Combinators and categorial grammar

Abstract

From Ajdukiewicz onwards categorial grammar has failed to characterize adequately the twin roles of variable-binding operators and the variables they bind. Categorial grammars are, however, adequate for languages using combinators and dispensing with bound variables, but the combinators used hitherto have been insufficiently flexible to eliminate bound variables from languages which allow both higher-order quantification and multi-place functors, such as those of Lesniewski. This paper introduces seven multigrade combinators and shows how they can be used to eliminate bound variables from Lesniewskian languages, yielding logical languages as powerful as these but in perfect harmony with Ajdukiewicz’s type of grammar. An alternative to multigrade combinators will also be considered and the significance of the result for the understanding of languages with more flexible category assignments is studied. © 1989 by the University of Notre Dame. All rights reserved.