Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/892

 Title: Methods for Solving Necessary Equivalences Authors: Brown, Frank Keywords: Solving Necessary EquivalencesModal LogicNonmonotonic Logic Issue Date: 2004 Publisher: Institute of Information Theories and Applications FOI ITHEA Abstract: Nonmonotonic Logics such as Autoepistemic Logic, Reflective Logic, and Default Logic, are usually defined in terms of set-theoretic fixed-point equations defined over deductively closed sets of sentences of First Order Logic. Such systems may also be represented as necessary equivalences in a Modal Logic stronger than S5 with the added advantage that such representations may be generalized to allow quantified variables crossing modal scopes resulting in a Quantified Autoepistemic Logic, a Quantified Autoepistemic Kernel, a Quantified Reflective Logic, and a Quantified Default Logic. Quantifiers in all these generalizations obey all the normal laws of logic including both the Barcan formula and its converse. Herein, we address the problem of solving some necessary equivalences containing universal quantifiers over modal scopes. Solutions obtained by these methods are then compared to related results obtained in the literature by Circumscription in Second Order Logic since the disjunction of all the solutions of a necessary equivalence containing just normal defaults in these Quantified Logics, is equivalent to that system. URI: http://hdl.handle.net/10525/892 ISSN: 1313-0463 Appears in Collections: Volume 11 Number 4

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