Logicians Yap, Kooi Explain Viral Birthday Logic Puzzle

You’ve probably seen the “birthday logic puzzle” that’s gone viral in the past few days. If you haven’t, you might want to try to solve it yourself. Here it is:

be00992c-012d-4216-9e7a-2751a79c75c4-620x372

Two dynamic epistemic logicians, Audrey Yap (UVic) and Barteld Kooi (Groningen) explained the solution (and how to get it) on facebook.  “Dynamic” here modifies “epistemic”, not “logicians:”  there is something called “dynamic epistemic logic” which is used here.  FWIW, I know that Audrey at least is very dynamic.

Audrey’s solution, posted with her kind permission:

These are all the possibilities at the start. The red lines represent Albert’s uncertainty, and the blue lines represent Bernard’s uncertainty. So there’s a red line between May 15 and May 16 because Albert would only know it’s May and not what date. And there’s a blue line between May 15 and Aug 15 because Bernard would only know it’s the 15th and not what month.

initialuncert
​Then the first important piece of information is that Albert knows that Bernard doesn’t know the date. This eliminates a lot of dates, because if Albert is certain that Bernard doesn’t know the date, we can’t be in a month where Bernard might know the date. That effectively eliminates May and June, because in both of those months, there’s a possibility Bernard could already know the date.

first
​And then the next interesting thing we learn is that, after learning that piece of information, Bernard does know the date. So here’s what it looks like with May and June eliminated and how we figure out what to do with that information. Since Bernard now knows the date, it can’t be the 14th, since then he still wouldn’t know.

second
​Then last, when we see that Albert actually learned the date from hearing the fact that Bernard does, know there’s only one date it could possibly be. So here’s what it looks like when we eliminate the 14th as a possibility.

third

Barteld Kooi’s video explanation is here on facebook and also on YouTube:

Logic without Borders: Essays in Honor of Jouko Väänänen

A Festschrift for Jouko Väänänen‘s 60th birthday is now out with de Gruyter, edited by Åsa Hirvonen, Juha Kontinen, Roman Kossak, and Andrés Villaveces:

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

It’s expensive, but the table of contents features an all-star cast:

  1. Juliette Kennedy, On the “Logic without Borders” Point of View
  2. Samson Abramsky, Arrow’s Theorem by Arrow Theory
  3. John T. Baldwin, How Big Should the Monster Model Be?
  4. John P. Burgess, Modal Logic in the Modal Sense of Modality
  5. Xavier Caicedo, Lindström’s Theorem for Positive Logics, a Topological View
  6. Zoé Chatzidakis, Model Theory of Fields With Operators – a Survey
  7. Carlos Augusto Di Prisco, Some Aspects of the Ramsey Theory of Real Numbers
  8. Mirna Džamonja, The Singular World of Singular Cardinals
  9. Curtis Franks, Logical Nihilism
  10. Pietro Galliani, The Doxastic Interpretation of Team Semantics
  11. Lauri Hella and Jouko Väänänen, The Size of a Formula as a Measure of Complexity
  12. Wilfrid Hodges, Notes on the History of Scope<
  13. Jan Hubička and Jaroslav Nešetřil, Universal Structures with Forbidden Homomorphisms
  14. Tapani Hyttinen, Counting Measure and Forking in Finite Models
  15. Richard Kaye and Tin Lok Wong, The Model Theory of Generic Cuts
  16. Juha Kontinen, On Natural Deduction in Dependence Logic
  17. Steven Lindell, Henry Towsner, and Scott Weinstein, Infinitary Methods in Finite Model Theory
  18. Maryanthe Malliaris and Saharon Shelah, Saturating the Random Graph with an Independent Family of Small Range
  19. Ilkka Niiniluoto, Constructive Realism in Mathematics
  20. Jeff B. Paris and Alena Vencovská, The Twin Continua of Inductive Methods
  21. Saharon Shelah, A.E.C. with Not Too Many Models
  22. ouko Väänänen, Pursuing Logic without Borders/li>
  23. A Radio Interview with Jouko Väänänen