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

AuthorsBlondeel, Marjon; Flaminio, Tommaso ; Schockaert, Steven; Godo, Lluis ; De Cock, Martine
KeywordsFuzzy modal logic
Complete axiomatizations
Nonmonotonic modal logic
Logic of only knowing
Fuzzy logic
Logic of only knowing
Autoepistemic logic
Modal logic
Non-monotonic reasoning
Satisfiability checking
Issue Date2015
CitationFuzzy Sets and Systems 276: 74- 99 (2015)
AbstractAbstract 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 Łkc, 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 Łkc framework. © 2015 Elsevier B.V.
Identifiersdoi: 10.1016/j.fss.2015.02.018
issn: 0165-0114
uri: http://www.sciencedirect.com/science/article/pii/S0165011415001116
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