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Title: On the Relationships Among Quantified Autoepistemic Logic, its Kernel, and Quantified Reflective Logic
Authors: Brown, Frank
Keywords: Quantified Autoepistemic Logic
Quantified Reflective Logic
Modal Logic
Nonmonotonic Logic
Issue Date: 2004
Publisher: Institute of Information Theories and Applications FOI ITHEA
Abstract: A Quantified Autoepistemic Logic is axiomatized in a monotonic Modal Quantificational Logic whose modal laws are slightly stronger than S5. This Quantified Autoepistemic Logic obeys all the laws of First Order Logic and its L predicate obeys the laws of S5 Modal Logic in every fixed-point. It is proven that this Logic has a kernel not containing L such that L holds for a sentence if and only if that sentence is in the kernel. This result is important because it shows that L is superfluous thereby allowing the ori ginal equivalence to be simplified by eliminating L from it. It is also shown that the Kernel of Quantified Autoepistemic Logic is a generalization of Quantified Reflective Logic, which coincides with it in the propositional case.
ISSN: 1313-0463
Appears in Collections:Volume 11 Number 4

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