The Logic of Justification

Review of Symbolic Logic

Volumn 1, Issue 4, 2008, Pages 477-513

  Artemov, Sergei ^a  

^a CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84989195596     PISSN: 17550203     EISSN: 17550211     Source Type: Journal    
DOI: 10.1017/S1755020308090060     Document Type: Article

References (69)

1. Antonakos, E. (2007). Justified and common knowledge: limited conservativity. In Artemov, S., and Nerode, A., editors. Logical Foundations of Computer Science. International Symposium, LFCS 2007, New York, NY, June 2007, Proceedings, Volume 4514 of Lecture Notes in Computer Science. Berlin: Springer, pp. 1-11.
2. Artemov, S. (1995). Operational Modal Logic. Technical Report MSI 95-29. Ithaca, NY: Cornell University.
3. Artemov, S. (1999, August). Understanding Constructive Semantics. Spinoza lecture for European Association for logic, language and information. Utrecht.
4. Artemov, S. (2001). Explicit provability and constructive semantics. Bulletin of Symbolic Logic, 7(1), 1-36.
5. Artemov, S. (2006). Justified common knowledge. Theoretical Computer Science, 357 (1-3), 4-22.
6. Artemov, S. (2007). On two models of provability. In Gabbay, D. M., Zakharyaschev, M., and Goncharov, S. S., editors. Mathematical Problems From Applied Logic II. New York, NY: Springer, pp. 1-52.
7. Artemov, S. (2008). Symmetric logic of proofs. In Avron, A., Dershowitz, N., and Rabinovich, A., 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. Berlin: Springer, pp. 58-71.
8. Artemov, S., Beklemishev, L. (2005). Provability logic. In Gabbay, D., and Guenthner, F., editors. Handbook of Philosophical Logic (second edition), Vol. 13. Dordrecht, The Netherlands: Springer, pp. 189-360.
9. Artemov, S., Kazakov, E., Shapiro, D. (1999). Epistemic Logic With Justifications. Technical Report CFIS 99-12. Ithaca, NY: Cornell University.
10. Artemov, S., Kuznets, R. (2006). Logical omniscience via proof complexity. In Computer Science Logic 2006, Volume 4207. Springer Lecture Notes in Computer Science. Berlin: Springer, pp. 135-149.
11. Artemov, S., Nogina, E. (2004). Logic of Knowledge With Justifications From the Provability Perspective. Technical Report TR-2004011, New York: PhD Program in Computer Science CUNY.
12. Artemov, S., Nogina, E. (2005). Introducing justification into epistemic logic. Journal of Logic and Computation, 15(6), 1059-1073.
13. Artemov, S., Strassen, T. (1993). Functionality in the Basic Logic of Proofs. Technical Report IAM 93-004. Department of Computer Science, University of Bern, Switzerland.
14. Boolos, G. (1993). The Logic of Provability. Cambridge, MA: Cambridge University Press.
15. Brezhnev, V. (2000). On Explicit Counterparts of Modal Logics. Technical Report CFIS 2000-05. Ithaca, NY: Cornell University.
16. Brezhnev, V., &Kuznets, R. (2006). Making knowledge explicit: how hard it is. Theoretical Computer Science, 357(1-3), 23-34.
17. Dean, W., Kurokawa, H. (2007). From the knowability paradox to the existence of proofs. Synthese. Submitted.
18. Dean, W., Kurokawa, H. (2008). The knower paradox and the quantified logic of proofs. In Hieke, A., editor. Proceedings of the Austrian Ludwig Wittgenstein Society Vol. 31. Kirchberg am Wechsel, 2008.
19. Dretske, F. (1971). Conclusive reasons. Australasian Journal of Philosophy, 49, 1-22.
20. Dretske, F. (2005). Is knowledge closed under known entailment? the case against closure. In Steup, M., and Sosa, E., editors. Contemporary Debates in Epistemology. Malden, MA: Blackwell, pp. 13-26.
