Stratified Grammar Systems with Simple and Dynamically Organized Strata

Abstract

Stratified grammar systems have been introduced as a grammatical model of M. Minsky hypothesis concerning how the mind works. This grammatical model is a restricted model since it is assumed that the strata of the mind are ordered in a given linear ordering. In this paper, we consider stratified grammar systems with strata organized dynamically, according to the current sentential form to be written, to meet Minsky hypothesis that the strata of the mind are organized dynamically according to the current task to be processed. We study the generative power of these systems, which we shall call dynamic stratified grammar systems, and we show that they generate the family of matrix grammars. Also, we consider simple systems by limiting the number of components comprising the stratum to be at most two components with only one rule each. Then, we show that every dynamic stratified grammar system can be represented by an equivalent simple one which demonstrates the ideas of generating complicated behaviors through more or less coordinated activities of entities with simpler behaviors.