An algebraic approach to the German noun phrase, Linguistic Analysis

Abstract: We analyze the German noun phrase by assigning appropriate types to each noun, adjective and determiner, so that the type of the whole noun phrase can be checked by a calculation. In particular, the types will serve to distinguish between strong and weak declension of the adjective. The types are elements of the free pregroup generated by a partially ordered set; but very little of this mathematical apparatus is required for applications limited to the noun phrase. How does a child growing up in Germany know to say “der kleine Mann”, but “ein kleiner Mann”? Native German speakers will make the correct distinction, without being told that there is a difference between the strong and weak declension of the adjective. Evidently, speakers of German, or of any other language for that matter, carry out rapid subconscious calculations, employing internalized rules of grammar that they may not consciously be aware of. As far as we know, the weak versus strong distinction is peculiar to Germanic languages. The purpose of this article is to demonstrate that agreement can be handled by the algebraic notion of pregroup [1]. It is part of an ongoing investigation of German sentence structure with the help of pregroups. This mathematical technique had been shown to be applicable to German word order [2] and is being further elaborated in an article in preparation [3]. Here we shall concentrate on a pregrou