Morphological Templates and Conceptual Mechanisms: Toward Grounding the Al-Khalīlian Mathematical System within Cognitive Linguistics

Abstract

This paper addresses a pivotal topic that bridges rigorous Khalīlian mathematics with contemporary cognitive linguistics. It investigates the mechanisms by which the abstract mathematical principles of morphological templates are embodied in the genuine cognitive processes employed by Arabic speakers. Furthermore, it seeks to answer a fundamental question: How can strict mathematical structures transform into real, perceivable cognitive mechanisms?
To answer this problem, the paper presents an integrative equation linking mathematics and cognitive linguistics, alongside an applied study of verbs derived from a single root. The paper concludes that the Arabic morphological system represents an integrated model combining mathematical rigor with cognitive vitality, and that cognitive linguistics provides the theoretical bridge connecting abstract formalism with pragmatic language use.