Absolute versus probabilistic classification in a logical setting

13 years 4 months ago

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Suppose we are given a set W of logical structures, or possible worlds, a set of logical formulas called possible data and a logical formula . We then consider the classification problem of determining in the limit and almost always correctly whether a possible world M satisfies , from a complete enumeration of the possible data that are true in M. One interpretation of almost always correctly is that the classification might be wrong on a set of possible worlds of measure 0, with respect to some natural probability distribution over the set of possible worlds. Another interpretation is that the classifier is only required to classify a set W of possible worlds of measure 1, without having to produce any claim in the limit on the truth of for the members of the complement of W in W. We compare these notions with absolute classification of W with respect to a formula that is almost always equivalent to in W, hence investigate whether the set of possible worlds on which the classificat...

Sanjay Jain, Eric Martin, Frank Stephan

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