Logical Foundations of the Mandombe System: Toward an African Axiomatic Framework

Abstract

Keywords

Mandombe, logic, axiomatic systems, African philosophy, epistemology

This article defines a formal logic whose syntax and semantics are grounded in the internal geometry of the Mandombe writing system. Building on previous work that presents Mandombe as a cognitive grammar of reasoning, I introduce M-Logic₀, a propositional calculus whose connectives and inference rules are constrained by mvuala–kisimba configurations and their allowed rotations, reflections and concatenations. I give a sequent formulation of M-Logic₀ with a distinguished inconsistency constant ⊥ᴹ and a restricted explosion rule that reflects the way forbidden geometric moves are treated in actual Nsanda teaching.

On the semantic side I define mvuala-models: diagrammatic valuation frames in which formulas are interpreted as regions and paths in oriented Mandombe cells. Truth, incompatibility and implication are read from geometric relations such as inclusion, mirror opposition and forced path extension. I prove soundness of M-Logic₀ with respect to mvuala-models and outline a completeness result for its positive implicational fragment. I then sketch a cyclic extension, M-Logic₁, that internalises temporal and cosmological rotation and connects the logical operators to the rotational-square equivalence (RSE) machinery developed in Mazayi Mandombe. 

The article ends by positioning this logical layer relative to higher structures such as Mandombe Geometric Algebra and its applications in reservoir computing and materials science, where the same generators are already used as operators on high-dimensional state spaces. The goal is not to imitate existing Western logics but to articulate a coherent, testable African axiomatic framework that can serve as a native base for formal reasoning, computation and epistemology.

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