Complexity results for logics of local reasoning and inconsistent belief

Fagin, Halpern, Moses, and Vardi have proposed a framework of epistemic agents with multiple “frames of mind” (local-reasoning structures), to solve problems concerning inconsistent knowledge and logical omniscience. We investigate a class of related modal logics. These logics replace the usual closure under full conjunction for the operator with progressively weaker versions, and comprise a hierarchy with the traditional modal logic K at the top, and an infinite number of logics ordered by inclusion under it, all strictly stronger than N, the weakest monotonic modal logic. Previous results have used N to represent local-reasoning structures. Our result shows that there are stronger logics applicable to such structures, suggesting that stronger forms of inference can be used to represent imperfect knowledge-based agents and protocols. Further, it is shown that the satisfiability question for each of these logics is PSPACE-complete, strictly harder than for N. This also answers a...

• Type: Conference
• Year: 2005
• Where: TARK
• Authors: Martin Allen
• Keywords: Local-reasoning Structures, Modal Logic, Related Modal Logics, TARK 2005