A Mathematical Theory of Hints pp 32-39 | Cite as

# The Mathematical Concept of a Hint

## Abstract

Information is always relative to one or several questions which may be put forward. Thus, in order to model information, it is necessary to represent questions and possible answers to these questions formally. Once a precise question is fixed, the set of possible answers to the question can be specified. Let’s denote this set *Ө*. The generic elements of *Ө* will be denoted by symbols like *θ*,*θʹ*,*θʺ*,*θi...* etc. Each element *θ* of *Ө* represents a possible answer to the given question. Unless explicitly said, *Ө* is throughout this book assumed to be complete in the sense that the true (but unknown) answer is exactly one of the elements of *Ө*. This is a *closed world assumption.* An open world assumption which allows for the possibility that the true answer could be outside *Ө* would also be possible, see Smets (1988).

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