A Temporal Relevant Logic Approach to Modeling and Reasoning about Epistemic Processes

Almost all existing approaches to modeling epistemic processes are somehow based on classical mathematical logic or its various classical conservative extensions. There are some inherent difficulties and/or problems in these approaches. On the other hand, although any epistemic process must be a time-dependent process such that both the truth-values of propositions/beliefs and the relationships among them may depend on time, until now, there are few approaches proposed for reasoning about the dynamics of epistemic processes with some explicit means to deal with the notion of time. This paper proposes a temporal relevant logic approach to modeling and reasoning about epistemic processes. We show that the approach has not the inherent difficulties and/or problems in those approaches based on classical mathematical logic or its various classical conservative extensions, and the dynamics of epistemic processes can be reasoned about based on the temporal relevant logic if we consider that each epistemic state in epistemic processes corresponds to a time point. This work provides a fundamental basis for constructing grid theorists working based on the Theory Grid.