Editing Relevance (section)

== Logic ==
[[File:Relevance.jpg|thumb|Graphic of relevance in [[digital ecosystem]]s]]

In formal reasoning, relevance has proved an important but elusive concept. It is important because the solution of any problem requires the prior identification of the relevant elements from which a solution can be constructed. It is elusive, because the meaning of relevance appears to be difficult or impossible to capture within conventional [[logical system]]s. The obvious suggestion that q is relevant to p if q is implied by p breaks down because under standard definitions of [[material conditional|material implication]], a false proposition implies all other propositions. However though 'iron is a metal' may be implied by 'cats lay eggs' it doesn't seem to be relevant to it the way in which 'cats are mammals' and 'mammals give birth to living young' are relevant to each other. If one states "I love ice cream", and another person responds "I have a friend named Brad Cook", then these statements are not relevant. However, if one states "I love ice cream", and another person responds "I have a friend named Brad Cook who also likes ice cream", this statement now becomes relevant because it relates to the first person's idea.

Another proposal defines relevance or, more accurately, irrelevance information-theoretically.<ref>{{cite book |last1=Apgar |first1=David |title=Risk Intelligence |date=2006 |publisher=Harvard Business Publishing |location=Cambridge, MA}}</ref> It is easiest to state in terms of variables, which might reflect the values of measurable hypotheses or observation statements. The conditional entropy of an observation variable e conditioned on a variable ''h'' characterizing alternative hypotheses provides a measure of the irrelevance of the observation variable ''e'' to the set of competing hypotheses characterized by ''h''. It is useful combined with measures of the information content of the variable ''e'' in terms of its entropy. One can then subtract the content of ''e'' that is irrelevant to ''h'' (given by its conditional entropy conditioned on ''h'') from the total information content of ''e'' (given by its entropy) to calculate the amount of information the variable e contains about the set of hypotheses characterized by ''h''. Relevance (via the concept of irrelevance) and information content then characterize the observation variable and can be used to measure its sensitivity and specificity (respectively) as a test for alternative hypotheses.

More recently a number of theorists{{who|date=December 2011}} have sought to account for relevance in terms of "[[possible world]] logics" in [[intensional logic]]. Roughly, the idea is that [[logical truth|necessary truth]]s are true in all possible worlds, [[contradiction]]s (logical falsehoods) are true in no possible worlds, and [[Contingency (philosophy)|contingent]] propositions can be ordered in terms of the number of possible worlds in which they are true. Relevance is argued to depend upon the "remoteness relationship" between an actual world in which relevance is being evaluated and the set of possible worlds within which it is true.