Next: THE NEED FOR NONMONOTONIC Up: AN EXAMPLE FOR Previous: ARTIFICIAL NATURAL LANGUAGE

# THE USE OF LOGICAL FORMULAS

When my understander has digested the story of Mr. Hug, it will have added one or more predicate calculus sentences to its data base. One sentence will do if it has the form

In this form, all the entities involved in expressing the facts of the story are existentially quantified variables. The only constants in the formula would have been present in the system previously. However, it is probably better to use a collection of sentences introducing a collection of individual constants. In this case, there will be 20 or so new individual constants representing people, groups of people, the main event and its sub-events, places, organizations, etc.

In representing the robbers, the system has a choice of representing them by three individual constants, R1, R2, and R3 or by using a single symbol G1 to represent the group of robbers. A good system will probably use both. If the number of robbers were not specified, we would have to use a constant for the group. We have to identify the robber who operated the elevator while the others pushed Mr. Hug into the shaft. We shall call him R1. The other two are not discriminated in the story, but there is no harm in our calling them R2 and R3, even if there is no information to discriminate them. If there were 20 robbers, it would be a mistake to give them all individual names. Suppose it had further been stated that as the robbers left one of them threatened to return and kill Mr. Hug later but that it was not stated whether this robber was the same one who operated the elevator. We could designate this robber by R4, but we would not have sentences asserting that R4 was distinct from R1, R2 and R3; instead we would have a sentence asserting that R4 was one of these. It is tempting to identify the group of robbers with the set R1, R2, R3, but we may want to give the group some properties not enjoyed by the set of its members. Sentences with plural subjects express some rather tricky concepts. Thus, the group robbed the store, and this is not an assertion that each member robbed the store.

The ``members of the police emergency squad'' presents a similar problem. We don't want to assert how many there were. In this connection, it may be worthwhile to distinguish between what happened and what we wish to assert about what happened. A language adequate to describe what happened would not have to leave the number of policemen present vague and could give them each a name. In my old jargon, such a language would be metaphysically adequate though not epistemologically adequate. Devising a language that is only metaphysically adequate may be a worthwhile stage on the way to an epistemologically adequate system. By ``devising a language'' I mean defining a collection of predicate and constant symbols and axiomatizing their general properties. This language should not be peculiar to the story of Mr. Hug, but we should not require that it be completely general in the present state of the science.

It is not obvious how to express what we know when we are told that Mr. Hug is a furniture salesman. A direct approach is to define an abstract entity called Furniture and a function called salesmen and to assert .

This will probably work although the logical connection between the abstract entity Furniture and concrete chairs and tables needs to be worked out. It would be over-simplified to identify Furniture with the set of furniture in existence at that time, because one could be a salesman of space shuttles even though there don't exist any yet. In my opinion, one should resist a tendency to apply Occam's razor prematurely. Perhaps we can identify the abstract Furniture with the an extension of the predicate that tells us whether an object should be regarded as a piece of furniture, perhaps not. It does no harm to keep them separate for the time being. This case looks like an argument for using second order logic so that the argument of salesmen could be the predicate furniture that tells whether an object is a piece of furniture. However, there are various techniques for getting the same result without the use of second order logic.

Next: THE NEED FOR NONMONOTONIC Up: AN EXAMPLE FOR Previous: ARTIFICIAL NATURAL LANGUAGE

John McCarthy
Tue May 14 09:36:52 PDT 1996