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Why Do We Need Justification Logic?

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Games, Norms and Reasons

Part of the book series: Synthese Library ((SYLI,volume 353))

Abstract

Since Plato, the notion of justification has been an essential component of epistemic studies (cf. [17, 24, 26, 28, 38, 44, 51], and many others). However, until recently, the notion of justification was conspicuously absent in the mathematical models of knowledge within the epistemic logic framework. Commencing from seminal works [30, 55], the notions of Knowledge and Belief have acquired formalization by means of modal logic with modals F is known and F is believed. Within this approach, the following analysis was adopted: For a given agent,

* This work has been partially supported by NSF grant 0830450, CUNY Collaborative Incentive Research Grant CIRG1424, and PSC CUNY Research Grant PSCREG-39-721.

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Notes

  1. 1.

    Dretske [18].

  2. 2.

    Admissible evidence here is not certain evidence, but rather relevant evidence. Here is an example from [22]. “What might serve as admissible evidence for the statement, ‘George Bush is editor of The New York Times’? Clearly the editorial page of any copy of The New York Times would serve, while no page of Mad Magazine would do (although the magazine might very well contain the claim that George Bush does edit the Times). Admissible evidence need not be evidence of a fact, nor need it be decisive – it could happen that The New York Times decides to omit its editor’s name, or prints the wrong one by mistake. Nonetheless, what the Times prints would count as evidence, and what Mad prints would not.”

References

  1. E. Antonakos. Justified and common knowledge: Limited conservativity. In S. Artemov and A. Nerode, editors, Logical Foundations of Computer Science. International Symposium, LFCS 2007, New York, NY, USA, June 2007, Proceedings, volume 4514 of Lecture Notes in Computer Science, pages 1–11. Springer, 2007.

    Google Scholar 

  2. S. Artemov. Operational modal logic. Technical Report MSI 95-29, Cornell University, 1995.

    Google Scholar 

  3. S. Artemov. Explicit provability and constructive semantics. Bulletin of Symbolic Logic, 7(1):1–36, 2001.

    Article  Google Scholar 

  4. S. Artemov. Justified common knowledge. Theoretical Computer Science, 357(1–3):4–22, 2006.

    Article  Google Scholar 

  5. S. Artemov. Symmetric logic of proofs. In A. Avron, N. Dershowitz, and A. Rabinovich, editors, Pillars of Computer Science, Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday, volume 4800 of Lecture Notes in Computer Science, pages 58–71. Springer, Berlin, Germany, February 2008.

    Google Scholar 

  6. S. Artemov. The logic of justification. The Review of Symbolic Logic, 1(4):477–513, December 2008.

    Article  Google Scholar 

  7. S. Artemov, E. Kazakov, and D. Shapiro. Epistemic logic with justifications. Technical Report CFIS 99-12, Cornell University, 1999.

    Google Scholar 

  8. S. Artemov and R. Kuznets. Logical omniscience via proof complexity. In Computer Science Logic 2006, volume 4207, pages 135–149. Springer Lecture Notes in Computer Science, Berlin, Germany, 2006.

    Google Scholar 

  9. S. Artemov and E. Nogina. Introducing justification into epistemic logic. Journal of Logic and Computation, 15(6):1059–1073, 2005.

    Article  Google Scholar 

  10. S. Artemov and E. Nogina. Topological semantics of justification logic. In E.A. Hirsch, A. Razborov, A. Semenov, and A. Slissenko, editors, Computer Science – Theory and Applications. Third International Computer Science Symposium in Russia, CSR 2008 Moscow, Russia, June 7–12, 2008 Proceedings, volume 5010 of Lecture Notes in Computer Science, pages 30–39. Springer, Berlin, Germany, 2008.

    Google Scholar 

  11. S. Artemov and E. Nogina. The topology of justification. Journal of Logic and Logical Philosophy, 17(1–2):58–71, 2008.

    Google Scholar 

  12. S. Artemov and T. Strassen. Functionality in the basic logic of proofs. Technical Report IAM 93-004, Department of Computer Science, University of Bern, Switzerland, 1993.

    Google Scholar 

  13. V. Brezhnev. On the logic of proofs. In Proceedings of the Sixth ESSLLI Student Session, Helsinki, pages 35–46, 2001. http://www.helsinki.fi/esslli/

  14. V. Brezhnev and R. Kuznets. Making knowledge explicit: How hard it is. Theoretical Computer Science, 357(1–3):23–34, 2006.

