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A nonmonotonic temporal logic and its Kripke semantics. (English) Zbl 0738.03009

Summary: Human commonsense reasoning is at the same time nonmonotonic and temporal. This paper proposes a logic for nonmonotonic temporal reasoning. The nonmonotonic temporal logic “autoepistemic temporal logic” (ATL) is an extension of both autoepistemic logic, a kind of nonmonotonic logic, and propositional temporal logic (PTL). A spatio- temporal logic ST5, which is suitable for reasoning about multiprocess networks, is also proposed, and a close relationship is exhibited between the semantics of ATL and ST5. Stable expansions of premises of a certain type are then characterized in terms of statewise autoepistemic stable expansions. The result may also provide a general approach to constructing nonmonotonic logics with possible-worlds semantics.

MSC:

03B60 Other nonclassical logic
03B45 Modal logic (including the logic of norms)
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