21. Fagin, R., Halpern, J. (1985) Belief, awareness, and limited reasoning: preliminary report. In Joshi, A. K., editor Proceedings of the Ninth International Joint Conference on Artificial Intelligence (IJCAI-85). Los Altos, CA: Morgan Kaufmann, pp. 491-501.
22. Fagin, R., Halpern, J. (1988). Belief, awareness, and limited reasoning. Artificial Intelligence, 34(1), 39-76.
23. Fagin, R., Halpern, J., Moses, Y., Vardi, M. (1995). Reasoning About Knowledge. Cambridge, MA: MIT Press.
24. Fitting, M. (2003). A Semantics for the Logic of Proofs. Technical Report TR-2003012, PhD Program in Computer Science. City University of New York.
25. Fitting, M. (2005). The logic of proofs, semantically. Annals of Pure and Applied Logic, 132(1), 1-25.
26. Fitting, M. (2007, February). Intensional Logic. Stanford Encyclopedia of Philosophy. Available from: http://plato. stanford. edu.
27. Fitting, M., Mendelsohn, R. L. (1998). First-Order Modal Logic. Dordrecht, The Netherlands: Kluwer Academic.
28. Frege, G. (1952). On sense and reference. In Geach, P., and Black, M., editors. Translations of the Philosophical Writings of Gottlob Frege. Oxford: Blackwell, pp. 56-78.
29. Gettier, E. (1963). Is justified true belief knowledge? Analysis, 23, 121-123.
30. Gödel, K. (1986). Eine Interpretation des intuitionistischen Aussagenkalkuls. Ergebnisse Math. Kolloq., 14, 39-40, 1933.
31. Feferman, S. et al., editors. Kurt Gödel Collected Works. Vol. 1. Oxford: Oxford University Press; New York, NY: Clarendon Press, pp. 301-303.
32. Gödel, K. (1995). Vortrag bei Zilsel/Lecture at Zilsel's (1938a). In Feferman, S., Dawson, J. W., Jr., Goldfarb, W., Parsons, C., and Solovay, R. M., editors. Unpublished Essays and Lectures, Volume III of Kurt Gödel Collected Works. New York: Oxford University Press, pp. 86-113.
33. Goldman, A. (1967). A causal theory of knowing. The Journal of Philosophy, 64, 335-372.
34. Goris, E. (2007). Explicit proofs in formal provability logic. In Artemov, S., and Nerode, A., editors. Logical Foundations of Computer Science. International Symposium, LFCS 2007, New York, NY, June 2007, Proceedings, Volume 4514 of Lecture Notes in Computer Science. Berlin: Springer, pp. 241-253.
35. Hendricks, V. F. (2003). Active Agents. Journal of Logic, Language and Information, 12(4), 469-495.
36. Hendricks, V. F. (2005). Mainstream and Formal Epistemology. New York, NY: Cambridge University Press.
37. Heyting, A. (1934). Mathematische Grundlagenforschung. Intuitionismus. Beweistheorie. Berlin, Germany: Springer.
38. Hintikka, J. (1962). Knowledge and Belief. Ithaca, NY: Cornell University Press.
39. Hintikka, J. (1975). Impossible possible worlds vindicated. Journal of Philosophical Logic, 4, 475-484.
40. Kleene, S. (1945). On the interpretation of intuitionistic number theory. The Journal of Symbolic Logic, 10(4), 109-124.
41. Krupski, N. V. (2006). On the complexity of the reflected logic of proofs. Theoretical Computer Science, 357(1), 136-142.
42. Krupski, V. N. (2001). The single-conclusion proof logic and inference rules specification. Annals of Pure and Applied Logic, 113(1-3), 181-206.
43. Krupski, V. N. (2006). Referential logic of proofs. Theoretical Computer Science, 357(1), 143-166.
44. Kuznets, R. (2000). On the complexity of explicit modal logics. In Clote, P. G. and Schwichtenberg, H., eds. Computer Science Logic 2000, Volume 1862 of Lecture Notes in Computer Science. Berlin: Springer-Verlag, pp. 371-383.
45. Kuznets, R. (2008). Complexity Issues in Justification Logic. PhD thesis, CUNY Graduate Center. Available from: http://kuznets. googlepages. com/PhD. pdf. Accessed May 2008.
