Human factors in continuous time-concerned cooperative systems represented by NΣ-labeled calculus

N Σ- labeled calculus is a generalization of N-labeled calculus so as to describe time-concerned recognition, knowledge, belief and decision of humans or computer programs together with related external physical or logical phenomena. N -labeled calculus is the smallest formal system applicable to verification and analysis of cooperative real-timing systems on natural number time introduced as an adaptation of tense arithmetic ( TA ). A merging problem of vehicles with misunderstanding or incorrect recognition is discussed as an example of cooperating systems controlling continuously changing objects including human factor. Euler’s approximation is introduced in order to represent the continuously changing objects. Through this example, relationship among artificial intelligence, external environment and human factors is investigated.