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Current applied intelligent systems have crucial shortcomings either in reasoning the gathered knowledge, or representation of comprehensive integrated information. To address these limitations, we develop a formal transition system which is applied to the common artificial intelligence (AI) systems, to reason about the findings. The developed model was created by combining the Public Announcement Logic (PAL) and the Linear Temporal Logic (LTL), which will be done to analyze both single-framed data and the following time-series data. To do this, first, the achieved knowledge by an AI-based system (i.e., classifiers) for an individual time-framed data, will be taken, and then, it would be modeled by a PAL. This leads to developing a unified representation of knowledge, and the smoothness in the integration of the gathered and external experiences. Therefore, the model could receive the classifier's predefined -or any external- knowledge, to assemble them in a unified manner. Alongside the PAL, all the timed knowledge changes will be modeled, using a temporal logic transition system. Later, following by the translation of natural language questions into the temporal formulas, the satisfaction leads the model to answer that question. This interpretation integrates the information of the recognized input data, rules, and knowledge. Finally, we suggest a mechanism to reduce the investigated paths for the performance improvements, which results in a partial correction for an object-detection system.