Hermeneutic length of a dictionary
##Context and purpose Hermeneutics is the science of interpretation of the human speech. Since this interpretation is founded on the adoption of a language, that dictionaries aim to define, it would be interesting to define the quality of a dictionary.
One of the measures of this quality could be what I call the hermeneutic length of a dictionary.
###Definition of the hermeneutic length Let's assume that a dictionary is simply a set of words, each related by its definition to other words of the dictionary. Then we see that by parsing recursively the definitions of all the words of a word's definition, with any start word, we can get soon or late back to the start word, no matter which path we followed through the definitions. This is what we call a loop.
We see that a word can have zero or several loops. We call hermeneutic length of a word the minimum loop length of this word.
###Score of a dictionary Based on this hermeneutic length of a word for a given dictionary, the puropose is to define a score function that takes into account the dictionary's size and that associates to every word an intuitive quantity (e.g. a percentage). Based on the scores of the dictionary's word, one should then be able to define a dictionary score function whose result should be an intuitive quantity representing the quality of the dictionary (e.g. a percentage).
The score function that has been chosen for the moment is the simplest one:
If w is a word, l the length of its shortest loop and N the size of the dictionary:
S(w) = l/N
So the total score of the dictionary S would be the sum of the scores of the dictionary's words:
S = Σ_w (S(w))
Another possibility would be the geometric score:
S = N*(Π_w (S(w)))^1/N
###Relevance of a word We do not consider a "word" every real word of the dictionary. The purpose is to concentrate on those that have a lexical meaning, not just a grammatical one. Concretely, only verbs, nouns, adjectives and adverbs of 2 or more letters.
##Project
###Modus operandi
As a first step, the code must build a square boolean matrix of the same size as the dictionary. Each word will be associated to an integer ranging from 0 to N-1 via an index. Each line of the matrix will represend the corresponding word's definition, with true for each column corresponding to a word that appears in the line's word's definition, and false otherwise.
Once this matrix is built, the hermeneutic length of a given word will be easily obtained by multiplying the matrix with itself a certain number of times (with && operator as multiplication and || operator as addition - even if it does not form a group, we don't care).
###Code plan
- TransMatrix.java builds a
TreeMap<String,TreeSet<String>>representation of the transition matrix. It is not factored yet and abundantly depends on the structure of the dictionary and of its HTML pages. - Scores.java is a source-independent score calculator. It takes a
TreeMap<String,TreeSet<String>>representation of the transition matrix and builds the associated boolean matrix, from which it can the calculate different values such as the mean number of relevant words in a definition, the score of a word or the score of the dictionary.