Quantification of Performance in a Logical Task With Uncertainty 



235 



subject does not know. For example, in Fig. 3, the convergence of arrows 

 leading from lights I, 2, and 6 upon C (the center light) induces the following 

 questions: Which combinations of 1, 2, and 6 are necessary or sufficient or 

 both to light C? Is one or more of them an inhibitor? If so, which one? 

 Similar ambiguities are apparent at the other three junctures, that is at lights 



Fig. 3. Problem 2 displayed in time sequence 



1, 2, and 9. A single arrow leading to a light presents no ambiguity. This is 

 in consequence of the condition explained to the subject that each arrow 

 'means' something, hence a single arrow can mean only 'necessary and sufficient', 

 otherwise its presence or absence would make no difference. 



The subject can now ask specific questions. He can ask, for example, a 

 question about each converging juncture. The question can pertain to the 



d)— 



^c 



Fig. 4. Problem 3 displayed in time sequence 



meaning of the arrows or to the combinations necessary or sufficient to light 

 the bulb on which the arrows of the juncture converge. In the first case, he 

 will be labeling arrows, in the second case the lights. Or he may proceed in a 

 different way. Noting that all the possibilities of solution are displayed by the 

 circled buttons in their proper time sequence, he may ask how each button is 

 involved in the solution when its turn comes, by being pushed or not by being 

 pushed. 



Note that each of these perceptions of the problem implies a different 

 'information content'. According to one scheme, one seeks a 'yes' or 'no' 

 answer to every non-null combination at a juncture. There are sixteen such 

 combinations in all in both problems, hence sixteen bits of uncertainty if the 

 'yes's' and 'no's' are assumed independent. They are not independent, but 

 this interdependence can be arrived at a priori only by deduction, wliich may 

 or may not be made. Thus the uncertainty of the situation depends on the 



