Dipartimento di Lettere e Filosofia (DILEF), via della Pergola 60
Tuesday, October 15, 4.30 p.m., sala altana (2nd floor)
Alexandru Baltag (Institute of Logic, Language and Computation, Amsterdam) - personal webpage
SURPRISE! Or How to Avoid Unexpected Exams
Abstract: The Hangman puzzle, in its "Unexpected Examination" version, is a well-known paradox in epistemic logic literature, that involves circularity and self-reference. It involves a Teacher announcing her students that the exam's date (known only to be sometimes next week) will be a "surprise'': even in the evening before the exam, the students will still not be sure that the exam is tomorrow. Intuitively, one can prove (by backward induction, starting with Friday) that, if this announcement is true, then the exam cannot take place in any day of the week. So, using this argument, the students come to "know" that the announcement is false: the exam cannot be a surprise. Given this reasoning, they just dismiss the announcement as false, and... then, whenever the exam will come (say, on Tuesday) it will indeed be a complete surprise!
I discuss the various solutions in the literature, including some new solutions. Time-permitting, I sketch some new directions of approaching this puzzle: one based on a theory of doxastic attitudes, epistemic norms and dynamic belief revision; another based on the topological concepts of Cantor-Bendixson derivative and the perfect core of a set; and a third based on a game-theoretic analysis. The conclusion of my discussion will come as a... surprise! (Or so I hope!)