Learning categorial grammar by unification with negative constraints

On Learnability of Restricted Classes of Categorial Grammars

“…We present basic concepts of the theory of categorial grammars, after [6], [13], [10]. In classical categorial grammar, each symbol in the alphabet is associated with a finite number of types.…”

“…We recall an algorithm of finding the rigid grammar RG B (D), after [6], [13]. We write X → A iff type A is assigned to structure X by the algorithm.…”

“…It does not mean that the learning functions for G k , defined in [9], [10], are suitable for these subclasses of G k . So, our main goal is to show how can Kanazawa's learning functions for G k be relativized to subclasses of G k determined by negative constraints in the sense of Marciniec [13], [14]. We also find a new (not responsive, but conservative) learning function for the class of minimal grammars belonging to G k .…”

“…After Marciniec [13], we consider a rather abstract formulation of negative constraints, expressed by some general conditions to be fulfilled by the class of grammars. For instance, the class G k of k-valued categorial grammars, studied in Kanazawa [10], is further restricted by intersecting it with a class B satisfying these abstract conditions (see section 4).…”

“…Kanazawa [10] studied Gold-style learning functions based on these algorithms. Marciniec [13] designed some modification of algorithms from [6] sensitive to negative data.…”