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Semantic Communication: From Philosophical Conceptions Towards a Mathematical Framework

Javad Gholipour, Rafael F. Schaefer, Gerhard P. Fettweis

TL;DR

The paper addresses semantic communication by grounding it in a rigorous philosophical framework (GDI) and Levels of Abstraction, enabling a domain-independent notion of semantic content. It proposes a probabilistic model that links semantics $W$ and messages $M$ and introduces context $Q$ to disambiguate interpretation, showing that Shannon's model is a special case of this broader framework. Focusing on the subproblem where semantic ambiguity arises only from physical channel noise, it derives a semantic-capacity lower bound and an achievable rate region that exceeds Shannon capacity by the term $H(X|S)$, while preserving the standard joint-typicality decoding arguments. The paper also details codebook generation, encoding, and decoding procedures for the discrete memoryless semantic channel, establishing a foundation for extending semantic-noise models and multi-user scenarios in future work.

Abstract

Semantic communication has emerged as a promising paradigm to address the challenges of next-generation communication networks. While some progress has been made in its conceptualization, fundamental questions remain unresolved. In this paper, we propose a probabilistic model for semantic communication that, unlike prior works primarily rooted in intuitions from human language, is grounded in a rigorous philosophical conception of information and its relationship with data as Constraining Affordances, mediated by Levels of Abstraction (LoA). This foundation not only enables the modeling of linguistic semantic communication but also provides a domain-independent definition of semantic content, extending its applicability beyond linguistic contexts. As the semantic communication problem involves a complex interplay of various factors, making it difficult to tackle in its entirety, we propose to orthogonalize it by classifying it into simpler sub-problems and approach the general problem step by step. Notably, we show that Shannon's framework constitutes a special case of semantic communication, in which each message conveys a single, unambiguous meaning. Consequently, the capacity in Shannon's model-defined as the maximum rate of reliably transmissible messages-coincides with the semantic capacity under this constrained scenario. In this paper, we specifically focus on the sub-problem where semantic ambiguity arises solely from physical channel noise and derive a lower bound for its semantic capacity, which reduces to Shannon's capacity in the corresponding special case. We also demonstrate that the achievable rate of all transmissible messages for reliable semantic communication, exceeds Shannon's capacity by the added term H(X|S).

Semantic Communication: From Philosophical Conceptions Towards a Mathematical Framework

TL;DR

The paper addresses semantic communication by grounding it in a rigorous philosophical framework (GDI) and Levels of Abstraction, enabling a domain-independent notion of semantic content. It proposes a probabilistic model that links semantics and messages and introduces context to disambiguate interpretation, showing that Shannon's model is a special case of this broader framework. Focusing on the subproblem where semantic ambiguity arises only from physical channel noise, it derives a semantic-capacity lower bound and an achievable rate region that exceeds Shannon capacity by the term , while preserving the standard joint-typicality decoding arguments. The paper also details codebook generation, encoding, and decoding procedures for the discrete memoryless semantic channel, establishing a foundation for extending semantic-noise models and multi-user scenarios in future work.

Abstract

Semantic communication has emerged as a promising paradigm to address the challenges of next-generation communication networks. While some progress has been made in its conceptualization, fundamental questions remain unresolved. In this paper, we propose a probabilistic model for semantic communication that, unlike prior works primarily rooted in intuitions from human language, is grounded in a rigorous philosophical conception of information and its relationship with data as Constraining Affordances, mediated by Levels of Abstraction (LoA). This foundation not only enables the modeling of linguistic semantic communication but also provides a domain-independent definition of semantic content, extending its applicability beyond linguistic contexts. As the semantic communication problem involves a complex interplay of various factors, making it difficult to tackle in its entirety, we propose to orthogonalize it by classifying it into simpler sub-problems and approach the general problem step by step. Notably, we show that Shannon's framework constitutes a special case of semantic communication, in which each message conveys a single, unambiguous meaning. Consequently, the capacity in Shannon's model-defined as the maximum rate of reliably transmissible messages-coincides with the semantic capacity under this constrained scenario. In this paper, we specifically focus on the sub-problem where semantic ambiguity arises solely from physical channel noise and derive a lower bound for its semantic capacity, which reduces to Shannon's capacity in the corresponding special case. We also demonstrate that the achievable rate of all transmissible messages for reliable semantic communication, exceeds Shannon's capacity by the added term H(X|S).
Paper Structure (7 sections, 1 theorem, 15 equations, 8 figures)

This paper contains 7 sections, 1 theorem, 15 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Probabilistic Model of Semantic Communication
  3. Main Results
  4. Codebook Generation
  5. Encoding
  6. Decoding
  7. Conclusion

Key Result

Theorem 1

For the discrete memoryless semantic communication channel (Figure Fig1), where the semantic noise is only caused by the physical channel noise and the semantic channel is noiseless, the following rate region is achievable: where $R$ represents the semantic rate and $R'$ denotes the message rate expressing each semantic.

Figures (8)

  • Figure 1: The discrete memoryless semantic communication channel.
  • Figure 2: Interrelationship between semantics $W$ and the messages $M$, (a): in general, and (b): for a given context $Q$.
  • Figure 3: General semantic-message encoder given the context $Q$.
  • Figure 4: Semantic-message encoder given the context $Q$, for the extreme case, where the semantic set $\mathcal{W}$ and the message set $\mathcal{M}$ have one-to-one relation.
  • Figure 5: Semantic channel noise in Shannon's model, an extreme case of semantic communication, illustrated as mismatched codebooks between the sender (a) and receiver (b).
  • ...and 3 more figures

Theorems & Definitions (7)

  • Remark 1
  • Theorem 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Proof 1
  • Remark 5