Complexity Parameters for First-Order Classes

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Complexity Parameters for First-Order Classes
We study several complexity parameters for first order formulas and their suitability for first order learning models. We show that the standard notion of size is not captured by sets of parameters that are used in the literature and thus they cannot give a complete characterization in terms of learnability with polynomial resources. We then identify an alternative notion of size and a simple set of parameters that are useful for first order Horn Expressions. These parameters are the number of clauses in the expression, the maximum number of distinct terms in a clause, and the maximum number of literals in a clause. Matching lower bounds derived using the Vapnik Chervonenkis dimension complete the picture showing that these parameters are indeed crucial.
Marta Arias, Roni Khardon
Added 07 Jul 2010
Updated 07 Jul 2010
Type Conference
Year 2003
Where ILP
Authors Marta Arias, Roni Khardon
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