Methods for Solving Necessary Equivalences


Autoria(s): Brown, Frank
Data(s)

28/12/2009

28/12/2009

2004

Resumo

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.

Identificador

1313-0463

http://hdl.handle.net/10525/892

Idioma(s)

en

Publicador

Institute of Information Theories and Applications FOI ITHEA

Palavras-Chave #Solving Necessary Equivalences #Modal Logic #Nonmonotonic Logic
Tipo

Article