Studia Logica 69 (1):171-191 (2001)
We define a tableau calculus for the logic of only knowing and knowing at most ON, which is an extension of Levesque's logic of only knowing O. The method is based on the possible-world semantics of the logic ON, and can be considered as an extension of known tableau calculi for modal logic K45. From the technical viewpoint, the main features of such an extension are the explicit representation of "unreachable" worlds in the tableau, and an additional branch closure condition implementing the property that each world must be either reachable or unreachable. The calculus allows for establishing the computational complexity of reasoning about only knowing and knowing at most. Moreover, we prove that the method matches the worst-case complexity lower bound of the satisfiability problem for both ON and O. With respect to , in which the tableau calculus was originally presented, in this paper we both provide a formal proof of soundness and completeness of the calculus, and prove the complexity results for the logic ON.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
Only Knowing with Degrees of Confidence.Arild Waaler, Johan W. Klüwer, Tore Langholm & Espen H. Lian - 2007 - Journal of Applied Logic 5 (3):492-518.
Similar books and articles
The Relative Complexity of Analytic Tableaux and SL-Resolution.André Vellino - 1993 - Studia Logica 52 (2):323 - 337.
Cut-Free Tableau Calculi for Some Propositional Normal Modal Logics.Martin Amerbauer - 1996 - Studia Logica 57 (2-3):359 - 372.
Knowing-That, Knowing-How, and Knowing Philosophically.Stephen Hetherington - 2008 - Grazer Philosophische Studien 77 (1):307-324.
A Reasoning Method for a Paraconsistent Logic.Arthur Buchsbaum & Tarcisio Pequeno - 1993 - Studia Logica 52 (2):281 - 289.
Simultaneous Rigid Sorted Unification for Tableaux.P. J. Martín & A. Gavilanes - 2002 - Studia Logica 72 (1):31-59.
Added to index2009-01-28
Total downloads18 ( #268,031 of 2,158,887 )
Recent downloads (6 months)1 ( #353,783 of 2,158,887 )
How can I increase my downloads?