Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-09T01:29:43.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Decidability for some justification logics with negative introspection

Published online by Cambridge University Press:  12 March 2014

Thomas Studer
Thomas Studer*
Affiliation:
Institut für Informatik und Angewandte Mathematik, Universität Bern, Neubrückstrasse 10, 3012 Bern, Switzerland, E-mail:[email protected], URL: http://www.iam.unibe.ch/~tstuder
Get access Rights & Permissions [Opens in a new window]

Abstract

Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013 , pp. 388 - 402
Copyright
Copyright © Association for Symbolic Logic 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Artemov, Sergei N., Operational modal logic, Technical Report MSI 95–29, Cornell University, 12 1995.Google Scholar
[2]Artemov, Sergei N., Explicit provability and constructive semantics, The Bulletin of Symbolic Logic, vol. 7 (2001), no. 1, pp. 1–36.CrossRefGoogle Scholar
[3]Artemov, Sergei N., The logic of justification, The Review of Symbolic Logic, vol. 1 (2008), no. 4, pp. 477–513.CrossRefGoogle Scholar
[4]Artemov, Sergei N., Kazakov, E. L., and Shapiro, D., Logic of knowledge with justifications, Technical Report CFIS 99–12, Cornell University, 1999.Google Scholar
[5]Artemov, Sergei N. and Kuznets, Roman, Logical omniscience as a computational complexity problem, TARK '09 (Heifetz, Aviad, editor), ACM, Stanford University, California, 07 6–8, 2009, pp. 14–23.Google Scholar
[6]Artemov, Sergei N. and Nogina, Elena, Logic of knowledge with justifications from the provability perspective. Technical Report TR-2004011, CUNY Ph.D. Program in Computer Science, 08 2004.Google Scholar
[7]Bucheli, Samuel, Kuznets, Roman, Renne, Bryan, Sack, Joshua, and Studer, Thomas, Justified belief change, LogKCA '10 (Arrazola, Xabier and Ponte, María, editors), University of the Basque Country Press, 2010, pp. 135–155.Google Scholar
[8]Bucheli, Samuel, Kuznets, Roman, and Studer, Thomas, Justifications for common knowledge, Journal of Applied Non-Classical Logics, vol. 21 (2011), no. 1, pp. 35–60.CrossRefGoogle Scholar
[9]Bucheli, Samuel, Kuznets, Roman, and Studer, Thomas, Partial realization in dynamic justification logic, WoLLIC 2011 (Beklemishev, Lev D. and de Queiroz, Ruy, editors), Lecture Notes in Artificial Intelligence, vol. 6642, Springer, 2011, pp. 35–51.Google Scholar
[10]Fitting, Melvin, The logic of proofs, semantically, Annals of Pure and Applied Logic, vol. 132 (2005), no. 1, pp. 1–25.CrossRefGoogle Scholar
[11]Jäger, Gerhard and Studer, Thomas, Extending the system ⊤0 of explicit mathematics: the limit and Mahlo axioms, Annals of Pure and Applied Logic, vol. 114 (2002), no. 1–3, pp. 79–101.CrossRefGoogle Scholar
[12]Krupski, Vladimir N., Operational logic of proofs with functionality condition on proof predicate, LFCS '97 (Adian, Sergei and Nerode, Anil, editors), Lecture Notes in Computer Science, vol. 1234, Springer, 1997, pp. 167–177.Google Scholar
[13]Krupski, Vladimir N.,The single-conclusion proof logic and inference rules specification, Annals of Pure and Applied Logic, vol. 113 (2001), no. 1–3, pp. 181–206.CrossRefGoogle Scholar
[14]Krupski, Vladimir N.,Reference constructions in the single-conclusion proof logic, Journal of Logic and Computation, vol. 16 (2006), no. 5, pp. 645–661.CrossRefGoogle Scholar
[15]Krupski, Vladimir N.,Referential logic of proofs, Theoretical Computer Science, vol. 357 (2006), no. 1–3, pp. 143–166.CrossRefGoogle Scholar
[16]Kuznets, Roman, On the complexity of explicit modal logics, CSL 2000 (Clote, Peter G. and Schwichtenberg, Helmut, editors), Lecture Notes in Computer Science, vol. 1862, Springer, 2000, pp. 371–383.Google Scholar
[17]Krupski, Vladimir N.,On decidability of the logic of proofs with arbitrary constant specifications, The Bulletin of Symbolic Logic, vol. 11 (2005), no. 1, p. 111, Abstract.Google Scholar
[18]Krupski, Vladimir N.,Complexity issues in justification logic, Ph.D. thesis, CUNY Graduate Center, 05 2008.Google Scholar
[19]Kuznets, Roman and Studer, Thomas, Justifications, ontology, and conservativity, Advances in modal logic 9 (Bolander, Thomas, Braiiner, Torben, Ghilardi, Silvio, and Moss, Lawrence, editors), College Publications, 2012, pp. 437–458.Google Scholar
[20]Mkrtychev, Alexey, Models for the logic of proofs, LFCS '97 (Adian, Sergei and Nerode, Anil, editors), Lecture Notes in Computer Science, vol. 1234, Springer, 1997, pp. 266–275.Google Scholar
[21]Pacuit, Eric, A note on some explicit modal logics, Proceedings of the 5th Panhellenic Logic Symposium, University of Athens, Athens, Greece, 07 25–28, 2005, pp. 117–125.Google Scholar
[22]Richter, Wayne and Aczel, Peter, Inductive definitions and reflecting properties of admissible ordinals, Generalized recursion theory (Fenstad, J. E. and Hinman, P. G., editors), Studies in Logic and the Foundations of Mathematics, vol. 79, Elsevier, 1974, pp. 301–381.Google Scholar
[23]Rubtsova, Natalia M., On realization of S5-modality by evidence terms, Journal of Logic and Computation, vol. 16 (2006), no. 5, pp. 671–684.CrossRefGoogle Scholar
[24]Sidon, Tatiana L., Provability logic with operations on proofs, LFCS '97 (Adian, Sergei and Nerode, Anil, editors), Lecture Notes in Computer Science, vol. 1234, Springer, 1997, pp. 342–353.Google Scholar
[25]Sidon, Tatiana Yavorskaya, Logic ofproofs and provability, Annals of Pure and Applied Logic, vol. 113 (2001), no. 1–3, pp. 345–372.Google Scholar