We apply basic notions of the theory of rough sets, due to Pawlak], to explicate certain properties of unification-based learning algorithms for categorial grammars, introduced in and further developed in e.g]. The outcomes of these algorithms can be used to compute both the lower and the upper approximation of the searched language with respect to the given, finite sample. We show that these methods are also appropriate for other kinds of formal grammars, e.g. context-free grammars and context-sensitive grammars.
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We use a syntactic interpretation of MALL in BCI with logical and , defined in [5], to prove the undecidability of the consequence relations for BCI with logical and and BCI with logical or , and the NP-completeness of BCI. Similar results are obtained for a variant of the Lambek calculus.
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