Psycholinguistic properties of Kernel, Satellites, Core, MinSets and the rest of each dictionary

The words in the Kernel (K) differ significantly from words in the rest of the Dictionary (D) for all three psycholinguistic variables: Kernel words are learned significantly younger, more concrete and more frequent than the words in the rest of the dictionary. The same effect was found in comparing Core (C) words with D words for age and frequency, but not for concreteness, where only the Satellite words (S) are more concrete than C and D. Hence, the effects get stronger as we move inward from the rest of the Dictionary to the Kernel to the Core for age and frequency (but not concreteness), as schematized in the left part of Figure 5.2. There were only two small exceptions to the overall pattern in the two smallest dictionaries: for WCDT, S was not more concrete than C and D as in the other three dictionaries, and for WILD, D was not less frequent than S. Apart from these two exceptions, our results replicated the patterns observed previously for four other dictionaries [VIN 16].

Figure 5.2. Moving outward from the Core (C) to the Satellite (S) layer of the Kernel (K) to the rest of the Dictionary (D, about 80%), words are increasingly frequent and younger (as indicated by darkness) (see Figure 5.1 for arrows identifying each of these structures). For a color version of this figure, see www.iste.co.uk/sharp/cognitive.zip

Figure 5.3. Word frequency, age and concreteness in Core (C), Satellites (S) and rest of the Dictionary (D). Top: words in the Core are learned earlier than the Satellites, which are in turn learned earlier than the rest of the Dictionary. The pattern is the same in all four dictionaries. Middle: In three of the four dictionaries, the Satellite words are more concrete than the Core words and the rest of the Dictionary (WADT, WBDT, WILD); no pattern for concreteness in WCDT. Bottom: Core words are more frequent than the Satellites, which are more frequent than the rest of the Dictionary. The pattern is the same across the four dictionaries for word frequency except that, in the smallest, WILD, there is no significant difference between Satellites and the rest of the Dictionary. For a color version of this figure, see www.iste.co.uk/sharp/cognitive.zip

The Kernel contains a very large number of word combinations that can form a MinSet, but each dictionary’s MinSet is composed of the same proportion of C and S words (from 57% C in the largest, WADT, to 88% C in the smallest, WILD). What is the complementary role of the Core and the Satellites in generating a MinSet?

To get a better idea of which Kernel words are included in MinSets, we compared their frequency, age and concreteness with those of randomly selected Kernel words. All MinSets are part-Core and part-Satellite. For a given dictionary, some Kernel words are in all MinSets, some in no MinSet, and the rest are in between. However, the number of MinSets for a given dictionary is too large to enumerate them all and calculate the percentage of MinSets in which each Satellite and Core word appears.^[1] We therefore used a Monte Carlo simulation to compare each dictionary’s real MinSets with randomly selected pseudo-MinSets of the same size and Core/Satellite ratio.

We then computed the average value of each psycholinguistic variable for each part-core and part-satellite independently between the MinSets and the pseudo-MinSets (see Figure 5.4).

With a few exceptions, the same pattern was observed for all four dictionaries. The Core words in the real MinSets are younger, more concrete and more frequent than those in the random pseudo-MinSets. The Satellite words in the real MinSets are less young and less frequent than their pseudo- MinSet counterparts; no clear pattern was observed for concreteness. T-tests for all paired comparisons between the MinSets and random samples were all highly significant (p < 0.01) with the exception of one comparison (concreteness for the Satellite part of WBDT MinSets).

Figure 5.4. Word frequency, age and concreteness within real MinSets versus random Pseudo-MinSets. Core/Satellite differences are magnified in MinSets compared with random samples of Core and Satellite words in the same proportion. For a color version of this figure, see www.iste.co.uk/sharp/cognitive.zip

• [1] A graph D is a dictionary graph (or dictionary for short) if each of its nodes (words), w, hasat least one predecessor (defining word), w’. The set of all words of D is denoted by W and itsset of arcs (the directed definitional links from each defining word w’ to each defined wordw) is denoted by L. A sub-dictionary of D is a subset D’ of W with the property that for any word w in W, eachpredecessor w’ of w in D also belongs to W. Mathematically speaking, (word w belongs toW) and (link(w’,w) belongs to L) together imply that (w’ belongs to W). If W is a strongly connected component (SCC) of D, then no proper subset W’ of W (i.e. nosubset W’ such that there is at least one word w belonging to W but not to W’) is a subdictionary of D. Hence, a sub-dictionary is always the union of a collection of SCCs: By contracting each SCC(i.e. replacing each SCC by one supernode), we obtain an acyclic graph. We can thus speak ofthe SCCs that precede a given SCC. An acyclic graph is a graph with no cycles, i.e. no sequence of the form (w1, w2, w3,..., wn,w1), in which each word in the sequence is used in the definition of the word that follows it inthe sequence. The union of a collection of SCCs is a sub-dictionary if and only if each predecessor of anSCC in the collection also belongs to the collection. To find a MinSet for the Core C, we first apply certain reductions (see [LEV 88, LIN 00] toobtain a smaller graph called the reduced Core and denoted by C’. Finding a MinSet for C’ isless difficult than finding one for C itself, although it remains a non-trivial task. Once aMinSet has been found for C’, it is easy to transform it into a MinSet for C. For the C’ of each of our dictionaries, we have been able to determine that they contain threeclasses of words: essential words (a word is essential if it belongs to every MinSet),superfluous words (a word is superfluous if it does not belong to any MinSet) and ordinarywords (a word is ordinary if it is neither essential nor superfluous). We still have to extend these results to the Core itself and to the full dictionary, but it is likelythat we will find essential words and superfluous words for these sets as well.