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On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief

Blondeel, Marjon, Flaminio, Tommaso, Schockaert, Steven, Godo, Lluis and De Cock, Martine 2015. On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief. Fuzzy Sets and Systems 276 , pp. 74-99. 10.1016/j.fss.2015.02.018

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Abstract

Autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs. Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent's rational beliefs on gradable propositions. It has recently been shown that, in the same way as autoepistemic logic generalizes answer set programming, fuzzy autoepistemic logic generalizes fuzzy answer set programming as well. Besides being related to answer set programming, autoepistemic logic is also closely related to several modal logics. To investigate whether a similar relationship holds in a fuzzy logical setting, we firstly generalize the main modal logics for belief to the setting of finitely-valued Łukasiewicz logic with truth constants View the MathML sourceŁkc, and secondly we relate them with fuzzy autoepistemic logics. Moreover, we show that the problem of satisfiability checking in these logics is NP-complete. Finally, we generalize Levesque's results on stable expansions, belief sets, and “only knowing” operators to our setting, and provide a complete axiomatization for a logic of “only knowing” in the View the MathML sourceŁkc framework.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Additional Information: Available online 4 March 2015
Publisher: Elsevier
ISSN: 0165-0114
Date of Acceptance: 26 February 2015
Last Modified: 05 Mar 2020 14:30
URI: http://orca.cf.ac.uk/id/eprint/76092

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