A modal logic which supports temporal belief reasoning in a multiagent environment

Numerous logics have been developed which independently support temporal reasoning or reasoning about an agent's beliefs. However, few of these logics have addressed the combination of these two areas. My goal is to construct a nonmonotonic logic which allows an agent to reason about its beliefs and beliefs of other agents over time. My secondary goal is to develop this logic in the propositional case using modal operators in order to express belief and time. My approach on the construction of the new logic progresses along two avenues. First, I selected Halpern's and Shoham's modal temporal logic in order to model time. However, their logic lacked an axiom schema to characterize the logic. Of necessity, I developed an axiom schema along with corresponding soundness and completeness proofs. Second, I developed a logic which supports nonmonotonic multi-agent belief reasoning. Here, I investigated Moore's autoepistemic logic to develop a multi-agent belief logic. However, Moore's logic only exists in the single agent case. Therefore, I developed the multi-agent version of Moore's logic along with the correspondence between the single agent versions of my new logic and Moore's logic. I then combined the refined temporal logic and multi-agent autoepistemic logic to create a nonmonotonic temporal dependent belief reasoning logic. Finally, I incorporated the assumption that an agent's beliefs persist through time into the logic. In summary, I produced a logic which supports nonmonotonic multi-agent temporal dependent belief reasoning. In addition, the logic has the ability to make the assumption that an agent's beliefs persist through time provided that no contradictory information exists.