    Article  Google Scholar 

  15. W. Dean and H. Kurokawa. From the knowability paradox to the existence of proofs. Synthese, 176(2):177–225, September 2010.

    Article  Google Scholar 

  16. W. Dean and H. Kurokawa. The knower paradox and the quantified logic of proofs. In A. Hieke, editor, Austrian Ludwig Wittgenstein Society, volume 31, Kirchberg am Wechsel, Austria, August 2008.

    Google Scholar 

  17. F. Dretske. Conclusive reasons. Australasian Journal of Philosophy, 49:1–22, 1971.

    Article  Google Scholar 

  18. F. Dretske. Is knowledge closed under known entailment? The case against closure. In M. Steup, and E. Sosa, editors, Contemporary Debates in Epistemology, pages 13–26. Blackwell, Oxford, 2005.

    Google Scholar 

  19. R. Fagin and J. Halpern. Belief, awareness, and limited reasoning: Preliminary report. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence (IJCAI-85), pages 491–501. Morgan Kaufmann, Los Angeles, CA, August 1985.

    Google Scholar 

  20. R. Fagin and J. Halpern. Belief, awareness, and limited reasoning. Artificial Intelligence, 34(1):39–76, 1988.

    Article  Google Scholar 

  21. R. Fagin, J. Halpern, Y. Moses, and M. Vardi. Reasoning About Knowledge. MIT Press, Cambridge 1995.

    Google Scholar 

  22. M. Fitting. The logic of proofs, semantically. Annals of Pure and Applied Logic, 132(1):1–25, 2005.

    Article  Google Scholar 

  23. M. Fitting. A quantified logic of evidence. Annals of Pure and Applied Logic, 152(1–3):67–83, March 2008.

    Article  Google Scholar 

  24. E. Gettier. Is justified true belief knowledge? Analysis, 23:121–123, 1963.

    Google Scholar 

  25. K. Gödel. Vortrag bei Zilsel/Lecture at Zilsel’s (1938a). In S. Feferman, J.W. Dawson, Jr., W. Goldfarb, C. Parsons, and R.M. Solovay, editors, Unpublished Essays and Lectures, volume III of Kurt Gödel Collected Works, pages 86–113. Oxford University Press, Oxford, 1995.

    Google Scholar 

  26. A. Goldman. A causal theory of knowing. The Journal of Philosophy, 64:335–372, 1967.

    Article  Google Scholar 

  27. E. Goris. Feasible operations on proofs: The logic of proofs for bounded arithmetic. Theory of Computing Systems, 43(2):185–203, August 2008. Published online in October 2007.

    Article  Google Scholar 

  28. V.F. Hendricks. Active agents. Journal of Logic, Language and Information, 12(4):469–495, 2003.

    Article  Google Scholar 

  29. V.F. Hendricks. Mainstream and Formal Epistemology. Cambridge University Press, New York, NY, 2005.

    Book  Google Scholar 

  30. J. Hintikka. Knowledge and Belief. Cornell University Press, Ithaca, NY, 1962.

    Google Scholar 

  31. J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475–484, 1975.

    Article  Google Scholar 

  32. S. Kleene. On the interpretation of intuitionistic number theory. The Journal of Symbolic Logic, 10(4):109–124, 1945.

    Article  Google Scholar 

  33. N.V. Krupski. On the complexity of the reflected logic of proofs. Theoretical Computer Science, 357(1):136–142, 2006.

    Article  Google Scholar 

  34. V.N. Krupski. The single-conclusion proof logic and inference rules specification. Annals of Pure and Applied Logic, 113(1–3):181–206, 2001.

    Article  Google Scholar 

  35. V.N. Krupski. Referential logic of proofs. Theoretical Computer Science, 357(1):143–166, 2006.

    Article  Google Scholar 

  36. R. Kuznets. On the complexity of explicit modal logics. In Computer Science Logic 2000, volume 1862 of Lecture Notes in Computer Science, pages 371–383. Springer, Berlin, Germany, 2000.

