Formal System and Semantics of NΣ-Labeled Calculus

NΣ-labeled calculus is a formal system for representation, verification and analysis of time-concerned recognition, knowledge, belief and decision of humans or computer programs together with related external physical or logical phenomena. In this paper, its formal system and semantics with its soundness are introduced. And also it is shown that this calculus is undecidable even if the base theory is Presburger arithmetic.