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.
Dretske [18].
- 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
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.
S. Artemov. Operational modal logic. Technical Report MSI 95-29, Cornell University, 1995.
S. Artemov. Explicit provability and constructive semantics. Bulletin of Symbolic Logic, 7(1):1–36, 2001.
S. Artemov. Justified common knowledge. Theoretical Computer Science, 357(1–3):4–22, 2006.
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.
S. Artemov. The logic of justification. The Review of Symbolic Logic, 1(4):477–513, December 2008.
S. Artemov, E. Kazakov, and D. Shapiro. Epistemic logic with justifications. Technical Report CFIS 99-12, Cornell University, 1999.
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.
S. Artemov and E. Nogina. Introducing justification into epistemic logic. Journal of Logic and Computation, 15(6):1059–1073, 2005.
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.
S. Artemov and E. Nogina. The topology of justification. Journal of Logic and Logical Philosophy, 17(1–2):58–71, 2008.
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.
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/
V. Brezhnev and R. Kuznets. Making knowledge explicit: How hard it is. Theoretical Computer Science, 357(1–3):23–34, 2006.
W. Dean and H. Kurokawa. From the knowability paradox to the existence of proofs. Synthese, 176(2):177–225, September 2010.
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.
F. Dretske. Conclusive reasons. Australasian Journal of Philosophy, 49:1–22, 1971.
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.
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.
R. Fagin and J. Halpern. Belief, awareness, and limited reasoning. Artificial Intelligence, 34(1):39–76, 1988.
R. Fagin, J. Halpern, Y. Moses, and M. Vardi. Reasoning About Knowledge. MIT Press, Cambridge 1995.
M. Fitting. The logic of proofs, semantically. Annals of Pure and Applied Logic, 132(1):1–25, 2005.
M. Fitting. A quantified logic of evidence. Annals of Pure and Applied Logic, 152(1–3):67–83, March 2008.
E. Gettier. Is justified true belief knowledge? Analysis, 23:121–123, 1963.
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.
A. Goldman. A causal theory of knowing. The Journal of Philosophy, 64:335–372, 1967.
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.
V.F. Hendricks. Active agents. Journal of Logic, Language and Information, 12(4):469–495, 2003.
V.F. Hendricks. Mainstream and Formal Epistemology. Cambridge University Press, New York, NY, 2005.
J. Hintikka. Knowledge and Belief. Cornell University Press, Ithaca, NY, 1962.
J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475–484, 1975.
S. Kleene. On the interpretation of intuitionistic number theory. The Journal of Symbolic Logic, 10(4):109–124, 1945.
N.V. Krupski. On the complexity of the reflected logic of proofs. Theoretical Computer Science, 357(1):136–142, 2006.
V.N. Krupski. The single-conclusion proof logic and inference rules specification. Annals of Pure and Applied Logic, 113(1–3):181–206, 2001.
V.N. Krupski. Referential logic of proofs. Theoretical Computer Science, 357(1):143–166, 2006.
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.
R. Kuznets. Complexity Issues in Justification Logic. PhD thesis, CUNY Graduate Center, 2008. http://kuznets.googlepages.com/PhD.pdf
K. Lehrer and T. Paxson. Knowledge: Undefeated justified true belief. The Journal of Philosophy, 66:1–22, 1969.
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/
J. McCarthy, M. Sato, T. Hayashi, and S. Igarishi. On the model theory of knowledge. Technical Report STAN-CS-78-667, Stanford University, 1978.
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.
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.
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.
R. Nozick. Philosophical Explanations. Harvard University Press, Cambridge, 1981.
E. Pacuit. A note on some explicit modal logics. Technical Report PP-2006-29, University of Amsterdam. ILLC Publications, 2006.
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.
B. Renne. Propositional games with explicit strategies. Electronic Notes on Theoretical Computer Science, 165:133–144, 1999.
B. Renne. Dynamic Epistemic Logic with Justification. PhD thesis, CUNY Graduate Center, May 2008.
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.
N. Rubtsova. On realization of S5-modality by evidence terms. Journal of Logic and Computation, 16:671–684, 2006.
R.C. Stalnaker. Knowledge, belief and counterfactual reasoning in games. Economics and Philosophy, 12:133–163, 1996.
A.S. Troelstra and H. Schwichtenberg. Basic Proof Theory. Cambridge University Press, Amsterdam, 1996.
A.S. Troelstra and D. van Dalen. Constructivism in Mathematics, Volumes 1, 2. North–Holland, Amsterdam, 1988.
J. van Benthem. Reflections on epistemic logic. Logique & Analyse, 133–134:5–14, 1993.
G.H. von Wright. An Essay in Modal Logic. North-Holland, Amsterdam, 1951.
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.
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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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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