Catching The Cheshire Cat

I N T R O D U C T I O N In Alice's Adventures in Wonderland by Lewis Carrel many of Alice's friends have names that consists of two words, for example: the March Hare, the Mock Turtle, and the Cheshire Cat. '['he individual words in these combinations, if we ignore capitalisation, might be quite common. Individual words usually mean different things when they am free. l:or example, in "The March against Apartheid", and "The March I tare", "march" means totally different things. There is obviously a strong link between "the" and "march", but the link between "march" and "hare" is definitely stronger, at least in Lt;wis Carrol's text. The goal of this paper is to propose a statistic that measures the strength ol7 such glue between words in a sampled text. Finding tile names {)17 Alice's friends can be done by searching for two adjacent words with initial capit~d letters. ()no use of statistical associations could he to find translatable concepts and phrases, that might be expressed with a different number of words in another language. Another possibly interesting use of statistical associations is to predict whether words constitute new or given information in speech. It has been proposed (e.g. H o r n e & Johansson, 1993) that the stress of words in speech is highly dependent on the informational content of the word. Also, statistical associations are not incompatible with the first stages of the "hypothesis space" proposed by Processability Theory (personal communication with Manfred Pienemann of Sydney University, see also Meisel & al., 1981). There are different methods of calculating statistical associations. Yang & Chute (1992) showed that a linear least square mapping of natural language to canonical terms is both feasible, and a way of detecting synonyms. Their method does not seem to detect dependencies in the order of words however. To do this we need a measure that is sensitive to the order between words. In this paper we will use a variant of mutual infi)rmation that derives from Shannon's theory of information. (as discussed in e.g., Salton & McGill, 1983) Definit ions and assumpt ions The definition of a word in a meaninglul way is [:ar from easy, but a working definition, for technical purposes, is to assume that a word equals a string of letters. These 'words' are separated by non-letters. The case of letters is ignored, i.e. converted into lower case. For example: "there's" are two 'words': "there" and ~IS". A collocation consists of a word and the word that immediate@ follows. Index I will refer to the first word and 2 to the second word. Index 12 will refer to word 1 followed by word2, and similarly for 2 I. Another assumption is that natural language is morn predictive in the (left-to-right) temporal order, than in tile reversed order. This is motiwtted by the simple obserwttion that speech comes into the system through the ears serially. For example: consider the French phrase "un ben viu hlanc" (Lit. "a good wine white"). "Ben" can (relatively often) be followed by "vin", but usually not "vin" by "ben". The same kind of link exists between "vin" and "bhmc", but not between "blanc" and "vin". This linking affects the intonation of French phrases, and also that intonation supports these kinds of links. Note, that this is not an explana-. tion of either intonation or syntax: we mosl likely have to consider massive interaction be-. tween different modalities of language.