Mathematical Model for Transformation of Sentences from Active Voice to Passive Voice

TL;DR

This paper introduces a mathematical model using Boolean groups and permutation groups to transform sentences from active to passive voice, supported by a computer program for grammar software development.

Contribution

It presents a novel mathematical framework for sentence transformation based on group theory, specifically Boolean and permutation groups, which is a new approach in linguistic modeling.

Findings

Boolean groups represent sentence constituents.

Permutation groups model phrase sequences.

Isomorphism maps enable sentence transformation.

Abstract

Formal work in linguistics has both produced and used important mathematical tools. Motivated by a survey of models for context and word meaning, syntactic categories, phrase structure rules and trees, an attempt is being made in the present paper to present a mathematical model for structuring of sentences from active voice to passive voice, which is is the form of a transitive verb whose grammatical subject serves as the patient, receiving the action of the verb. For this purpose we have parsed all sentences of a corpus and have generated Boolean groups for each of them. It has been observed that when we take constituents of the sentences as subgroups, the sequences of phrases form permutation roups. Application of isomorphism property yields permutation mapping between the important subgroups. It has resulted in a model for transformation of sentences from active voice to passive voice. A computer program has been written to enable the software developers to evolve grammar software for sentence transformations.