Research on a General State Formalization Method from the Perspective of Logic

Siyuan Qiu and Jianfeng Xu ()
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Siyuan Qiu: School of Computer Science, Shanghai Jiao Tong University, Shanghai 200030, China
Jianfeng Xu: Koguan School of Law, China Institute for Smart Justice, School of Computer Science, Shanghai Jiao Tong University, Shanghai 200030, China

Mathematics, 2025, vol. 13, issue 20, 1-36

Abstract: As information plays an ever more central role across disciplines, the lack of a precise and reusable definition of state impedes comparison, measurement, and verification. Building on Objective Information Theory (OIT), this paper proposes a logic-based framework that defines the state of an object or system at a time point (or interval) as the semantic valuation of a set of well-formed formulas over a given domain and interpretation. Within first-order and higher-order logic—extended to infinitary logic when needed—we show how finite and broad classes of infinite structures can be characterized, drawing on core results from model theory. We then instantiate the framework in economics, sociology, computer science, and natural language, demonstrating that logic provides a unifying language for representing, reasoning about, and relating states across domains. Finally, we refine OIT by supplying a universal state representation that supports cross-domain exchange, measurement, and verification.

Keywords: objective information theory; logical systems; states; formal methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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