Abstract
An elementary formal system (EFS) is a logic program such as a Prolog program, for instance, that directly manipulates strings. Arikawa and his co-workers proposed elementary formal systems as a unifying framework for formal language learning. In the present paper, we introduce advanced elementary formal systems (AEFSs), i.e., elementary formal systems which allow for the use of a certain kind of negation, which is nonmonotonic, in essence, and which is conceptually close to negation as failure. We study the expressiveness of this approach by comparing certain AEFS definable language classes to the levels in the Chomsky hierarchy and to the language classes that are definable by EFSs that meet the same syntactical constraints. Moreover, we investigate the learnability of the corresponding AEFS definable language classes in two major learning paradigms, namely in Gold's model of learning in the limit and Valiant's model of probably approximately correct learning. In particular, we show which learnability results achieved for EFSs extend to AEFSs and which do not.
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