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Journal of Arabic Sciences and Humanities

Corresponding Author

Saleh Belhassen

Authors ORCID

Ahmed Hakami: https://orcid.org/0000-0003-4996-3214

Article Type

Article

Keywords English

Arabic computational morphology, Machine translation enhancement, Mathematical linguistics, Non-concatenative morphology, Pattern matrix calculus, Morphological meaning inference

Abstract English

The computational processing of Arabic morphology presents a substantial challenge due to its intricate, non-concatenative root-and-pattern structure, which often leads to semantic ambiguity in translation. This paper introduces the Pattern Matrix Calculus (PMC), a mathematical and algorithmic framework that formalizes Arabic derivational morphology as an algebra of computable functions. Word formation is conceptualized as W = V(P(R)) — meaning that a word (W) is generated by applying a morphological pattern (P) to a consonantal root (R) and then adding vocalization (V). Derivational patterns are encoded as matrices, enabling operations such as comparison, composition, and direct inference of morphological meaning (i.e., the automatic derivation of semantic features associated with patterns, such as causative, reciprocal, or reflexive) using linear algebra techniques. This theory is translated into a modular algorithmic system for autonomous root extraction, pattern recognition, and translation enhancement. Evaluated on diverse corpora against state-of-the-art baselines including MADA/MADAMIRA, Farasa, and the Stanford Arabic Morphological Analyzer, the PMC achieves 94.7% pattern recognition accuracy and 91.2% morphological meaning precision, outperforming these analyzers. The system also demonstrates measurable gains in machine translation quality, with a BLEU score of 42.3 compared to 39.1 (MADA-enhanced) and 40.2 (Farasa-enhanced). This work bridges classical Arabic grammar with modern computational linguistics, offering a structured, computable approach to morphological analysis and translation enhancement.

Digital Object Identifier (DOI)

10.71422/1658-9602.1158

Accept Date

6 June 2026

Publication Date

10-24-2026

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