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

arXiv: https://arxiv.org/abs/2604.16471 · HTML: https://mlsanity.com/paper/2604.16471/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 44 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 2 of 2)

- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Semantic Communications: Principles and Challenges](https://mlsanity.com/paper/2201.01389/) (2021)

## Abstract (arXiv)

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.