Abstract
Justification Logic is a new generation of epistemic logics which along with the traditional modal knowledge/belief operators also consider justification assertions ‘t is a justification for F.’ In this paper, we introduce a prefixed tableau system for one of the major logics of this kind S4LPN, which combines the logic of proofs (LP) and epistemic logic S4 with an explicit negative introspection principle \(\neg t\!:\! F \to \Box \neg t\!:\! F\). We show that the prefixed tableau system for S4LPN is sound and complete with respect to Fitting-style semantics. We also introduce a hypersequent calculus HS4LPN and show that HS4LPN is complete as far as we confine ourselves to a case where only a single formula is to be proven. We establish this fact by using a translation from the prefixed tableau system to the hypersequent calculus. This completeness result gives us a semantic proof of cut-admissibility for S4LPN under the aforementioned restriction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Artemov, S.N.: Explicit Provability and Constructive Semantics. The Bulletin of Symbolic Logic 7(1), 1–36 (2000)
Artemov, S.N., Nogina, E.: Introducing Justification into Epistemic Logic. J. Log. Comput. 15(6) (2005)
Avron, A.: The Method of Hypersequents in the Proof Theory of Propositional Non-classical Logics. In: Hodges, W., Hyland, M., Steinhorn, C., Truss, J. (eds.) Logic: from foundations to applications. Proc. Logic Colloquium, Keele, UK, 1993, pp. 1–32. Oxford University Press, New York (1996)
Fitting, M.: Proof Methods for Modal and Intuitionistic Logic. Reidel Publishing Company (1983)
Fitting, M.: Semantics and Tableaus for LPS4. Technical report, CUNY Ph.D. Program in Computer Science Technical Report TR-2004016 (2004)
Fitting, M.: Modal Proof Theory. In: Handbook of Modal Logic. Elsevier, New York (2006)
Gödel, K.: Vortrag bei Zilsel (1938). In: Feferman, S., et al. (eds.) Kurt Gödel, Collected Works, vol. III. Oxford Univ. Press, New York (1995)
Nogina, E.: Epistemic Completeness of GLA. The Bulletin of Symbolic Logic 13(3), 407 (2007)
Renne, B.: Semantic Cut-Elimination for Two Explicit Modal Logics. In: Huitnink, J., Katrenko, S. (eds.) Proceedings of the 11th ESSLLI Student Session, Málaga, Spain, pp. 148–158 (2006)
Yavorskaya, T.: Logic of Proofs and Provability. Ann. Pure Appl. Logic 113(1-3) (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kurokawa, H. (2008). Tableaux and Hypersequents for Justification Logic. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2009. Lecture Notes in Computer Science, vol 5407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92687-0_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-92687-0_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92686-3
Online ISBN: 978-3-540-92687-0
eBook Packages: Computer ScienceComputer Science (R0)