Semantic Containers and Fuzzy Logic Context Operators

This paper proposes a formal framework for modeling contextual meaningthrough fuzzy logic - semantic containers. A semantic container is a multidimensionalmembership space in which a lexical item activates semantic dimensions graduallyrather than categorically. The framework defines a five-level hierarchy:Level 0 builds the base meaning vector M0(w) from morphological containersCM(m); Level 1 contextualizes word meaning as M(w, c) = Tc(M0(w)); Level 2composes sentence meaning through punctuation, predication, modifiers, andrelation operators; Level 3 accumulates local discourse; and Level 4 treats thedocument as a process of semantic convergence or dispersion.The framework also identifies a pre-compositional semantic-admission interface.Before a token sequence can safely enter morphological or contextual composition,the system must determine whether the observed form and intendedmeaning are sufficiently stable. Non-word typos, real-word errors, segmentationerrors, phrase-level attractors, and cross-lingual lexical transfer may requirenormalization, candidate preservation, or contrastive clarification. This interfaceis formalized through Olex, for observed-form stabilization, and Omeaning, forintended-meaning stabilization when the surface form is valid but semanticallyunstable.Across the hierarchy, level-specific operators instantiate a shared typed recursivepattern. The paper formalizes this pattern as the Recursive Principle Ψ,while explicitly limiting the claim: Ψ names an architectural family resemblanceamong typed fuzzy composition operators, not a proof that all linguistic compositionreduces to one untyped numerical function. The manuscript is thereforea theoretical and formal-architectural working paper. Numerical values and figuresare illustrative unless explicitly marked otherwise; empirical calibration isdelegated to the companion FOCAI-2027 experimental design.