Semantic Channel Theory: Deductive Compression and Structural Fidelity for Multi-Agent Communication
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913041709268992 |
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| author | Xu, Jianfeng |
| author_facet | Xu, Jianfeng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_16471 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semantic Channel Theory: Deductive Compression and Structural Fidelity for Multi-Agent Communication Xu, Jianfeng Logic in Computer Science Artificial Intelligence Information Theory Multiagent Systems 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. |
| title | Semantic Channel Theory: Deductive Compression and Structural Fidelity for Multi-Agent Communication |
| topic | Logic in Computer Science Artificial Intelligence Information Theory Multiagent Systems |
| url | https://arxiv.org/abs/2604.16471 |