Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
Learnable classes of categorial grammars
Learnable classes of categorial grammars
Satisfiability of equations in free groups is in PSPACE
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Handbook of Logic and Language
Handbook of Logic and Language
Fundamenta Informaticae
Fundamenta Informaticae
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Recently, learning algorithms in Gold's model [Gol67] have been proposed for some particular classes of classical categorial grammars [Kan98]. We are interested here in learning Lambek categorial grammars.In general grammatical inference uses unification and substitution. In the context of Lambek categorial grammars it seems appropriate to incorporate an operation on types based both on deduction (Lambek derivation) and on substitution instead of standard substitution and standard unification.The purpose of this paper is to investigate such operations defined both in terms of deduction and substitution in categorial grammars and to study a modified unification that may serve as a basis for learning in this framework. We consider some variants of definition : in particular we show that deduction and substitution do not permute. We then consider a modified unification, here called ||= -unification :we give a criterion for the existence and construction of ||= -unifiers in terms of group issues.