On the search for semantic primitives

Dailey (1986) has transformed the classic problem of the "vicious cycle or circle" into the neoclassical paradigm of "NP-completeness". As presented, there can be no disagreement with his conclusion that the problem of extracting a minimum set of semantic primitives from a monolingual dictionary is NP-complete. However, I believe (1) his use of NP-completeness is inappropriate to the problem of finding semantic primitives in a monolingual dictionary and (2) his notion of how a primitive must emerge from an examination of definitions is not sufficiently perceptive. Some suggestions for dealing with NP-complete problems include developing algorithms that are fast enough for small problems, that deal with special cases, or that exploit special features of a particular instance of the problem. With a large dictionary, such as Webster's Third New International Dictionary, it would seem that we are at a size where NP-completeness comes into play. Even here, it is possible to reduce the problem to a manageable level without invoking any special procedures, using only a correct formulation of the problem. The definienda and definitions of a monolingual dictionary can be mapped into a graph theoretic structure with nodes corresponding to definienda (as Dailey does), but with links going from a word occurring in a definition to the word being defined (opposite to Dailey's direction). The problem of finding semantic primitives in this model is then equivalent to finding what is called in digraph theory the point basis of a digraph, i.e., those nodes from which all others in the dictionary are reachable. Using straightforward algorithms to do this, the size of the problem can be reduced considerably. (In Litkowski 1978 and 1980, I show how this approach reduced an initial set of 20,000 verbs to 4,000 "more primitive" verbs. Amsler (1980) similarly used many heuristics in analyzing verb definitions in a monolingual pocket dictionary.) After applying such "gross" techniques for pruning, the problem is more tractable and it is possible to take advantage of special features of the problem at hand. In particular, it is possible to develop many heuristics which take into account many of the characteristics of a dictionary as well as many semantic considerations. These heuristics make it possible to reduce the problem even further, moving ever closer to semantic primitives. With all that has been said above, I do not want to leave the impression that the problem is in any sense easy. If that were the case, the literature would be replete with claims based on analysis of dictionaries that such and such constitute primitives. Such analysis is