now have the situation where a number of questions exist for which the 'correct' responses are known.
It is a general assumption in the field of IR that should a retrieval strategy fare well under a large number of experimental conditions then it is likely to perform well in an operational situation where relevance is not known in advance.
There is a concept of relevance which can be said to be objective and which deserves mention as an interesting source of speculation.
This notion of relevance has been explicated by Cooper.
It is properly termed 'logical relevance'.
Its usefulness in present day retrieval systems is limited.
However, it can be shown to be of some importance when it is related to the development of question-answering systems, such as the one recently designed by T. Winograd at Massachusetts Institute of Technology.
Logical relevance is most easily explicated if the questions are restricted to the yes-no type.
This restriction may be lifted - for details see Cooper's original paper.
Relevance is defined in terms of logical consequence.
To make this possible a question is represented by a set of sentences.
In the case of a yes-no question it is represented by two formal statements of the form 'p' and 'not-p'.
For example, if the query were 'Is hydrogen a halogen element?', the pair of statements would be the formal language equivalent of 'Hydrogen is a halogen element' and 'Hydrogen is not a halogen element'.
More complicated questions of the 'which' and 'whether' type can be transformed in this manner, for details the reader is referred to Belnap[5,6].
If the two statements representing the question are termed component statements then the subset of the set of stored sentences is a premiss set for a component statement if an only if the component statement is a logical consequence of that subset.
(Note we are now temporarily talking about stored sentences rather than stored documents.) A minimal premiss set for a component statement is one that is as small as possible in the sense that if any of its members were deleted, the component statement would no longer be a logical consequence of the resulting set.
Logical relevance is now defined as a two-place relation between stored sentences and information need representations (that is, the question represented as component statements).
The final definition is as follows:
A stored sentence is logically relevant to (a representation of) an information need if and only if it is a member of some minimal premiss set of stored sentences for some component statement of that need.
Although logical relevance is initially only defined between sentences it can easily be extended to apply to stored documents.
A document is