46. Lehrer, K., Paxson, T. (1969). Knowledge: undefeated justified true belief. The Journal of Philosophy, 66, 1-22.
47. Luper, S. (2005). The Epistemic Closure Principle. Stanford Encyclopedia of Philosophy.
48. McCarthy, J., Sato, M., Hayashi, T., Igarishi, S. (1978). On the Model Theory of Knowledge. Technical Report STAN-CS-78-667. Stanford, CA: Stanford University Press.
49. Meyer, J.-J. Ch., &van der Hoek, W. (1995). Epistemic Logic for AI and Computer Science. New York: Cambridge University Press.
50. Milnikel, R. (2007). Derivability in certain subsystems of the logic of proofs is-p 2-complete. Annals of Pure and Applied Logic, 145(3), 223-239.
51. Mkrtychev, A. (1997). Models for the logic of proofs. In Adian, S., and Nerode, A., editors. Logical Foundations of Computer Science '97, Yaroslavl', Volume 1234 of Lecture Notes in Computer Science. Berlin: Springer, pp. 266-275.
52. Moses, Y. (1998). Resource-bounded knowledge. In Vardi, M., editor. Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, March 7-9, 1988, Pacific Grove, California, Los Altos, CA: Morgan Kaufmann Publishers, pp. 261-276.
53. Neale, S. (1990). Descriptions. Cambridge, MA: MIT Press Books.
54. Nozick, R. (1981). Philosophical Explanations. Cambridge, MA: Harvard University Press.
55. Pacuit, E. (2005, July). A Note on Some Explicit Modal Logics. 5th Panhellenic Logic Symposium, Athens. University of Athens.
56. Pacuit, E. (2006). A Note on Some Explicit Modal Logics. Technical Report PP-2006-29. Amsterdam: University of Amsterdam. ILLC Publications.
57. Parikh, R. (1987). Knowledge and the problem of logical omniscience. In Ras, Z., and Zemankova, M., editors. ISMIS-87 (International Symposium on Methodology for Intellectual Systems). Amsterdam: North-Holland, pp. 432-439.
58. Rubtsova, N. (2005). Evidence-Based Knowledge for S5. Logic Colloquium 2005, Athens: University of Athens.
59. Rubtsova, N. (2006). Evidence reconstruction of epistemic modal logic S5. In Grigoriev, D., Harrison, J., Hirsch, E. A., editors. Computer Science-Theory and Applications. CSR 2006, Volume 3967 of Lecture Notes in Computer Science. Berlin: Springer, pp. 313-321.
60. Russell, B. (1905). On denoting. Mind, 14, 479-493.
61. Russell, B. (1912). The Problems of Philosophy. London: Williams and Norgate; New York, NY: Henry Holt and Company.
62. Russell, B. (1919) Introduction to Mathematical Philosophy. London: George Allen and Unwin. THE LOGIC OF JUSTIFICATION 513
63. Stalnaker, R. C. (1996). Knowledge, belief and counterfactual reasoning in games. Economics and Philosophy, 12, 133-163.
64. Troelstra, A. S. (1998). Realizability. In Buss, S., editor. Handbook of Proof Theory, Amsterdam, The Netherlands: Elsevier, pp. 407-474.
65. Troelstra, A. S., Schwichtenberg, H. (1996). Basic Proof Theory. Amsterdam, The Netherlands: Cambridge University Press.
66. Troelstra, A. S., van Dalen, D. (1988). Constructivism in Mathematics. Vols. 1, 2. Amsterdam, The Netherlands: North-Holland.
67. van Dalen, D. (1986). Intuitionistic logic. In Gabbay, D., and Guenther, F., editors. Handbook of Philosophical Logic. Vol. 3. Dordrecht, The Netherlands: Reidel pp. 225-340.
68. von Wright, G. H. (1951). An Essay in Modal Logic. Amsterdam, The Netherlands: North-Holland.
69. Yavorskaya Sidon, T. (2006). Multi-agent explicit knowledge. In Grigoriev, D., Harrison, J., and Hirsch, E. A., editors. Computer Science-Theory and Applications. CSR 2006, Volume 3967 of Lecture Notes in Computer Science. Berlin: Springer, pp. 369-380.