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Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/975

Title: On the Relationship between Quantified Reflective Logic and Quantified Default Logic
Authors: Brown, Frank
Keywords: Quantified Reflective Logic
Quantified Default Logic
Modal Logic
Nonmonotonic Logic
Issue Date: 2003
Publisher: Institute of Information Theories and Applications FOI ITHEA
Abstract: Reflective Logic and Default Logic are both generalized so as to allow universally quantified variables to cross modal scopes whereby the Barcan formula and its converse hold. This is done by representing both the fixed-point equation for Reflective Logic and the fixed-point equation for Default both as necessary equivalences in the Modal Quantificational Logic Z. and then inserting universal quantifiers before the defaults. The two resulting systems, called Quantified Reflective Logic and Quantified Default Logic, are then compared by deriving metatheorems of Z that express their relationships. The main result is to show that every solution to the equivalence for Quantified Default Logic is a strongly grounded solution to the equivalence for Quantified Reflective Logic. It is further shown that Quantified Reflective Logic and Quantified Default Logic have exactly the same solutions when no default has an entailment condition.
URI: http://hdl.handle.net/10525/975
ISSN: 1313-0463
Appears in Collections:Volume 10 Number 4

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