Researchers Propose Inferentialist Framework for Mathematical Foundations of Information Theory
A new arXiv paper proposes an inferentialist semantic theory of information using proof-theoretic semantics, aiming to provide rigorous mathematical-logical foundations for understanding information. The work replaces traditional truth-based definitions with inferability-based ones and introduces the concept of 'inferons' as primitive units of information. This theoretical framework could improve reasoning about complex information systems that modern society depends on.
Researchers have submitted a paper to arXiv proposing a novel approach to formalizing information theory through inferentialist semantics and proof-theoretic methods. The work addresses what the authors identify as a gap in existing logical and mathematical foundations for information, which they argue limits our ability to reason about complex information ecosystems. The framework has three components: conceptual analysis drawing on Dretske's work but replacing truth with inferability; proof-theoretic semantics that provides mathematical-logical tools for modeling information flow; and applications to distributed systems modeling. The authors argue their proof-theoretic approach offers advantages over existing model-theoretic frameworks and can address multiple categorizations of information (as range, correlation, and code), with particular focus on information-as-correlation. The work aims to ground information theory in inference and reasoning principles.
What's missing
The paper's own limitations and open questions are not detailed in the abstract provided. Specific validation of the proposed framework against existing information-theoretic models, empirical testing, or comparison of predictive power relative to established approaches is not mentioned.
What different sources said
- arXiv cs.AICenter
Towards an Inferentialist Account of Information Through Proof-theoretic Semantics
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