In this paper, we attempt to reconstruct the situation calculus on a dense flow of time. The proposed system: ISC, which is formulated in the framework of S2S (the monoadic second-order theory of two successor functions), allows to deal with temporal properties of time duration such as the continuity of fluents. Also it incorporates an intensional feature into the situation calculus so that the inferential process itself can be represented in ISC. On the basis of this modification, we define a nonmonotonice schema called epistemological minimization which selects the preferable model with respect to the information order in the inferential process. This method of nonmonotonic reasoning is useful for a temporal explanation problem because a sequence of events is interpreted sometimes depending on the information order in the inferential process rather than the chronological order of the actual process.