Semantic Channel Theory: Deductive Compression and Structural Fidelity for Multi-Agent Communication

• URL: http://arxiv.org/abs/2604.16471v1
• Date: Fri, 10 Apr 2026 02:08:24 GMT
• Title: Semantic Channel Theory: Deductive Compression and Structural Fidelity for Multi-Agent Communication
• Abstract summary: This paper develops a rigorous framework for semantic communication.<n>It integrates formal proof systems with Shannon-theoretic tools.<n>A semantic bottleneck is identified in broadcast settings.
• Score: 7.299890614172539
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic information model comprising Lsem-definable state sets linked by computable enabling maps, and define the semantic channel as a composition of Markov kernels whose supports respect the enabling structure. A fixed proof system induces an irredundant semantic core and a derivation-depth stratification, enabling four distortion measures of increasing semantic depth: Hamming, closure, depth, and a parameterized composite. Six families of computable semantic channel invariants are defined and their inter-relationships established, including a data processing bound, a semantic Fano bound, and an ideal-channel collapse theorem. The central quantitative result is a deductive compression gain: under closure-based fidelity, the minimum block length is determined by the irredundant core size rather than the full knowledge-base size. We instantiate the framework for heterogeneous multi-agent communication, introducing an overlap decomposition that yields necessary and sufficient conditions for closure-reliable communication. A semantic bottleneck phenomenon is identified in broadcast settings: vocabulary mismatch imposes irreducible fidelity limitations even over noiseless carriers. All results are verified on an explicit Datalog instance.

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