New Framework Integrates Formal Proof Systems with Shannon Theory for Semantic Communication
A new paper titled "Semantic Channel Theory: Deductive Compression and Structural Fidelity for Multi-Agent Communication" has been released on arXiv under the ID 2604.16471. It offers a detailed approach to semantic communication by integrating formal proof systems with concepts from Shannon's theory. The authors propose an information model built on Lsem-definable state sets connected through computable enabling maps. They define a semantic channel using Markov kernels aligned with this structure. The paper introduces a consistent proof system that leads to a refined semantic core and a hierarchy of derivation depth, resulting in four distortion measures. It also identifies six families of computable semantic channel invariants and highlights the advantages of deductive compression, which are unique compared to traditional information theory.
Key facts
- The paper develops a rigorous framework for semantic communication integrating formal proof systems with Shannon-theoretic tools.
- It introduces an axiomatic information model with Lsem-definable state sets linked by computable enabling maps.
- The semantic channel is defined 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.
- Four distortion measures are enabled: Hamming, closure, depth, and a parameterized composite.
- Six families of computable semantic channel invariants are defined and their inter-relationships established.
- Key results include a data processing bound, a semantic Fano bound, and an ideal-channel collapse theorem.
- The central quantitative result shows deductive compression gain under closure-based fidelity conditions.
Entities
Institutions
- arXiv