Hatsinsane series
This is a famous little puzzle in epistemic logic—that is, in the kind of logic in which we can reason not only about basic facts like the distribution of hats, but also about agents’ states of knowledge. Expressing it in pure first-order logic without primitive epistemic operators is a lot more … well … fun!
Three people, A, B and C, are each fitted with a hat. They all know that every hat is either blue or green and that at least one is green (i.e. they are not all blue). A and B can each see the other two people’s hats but not their own. C is blindfolded and sees nothing.
A is asked “Do you know the colour of your own hat?“
B and C hear A answer (truthfully) “No”.
B is then asked “Do you know the colour of your own hat?“
A and C hear B answer (truthfully) “No”.
C is then asked “Do you know the colour of your own hat?“
C answers truthfully… what?
A four-place relation to express “x knows at time t that the colour of y’s hat is c” may be a good start, but it isn’t enough to express what C knows about what B knows. Well, have fun!
Solver
Auto Parser Results
No errors found.