Operator Grammar - Information

Information

The importance of reductions in operator grammar is that they separate sentences that contain reduced forms from those that don’t (base sentences). All reductions are paraphrases, since they do not remove any information, just make sentences more compact. Thus, the base sentences contain all the information of the language and the reduced sentences are variants of these. Base sentences are made up of simple words without modifiers and largely without affixes, e.g. snow falls, sheep eat grass, John knows sheep eat grass, that sheep eat snow surprises John.

Each operator in a sentence makes a contribution in information according to its likelihood of occurrence with its arguments. Highly expected combinations have low information; rare combinations have high information. The precise contribution of an operator is determined by its selection, the set of words with which it occurs with high frequency. The arguments boots, hats, sheep, grass and snow differ in meaning according to the operators for which they can appear with high likelihood in first or second argument position. For example, snow is expected as first argument of fall but not of eat, while the reverse is true of sheep. Similarly, the operators eat, devour, chew and swallow differ in meaning to the extent that the arguments they select and the operators that select them differ.

Operator grammar predicts that the information carried by a sentence is the accumulation of contributions of each argument and operator. The increment of information that a given word adds to a new sentence is determined by how it was used before. In turn, new usages stretch or even alter the information content associated with a word. Because this process is based on high frequency usage, the meanings of words are relatively stable over time, but can change in accordance with the needs of a linguistic community.