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

TL;DR

This paper develops a formal framework for semantic communication integrating proof systems with Shannon theory, introducing measures and invariants that quantify semantic fidelity and compression in multi-agent systems.

Contribution

It introduces a rigorous axiomatic model for semantic channels, defines new distortion measures, and establishes bounds and invariants for semantic compression and reliable multi-agent communication.

Findings

Deductive compression gain depends on irredundant core size.

Semantic bottleneck limits fidelity in broadcast scenarios due to vocabulary mismatch.

Framework verified on an explicit Datalog instance.

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.