What question did this study set out to answer?

The main aim is to propose foundational axioms for a meaning space to extend the semantic regeneration framework.

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February 19, 2026Open Access

Preliminary Axiom Candidates for a Meaning Space: A Minimal Extension of Semantic Regeneration

Q: What does this research mean for the field?

Preliminary axioms for a meaning space provide a minimal structure for formalizing behavior observed in A/G-based numerical experiments. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Key Points

The main aim is to propose foundational axioms for a meaning space to extend the semantic regeneration framework.
Introduced three foundational assumptions: observability, operational closure, and regenerative equivalence.
Illustrated the axioms through A/G-based numerical experiments.
Focused on formalizing behaviors observed within these experiments.
The axioms provide a minimal structure for understanding the dynamics of meaning operators.
They serve as a foundation for a broader theory of meaning, trajectories, and equivalence classes.

Abstract

This short note proposes preliminary axioms for a meaning space, extending the semanticregeneration framework introduced in “A Minimal Mathematical Framework for SemanticRegeneration” (2026).We present three foundational assumptions—on observability, operational closure, andregenerative equivalence—and illustrate how these axioms provide a minimal structure forformalizing the behavior observed in A/G-based numerical experiments. These axioms arenot intended as final statements but as a basis for developing a general theory of meaningoperators, trajectories, and equivalence classes.

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