みなさま， LORIA-CNRSのHans van Ditmarsch教授により，以下の講演を行います． どうぞふるってご参加ください．

日時：9/13(金)15:00--17:00 場所：北陸先端科学技術大学院大学　情報 II 棟コラボ6

東条

********* One Hundred Prisoners and a Light Bulb

Consider this riddle:

"A group of 100 prisoners, all together in the prison dining area, are told that they will be all put in isolation cells and then will be interrogated one by one in a room containing a light with an on/off switch. The prisoners may communicate with one another by toggling the light-switch (and that is the only way in which they can communicate). The light is initially switched off. There is no fixed order of interrogation, or interval between interrogations, and the same prisoner will be interrogated again at any stage. When interrogated, a prisoner can either do nothing, or toggle the light-switch, or announce that all prisoners have been interrogated. If that announcement is true, the prisoners will (all) be set free, but if it is false, they will all be executed. While still in the dining room, and before the prisoners go to their isolation cells (forever), can the prisoners agree on a protocol that will set them free?"

In this presentation I will present a solution, however I will mainly address such puzzles of knowledge in general. There are many others, such as the ‘Muddy Children Puzzle’ (also known as the ‘Wisemen Puzzle’), ‘Surprise Examination’, ‘Monty Hall’, etc. They often involve a (seemingly) paradoxical aspect making agents knowledgeable by announcements of their ignorance. Their provenance and dissemination is intriguing. Haruyuki Kawabe kindly told me that in Japan, a version of the Muddy Children Puzzle with coloured hats is known as 'Dirac's Puzzle', after the physicist Paul Dirac who introduced some Japanese physicists to the riddle about 1938, and it seems one of them wrote a novel using the idea of the puzzle in 1940. There is a relation between such knowledge puzzles and the area in logic known as ‘dynamic epistemic logic’. More information on such puzzles is found in the book also entitled 'One Hundred Prisoners and a Light Bulb' (Copernicus, 2015) and on the webpage http://personal.us.es/hvd/lightbulb.html. The puzzlebook has been translated into Japanese by Haruyuki Kawabe.

Hans van Ditmarsch is a senior researcher at CNRS (the French National Research Organization), and based at LORIA in Nancy, where he is heading the research team CELLO (Computational Epistemic Logic in Lorraine). He is also affiliated to IMSc (Institute for Mathematical Sciences), in Chennai. His research is on the dynamics of knowledge and belief, information-based security protocols, modal logics, and combinatorics. He has been an editor of the Journal of Philosophical Logic. He is an author of the book Dynamic Epistemic Logic, an editor of the Handbook of Epistemic Logic.

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