Application of Semigroup Theory in Modeling Structural Equivalence in English Sentence Patterns

Abstract

Combining semigroup theory with the formal modeling of structural equivalence in English sentences patterns is the target area of this paper. In this study, we create a semigroup representing the grammatical structures of a given sentence NP, VP, PP and other relevant grammatical categories drawn from English abstract algebra and formal language theory. The sentences formation can be modeled as binary operations on sets, which in this context we call syntactic concatenation. Thus, the whole set of sentential patterns that are syntactically valid constitute a semigroup under associative composition.

Moreover, we define an additional equivalence relation over syntactic parse trees to define congruence’s over a semigroup, which further demonstrates algebraic structures on parsed trees. Through this process, one can classify sentences based on equivalence classes regardless of their lexical constituent irrespective their verbal content defining classes through grammatical structure using which gives it lexical freedom. This method allows for mathematically rigorous frameworks while identifying and comparing disparate sentence forms which could serve potential grammar learning or simplification algorithms in computation linguistics offer profound intersects between algebra and linguistics broadening paradigms for modeling natural language based on its structures.