Tuesdays,
11:45-1:45pm
GC 3305

Sergei Artemov
GC 4329, 212-817-8661
sartemov@gc.cuny.edu

Justification Logic offers new foundations for modal logic and formal epistemology by axiomatizing the notion of justification and defining knowledge according to Plato as the result of sufficient justification. A number of old questions in epistemology and related areas can be answered within Justification Logic: Goedel's intended proof semantics for modal logic, the Kolmogorov's proof semantics for intuitionistic logic, the logical omniscience problem, the Gettier problem, etc. Further applications of this new technique are anticipated in Computer Science and Artificial Intelligence, Games and Economics, Epistemology, and other areas.

The course offers a systematic exposition of the mathematical theory of knowledge and justification in a broad context of epistemology, mathematical logic, computer science.

S. Artemov, "Explicit provability and constructive semantics," The Bulletin for Symbolic Logic, v. 7, no. 1, pp.1-36, 2001.

S. Artemov, "Justified common knowledge," Theoretical Computer Science , v. 357, pp.~4-22, 2006.

S. Artemov and R. Kuznets, "Logical Omniscience Via Proof Complexity," Lecture Notes in Computer Science, v. 4207, Computer Science Logic 2006, pp.~135-149, 2006.

R.J. Aumann, "Agreeing to disagree," Annals of Statistics , v. 4(6), pp. 1236-1239, 1976.

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

M. Fitting, "The logic of proofs, semantically," Annals of Pure and Applied Logic, v. 132, no. 1, pp. 1-25, 2005.

E. Gettier, "Is Justified True Belief Knowledge?" Analysis , v. 23, pp. 121-123, 1963.

J. Hintikka, Knowledge and Belief, Cornell University Press, 1962.

J.-J.Ch. Meyer and W. van der Hoek, Epistemic Logic for AI and Computer Science, Cambridge University Press, 1995.

R. Parikh, "Logical omniscience," in: D. Leivant, editor, Logic and Computational Complexity, International Workshop LCC '94, Indianapolis, Indiana, USA, 13-16 October 1994,
Lecture Notes in Computer Science 960, Springer, 1995 pp. 22-29.