Computational approach to conjugation

Abstract

Lambek’s production grammar is a simple computational method for generating conjugational forms (inflected forms) of simple tenses step by step. The mathematical structure involved is the finitely generated partially ordered semi-group, also called “semi-Thue system” in mathematics, “rewriting system” in computer science and “production grammar” or Chomsky’s Type zero language ([1]) in linguistics. With each verb V, there is associated ap×n×mmatrix of conjugationalverb-forms, Ckij(V). The index i= 1,...n represents the (simple) tense, and the index j= 1,...,m represents the person-number and the index k= 1,...,p represents the pattern. Only simple tenses are considered here, whereas participles and compound tenses are disregarded. A production grammar, in general, provides a method for calculating Ckij(V) for a given (i,j,k,V). This method has been applied to English, French ([3]), Latin ([4]), Serbian and Croatian ([2]), Hebrew (Biblical), Turkish, Arabic, and Japanese, so far. We shall present a simple production grammar developed in [2] for generating 24 verb forms of Serbian and Croatian verb. In Serbian, as in Latin, each conjugational verb form can be regarded as one-word sentence. Hence, this production grammar is extended to sentence generation.