An Outline of 4-Valued Transition Statement Calculus

Abstract

This paper aims to establish a framework of 4-valued transition statement calculus so that we can characterize transition states and the changing process among them from logic. We briefly introduce interval adjacency and transition as preliminaries; create transition connectives that can reflect the direction and the multi-state of transition, and interpret the intuition meaning of truth-value of them. Emphasis here is on an analysis to the intension of a transition. We establish a formal system of 4-valued transition statement calculus $L^{\mathrm{T4}}$, and focus on the discussions of the valuation and the characteristics of $L^{\mathrm{T4}}$, in which soundness theorem and adequacy theorem are given.