Towards an Inferentialist Account of Information Through Proof-theoretic Semantics

2026-06-06 · Source: cs.AI updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Research Methodology & Innovation · Depth: Expert, medium

Summary

This paper introduces a novel inferentialist semantic theory of information, aiming to establish robust logical and mathematical foundations for a widely discussed but inadequately defined concept. It challenges traditional views, particularly Dretske's metaphysics, by replacing the requirement of "truth" with "inferability" as a fundamental property of information. The theory leverages proof-theoretic semantics (P-tS) to develop a mathematical-logical framework, introducing the "inferon" as a primitive unit of information whose meaning is derived from a global base of atomic rules rather than first-order models. This proof-theoretic approach contrasts with situation theory's model-theoretic perspective and focuses on "information-as-correlation" within van Benthem and Martinez's categorization. Furthermore, the P-tS tools provide a basis for mathematically modeling information flow in distributed systems, offering a reasoning-based understanding of their organization.

Key takeaway

For research scientists developing foundational theories of information or designing robust distributed systems, this work offers a critical shift from truth-based to inferability-based semantics. You should consider how proof-theoretic semantics and the "inferon" concept could enhance the rigor and reasoning capabilities of your information models, particularly when addressing complex information flow in distributed environments. This approach provides a new lens for understanding information's role in informatics.

Key insights

Information can be rigorously founded on inferability and proof-theoretic semantics, defining a primitive "inferon" from atomic rules.

Principles

• Meaning derives from inferential use.
• Information's core is inferability, not truth.
• Veridicality holds for inferentially derived information.

Method

Develop an inferentialist semantic theory by replacing "truth" with "inferability," then using proof-theoretic semantics (P-tS) to define an "inferon" from atomic rules, and apply this to model information flow in distributed systems.

Topics

• Inferentialism
• Proof-theoretic Semantics
• Information Theory
• Distributed Systems
• Inferon Concept
• Information Flow

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.