This gives us a list of other symbols which are stochastically equivalent to E . Again we weight by their probabilities, and include the DX j F case as of particularly high weight. Then we try to recognise this distribution, i.e. we choose the closest cluster of known distributions. Similar methods apply whenever E or F is a new word which has never been seen before. If one reflects on the way in which we use context to determine meaning of a new word in a page of text, it may be seen that this method holds out some promise.
Semantic meaning is inferred from other known meanings and the syntax of language.
If we take the narrowest of stochastic equivalence sets, we may replace some of the symbols in a context with a stochastic equivalence class, and generate a larger stochastic equivalence class by the process described above. Quasi-linguistic stream samples are of interest largely because they constitute abstractions of natural languages, and moreover the abstractions have been constructed so as to facilitate the inference of structures. A real number is a symbol, and so a time series of real numbers may be considered in this manner. There is of course a metric structure on the symbols which is usually presumed to be known. The interested reader is invited to investigate extensions of syntactic methods to real valued time series.