This paper deals with an aspect of the problem of automating the comprehension of expository texts, namely understanding word problems.
It will be shown that problems have a deep structure similar to the deep structure of a sentence, and that the task of the comprehender is to reveal and build this deep structure.
It will be indicated that the deep structure built from the natural language description of the problem has in it all elements necessary to answer a simple information retrieval question, an arithmetic question or an algebra question.
The idea of deep structure of a problem is not entirely new.
It can be traced back to an earlier paper by Paige and Simon in which they study the behavior of subjects solving word algebra problems and compare it to Bobrow's STUDENT program. 
They distinguish between ``direct'' and ``auxiliary'' translations of natural language expressions.
By ``direct'' translation the authors refer to the direct mapping of an English sentence into an algebraic expression. For instance, the sentence ``Three times a number plus 18 is equal to 78'' will be directly mapped into 3x + 18 = 78. 
This is the behavior that characterizes STUDENT and some of the subjects they studied.
However, some kinds of problems require ``auxiliary'' representations such as the construction of diagrams that capture the physical situation described by the problem. 
Later in the paper, they say:
Let us propose a hypothesis. 
We suppose that the subject constructs an  internal representation of the problem situation from the problem statement. 
We do not insist that this representation be ``visual'' in any literal sense, but we do require that it contain in implicit form the same relations that are implicit in the diagram.
The authors clearly establish that some subjects use internal representations that are functionally equivalent to diagrammatic representations depicting the physical situation described by the problem.
The notion of internal representation of a problem, now called deep structure of a problem, is further discussed in chapters 2 and 3 of Human Problem-Solving. 
In chapter 3, the authors assert:
In contrast to the theories of deep structure sketched by linguists, the internal structures we shall postulate for problem solving situations generally constitute large, complex, interrelated contexts that do not factor out in any simple way into components that are isomorphic with single sentences.
It is clear that the authors maintain that their notion of internal structure goes beyond the meaning of individual sentences.
The internal structure the authors postulate for problem solving is the notion of  problem-space.
One of the main points of this paper, however, will be that the internal representation of a problem stated in natural language is a structure that mediates between the English description of the problem and the problem-space representation, and that it cannot be identified with the problem-space representation of a problem.
In our opinion, the  problem-space representation derives from the deep representation, which is semantically based.
The problem-space representation underlies many problem-solving methods: logic, hill-climbing, means-end analysis, generate-and-test, etc.
In a problem-space representation, the semantic content of the terms that make up the problem has been removed. A river is not any longer a river in a problem-space representation, but just a token.