Sociolinguistic Evaluation of Alternative Mathematical Models: English Pronouns.

TLDR: In this article, the interplay of linguistics, social situations, and mathematical formalisms as they affect certain speaker-addressee relationships involving three people is studied. But the choice of best representation has been made on sociolinguistic grounds, and it turns out-to our delight-to combine, as mathematical characteristics, those of the minimum non-commutative group with those of a minimum (non-trivial) commutative groups.

Abstract: Some characteristics of pronoun sequences are structured so as to necessitate the postulation of components of discourse structures-larger than the sentencewhich can now be treated by the mathematical theory of groups (and in a manner accessible to the non-mathematician). Since dozens of variant formalisms can represent the six pronominal axes studied, criteria outside formalism are needed to evaluate them. In seeking for naturalness, sociolinguistic criteria (beyond grammar or lexicon as such) must be used. Once the choice of best representation has been made on sociolinguistic grounds, it turns out-to our delight-to combine, as mathematical characteristics, those of the minimum non-commutative group with those of the minimum (non-trivial) commutative group. This article studies the interplay of linguistics, social situations, and mathematical formalisms as they affect certain speaker-addressee relationships involving three people. In ?1 a few questions are raised about linguistic use of such relations, to suggest to the reader the general area of interest. ?2 develops, through the use of graphs, the small amount of mathematics needed by the mathematical layman in order to follow our argument. ??3-9 discuss and evaluate the many alternatives, partially ranking them in order of naturalness. ??10-13 return to more general considerations, and end with the conclusion that the choice arrived at empirically, for greatest naturalness, has interesting mathematical properties as well.*