Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6856088 | Fuzzy Sets and Systems | 2015 | 26 Pages |
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 Åukasiewicz logic with truth constants Åkc, 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 Åkc framework.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Marjon Blondeel, Tommaso Flaminio, Steven Schockaert, LluÃs Godo, Martine De Cock,