The information conveyed by words in sentences

A method is presented for calculating the amount of information conveyed to a hearer by a speaker emitting a sentence generated by a probabilistic grammar known to both parties. The method applies the work of Grenander (1967) to the intermediate states of a top-down parser. This allows the uncertainty about structural ambiguity to be calculated at each point in a sentence. Subtracting these values at successive points gives the information conveyed by a word in a sentence. Word-by-word information conveyed is calculated for several small probabilistic grammars, and it is suggested that the number of bits conveyed per word is a determinant of reading times and other measures of cognitive load.