arXiv:2605.05368math.LOcs.AI2026-05

用推理语义学构建信息的逻辑基础,重新定义信息本质。

Towards an Inferentialist Account of Information Through Proof-theoretic Semantics

论文配图:Towards an Inferentialist Account of Information Through Proof-theoretic Semantics
图 1 · 摘自论文原文
  • 以可推导性替代真值,建立基于推理的信息语义理论
  • 提出'推论元'(inferon)作为信息基本单位,支持分布式系统建模
  • 适合研究信息逻辑、认知系统与形式语义的学者

信息是当今时代最广泛讨论的概念之一,但尚未获得令人信服的逻辑或数学基础。缺乏这些基础,我们无法充分理解社会所依赖复杂系统生态。本文旨在通过发展一种推理主义信息语义理论迈出第一步。首先,进行概念分析:将信息的本体论从意向性、真值和可传递性重构为可推导性;其次,采用证明论语义(P-tS)实现推理主义的数学逻辑化,首次构建了推理主义信息基本单元——'推论元'(inferon)的理论框架;该方法与情境理论中的模型论观点形成对比,并能统一处理van Benthem和Martinez提出的三种信息理解方式:范围、相关性与编码。本文聚焦于信息作为相关性的理解。第三,面向系统:所发展的P-tS工具为分布式系统建模提供了数学基础,从而实现对信息流的基于推理的理论刻画。总体目标是建立一个概念严谨、逻辑自洽的信息理论,以推理为核心,扎根于信息在信息科学中的角色。

原文摘要 · Abstract (English)

Information is one of the most widely-discussed concepts of the current era. However, a great deal of insightful work notwithstanding, it is yet to be given wholly convincing logical or mathematical foundations. Without them, we lack adequate reasoning tools for understanding the complex ecosystems of systems upon which the society depends. We seek to rectify this by taking a first step towards developing an inferentialist semantic theory of information. There are three key interacting components. First, conceptual analysis: the metaphysics of information. Dretske expressed the key concepts of information in terms of intentionality, truth, and transmissibility. We replace truth with inferability, and trace the consequences of this replacement. Second, logic: proof-theoretic semantics (P-tS) provides a mathematical-logical realization of inferentialist reasoning. Using P-tS, we develop the first steps towards a mathematical-logical theory of an inferentialist primitive unit of information, the 'inferon'. This proof-theoretic approach counterpoints the model-theoretic view of information articulated in situation theory. Furthermore, we argue that it facilitates addressing all three components of van Benthem and Martinez's categorization of the understandings of information, as range, as correlation, and as code. Our focus is on information-as-correlation. Third, systems: the P-tS tools we develop provide the basis for a mathematical account of distributed systems modelling -- a key tool from informatics for understanding the organization of information processing systems. This yields a reasoning-based theory of information flow in models of distributed systems. Overall, we seek to give a conceptually rigorous mathematical-logical account of information and its role within informatics, grounded in inference and reasoning.

信息理论推理语义形式语义分布式系统

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