Abstract

Structural semiotics, as developed by A. J. Greimas and the Paris School, provides a powerful framework for analyzing narrative meaning through actantial roles, modalities, and hierarchical narrative structures. Despite its longstanding engagement with formal reasoning and diagrammatic tools, it has seen relatively few explicit mathematical formalizations. This article proposes a diagrammatic reconstruction of key Greimassian concepts using the language of symmetric monoidal and hypergraph categories. We treat the actantial model as a typing schema and introduce wiring diagrams as a formal semantics for representing narrative configurations, modal transformations, and actantial redistribution. Modal operations such as knowing-how-to-do, wanting-to-do, and causing-to-do are modeled as typed morphisms, while Frobenius structures account for duplication, erasure, and persistence of actants across narrative time. We show how operadic nesting captures hypotaxis, and how diagrammatic factorization yields higher-level abstractions corresponding to the hypotactical clusters of the canonical narrative schema. The approach is illustrated through a detailed analysis of Aesop’s The Fox & the Crow, culminating in a formal account of discoursivization via actorialization, spatialization, and temporalization. Rather than replacing structural semiotics, this work provides it with a compositional and mathematically explicit toolkit that clarifies existing concepts and opens new possibilities for comparative, computational, and interdisciplinary analysis.