Dynamic Many Valued Logic Systems in Theoretical Economics
Daniel Lu
TL;DR
The paper addresses how economic reasoning can be modeled when decisions depend on both subjective interpretations and objective outcomes, by developing a dynamic six-valued logic framework. It introduces SVL with truth values $\{T_s,F_s,U_s,T_o,F_o,U_o\}$ and a time-evolving belief-update mechanism, formalizing action selection through the Action Axiom, an Equivalence Valuation Function $\mathfrak{v}$, and time-indexed interpretations $I_t$. It contrasts strict rationality $\Gamma_R$ with an empirical-skeptic theory $\Gamma_{ES}$ and illustrates the approach via Monty Hall–style examples and formal translations from language to inference, highlighting limits of classical logic in epistemic economic reasoning. The framework aims to capture how subjective beliefs update in light of observed consequences, with potential implications for decision theory, policy analysis, and dynamic economic modeling under uncertainty, while acknowledging the need for further refinements such as latency, multi-action sets, and policy distortions.
Abstract
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of theoretical economics. This analysis is substantially expanded through a dynamic approach, where the truth of a valuation results in an updated interpretation or changes in the agent's subjective belief regarding the effectiveness of the selected action as well as the objective reality of the effectiveness of all other possible actions (i.e. consequence realization). Complications arise when the economic agent is presented with a set of actions that render ambiguous preference, or when the effectiveness of an action cannot be perceived upon its selection, thereby necessitating a different theory of choice and consequence realization.