This paper investigates whether the postmodern claim of unrestricted semantic indeterminacy, and its foundational Saussurean axiom of the arbitrary sign, are compatible with the structural architecture of Classical Arabic. We develop a formal mathematical model of Arabic non concatenative morphology in which lexical meaning is determined by the interaction between an invariant root and a morphosyntactic pattern. Within this framework, we establish a Morphological Correspondence Theorem, demonstrating that every lexical item is uniquely generated by a root pattern pair, and a Semantic Localization Theorem, proving that lexical meaning is determined at the derivational level prior to surface realization. To address Saussurean weaker notion of relative arbitrariness, we formalize it via conditional Kolmogorov complexity, defining arbitrariness algorithmically as the no rule property. We prove that general relative arbitrariness is formally undecidable, while Arabic relative arbitrariness is decidable and provably less than 1 for its motivated signifiers (Levels W and M), establishing a strict system complexity asymmetry over Indo-European languages.
We present a substantially implemented model of description of the inflectional morphology of Arabic nouns, with special attention to the management of dictionaries and other language resources by Arabic-speaking linguists. The breakthrough lies in the reversal of the traditional root-and-pattern Semitic model into pattern-and-root, giving precedence to patterns over roots. Our model includes broken plurals (BPs), i.e. plurals formed by modifying the stem. It is based on the traditional notions of root and pattern of Semitic morphology. However, as compared to traditional Arabic morphology, it keeps the formal description of inflection separate from that of derivation and semantics. As traditional Arabic dictionaries, the updatable dictionary is structured in lexical entries for lemmas, and the reference spelling is fully diacritized. In our model, morphological analysis of Arabic text is performed directly with a dictionary of words and without morphophonological rules. Our taxonomy for noun inflection is simple, orderly and detailed. We simplify the taxonomy of singular patterns by specifying vowel quantity as v or vv, and ignoring vowel quality. Root alternations and orthographical variations are encoded independently from patterns and in a factual way, without deep roots or morphophonological or orthographical rules. Nouns with a triliteral BP are classified according to 22 patterns subdivided into 90 classes, and nouns with a quadriliteral BP according to 3 patterns subdivided into 70 classes. These 160 classes become 300 inflectional classes when we take into account inflectional variations that affect only the singular. We provide a straightforward encoding scheme that we applied to 3 200 entries of BP nouns.