    Google Scholar 

  37. R. Kuznets. Complexity Issues in Justification Logic. PhD thesis, CUNY Graduate Center, 2008. http://kuznets.googlepages.com/PhD.pdf

  38. K. Lehrer and T. Paxson. Knowledge: Undefeated justified true belief. The Journal of Philosophy, 66:1–22, 1969.

    Article  Google Scholar 

  39. S. Luper. The epistemic closure principle. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy, Fall 2010 Edition. http://plato.stanford.edu/archives/ fall2010/entries/closureepistemic/

  40. J. McCarthy, M. Sato, T. Hayashi, and S. Igarishi. On the model theory of knowledge. Technical Report STAN-CS-78-667, Stanford University, 1978.

    Google Scholar 

  41. R. Milnikel. Derivability in certain subsystems of the logic of proofs is Π 2 p-complete. Annals of Pure and Applied Logic, 145(3):223–239, 2007.

    Article  Google Scholar 

  42. A. Mkrtychev. Models for the logic of proofs. In S. Adian and A. Nerode, editors, Logical Foundations of Computer Science ‘97, Yaroslavl’, volume 1234 of Lecture Notes in Computer Science, pages 266–275. Springer, Berlin, Germany, 1997.

    Chapter  Google Scholar 

  43. Y. Moses. Resource-bounded knowledge. In M. Vardi, editor, Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, March 7–9, 1988, Pacific Grove, California, pages 261–276. Morgan Kaufmann Pbl., 1988.

    Google Scholar 

  44. R. Nozick. Philosophical Explanations. Harvard University Press, Cambridge, 1981.

    Google Scholar 

  45. E. Pacuit. A note on some explicit modal logics. Technical Report PP-2006-29, University of Amsterdam. ILLC Publications, 2006.

    Google Scholar 

  46. R. Parikh. Knowledge and the problem of logical omniscience. In Z. Ras and M. Zemankova, editors, ISMIS-87 International Symposium on Methodology for Intellectual Systems, pages 432–439. North-Holland, 1987.

    Google Scholar 

  47. B. Renne. Propositional games with explicit strategies. Electronic Notes on Theoretical Computer Science, 165:133–144, 1999.

    Article  Google Scholar 

  48. B. Renne. Dynamic Epistemic Logic with Justification. PhD thesis, CUNY Graduate Center, May 2008.

    Google Scholar 

  49. N. Rubtsova. Evidence reconstruction of epistemic modal logic S5. In Computer Science – Theory and Applications. CSR 2006, volume 3967 of Lecture Notes in Computer Science, pages 313–321. Springer, Berlin 2006.

    Google Scholar 

  50. N. Rubtsova. On realization of S5-modality by evidence terms. Journal of Logic and Computation, 16:671–684, 2006.

    Article  Google Scholar 

  51. R.C. Stalnaker. Knowledge, belief and counterfactual reasoning in games. Economics and Philosophy, 12:133–163, 1996.

    Article  Google Scholar 

  52. A.S. Troelstra and H. Schwichtenberg. Basic Proof Theory. Cambridge University Press, Amsterdam, 1996.

    Google Scholar 

  53. A.S. Troelstra and D. van Dalen. Constructivism in Mathematics, Volumes 1, 2. North–Holland, Amsterdam, 1988.

    Google Scholar 

  54. J. van Benthem. Reflections on epistemic logic. Logique & Analyse, 133–134:5–14, 1993.

    Google Scholar 

  55. G.H. von Wright. An Essay in Modal Logic. North-Holland, Amsterdam, 1951.

    Google Scholar 

  56. T. Yavorskaya (Sidon). Multi-agent Explicit knowledge. In D. Grigoriev, J. Harrison, and E.A. Hirsch, editors, Computer Science – Theory and Applications. CSR 2006, volume 3967 of Lecture Notes in Computer Science, pages 369–380. Springer, Berlin, Germany, 2006.

    Google Scholar 

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acknowledgements

The author is very grateful to Walter Dean, Mel Fitting, Vladimir Krupski, Roman Kuznets, Elena Nogina, Tudor Protopopescu, and Ruili Ye, whose advice helped with this paper. Many thanks to Karen Kletter for editing this text. The author is also indebted to the anonymous referee whose valuable comments helped to sharpen some of the arguments. In particular, the last paragraph of Section 2.4.5 has been essentially suggested by the referee.

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Correspondence to Sergei Artemov* .

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Artemov*, S. (2011). Why Do We Need Justification Logic?. In: van Benthem, J., Gupta, A., Pacuit, E. (eds) Games, Norms and Reasons. Synthese Library, vol 353. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0714-6_2

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