning per word is connected only to the question of existing synonyms, and for the reason given above it is assumed here that only partial synonymy is possible and consequently the restriction is reasonable and does not change the principle character of semasiological lexica. An injective lexical map is therefore a good formal description of a semasiological lexicon. The relation is illustrated by figure 2.2.

 
Figure 2.2: Two sets are mapped onto each other by the injective map f; in the terminology resulting from procedural approaches to lexicon this would be called semasiological lexicon 

Thorsten Trippel Tue Nov 16 15:01:58 MET 1999