Vague Knowledge: Information without Transitivity and Partitions

Battle Count: 75

The paper is primarily a theoretical contribution to information economics and epistemology. While it provides conceptual foundations for understanding soft information (relevant to Liberti and Petersen 2019's work on hard vs. soft information in finance), it does not propose any trading strategies, quantitative models, or empirical methods directly applicable to quantitative trading. Its relevance is indirect: it explains why qualitative/vague signals (e.g., central bank guidance, analyst commentary) carry information despite lacking precision, which could inform how traders interpret soft information.

The theoretical framework is mathematically simple (binary relations, set operations, rough set boundaries). There is no algorithm to implement, no code to run, and no computational pipeline. The 'implementation' would involve applying the conceptual framework to specific economic scenarios, which is a modeling exercise rather than a software engineering task. The proofs are elementary and self-contained.

The paper is purely theoretical with formal definitions and proofs provided in the appendix. All mathematical arguments are self-contained and verifiable. No computational experiments or data are required. The model is simple (binary relations on a state space) and fully specified. However, there is no code or computational component to reproduce.