Basic Classes of Grammars with Prohibition

TL;DR

This paper introduces grammars with prohibition, a new class of formal grammars that surpass traditional grammars in expressive power, with applications in natural language processing, human-machine interaction, and computational theory.

Contribution

It defines and analyzes grammars with prohibition, demonstrating their higher computational power and potential for improved natural language modeling and human-computer interaction.

Findings

Grammars with prohibition are superrecursive, exceeding conventional formal grammars in computational power.

They provide more effective tools for natural language generation and learning processes.

Languages generated by these grammars have higher expressive capabilities than traditional grammars.

Abstract

A practical tool for natural language modeling and development of human-machine interaction is developed in the context of formal grammars and languages. A new type of formal grammars, called grammars with prohibition, is introduced. Grammars with prohibition provide more powerful tools for natural language generation and better describe processes of language learning than the conventional formal grammars. Here we study relations between languages generated by different grammars with prohibition based on conventional types of formal grammars such as context-free or context sensitive grammars. Besides, we compare languages generated by different grammars with prohibition and languages generated by conventional formal grammars. In particular, it is demonstrated that they have essentially higher computational power and expressive possibilities in comparison with the conventional formal grammars. Thus, while conventional formal grammars are recursive and subrecursive algorithms, many classes of grammars with prohibition are superrecursive algorithms. Results presented in this work are aimed at the development of human-machine interaction, modeling natural languages, empowerment of programming languages, computer simulation, better software systems, and theory of recursion.