A simulation relation between programs is defined which is

quasi-ordering. Mutual simulation is then an equivalence relation,

and by dividing out by it we abstract from a program such details as

how the sequencing is controlled and how data is represented. The

equivalence classes are approximations to the algorithms which are

realized, or expressed, by their member programs.

A technique is given and illustrated for proving simulation and

equivalence of programs; there is an analogy with Floyd's technique

for proving correctness of programs. Finally, necessary and

sufficient conditions for simulation are given.

Procedures are described for discovering the intention of a speaker

by relating the Conceptual Dependence representation of the speaker's

utterance to the computer's world model such that simple implications

can be made. These procedures function at levels higher than that of

structure of the memory. Computer understanding of natural language

is shown to consist of the following parts: assigning a conceptual

representation to an input; relating that representation to the

memory such as to extract the intention of the speaker; and selecting

the correct response type triggered by such an utterance according to

the situation.