Information Updates
Eric Pacuit
Philosophy
University of Maryland
Suppose that Ann, Bob and Carla are at a restaurant having dinner. A waiter takes their drink order: Ann orders red wine, Bob orders white wine, and Carla orders a beer.
A different waiter returns with a red wine, a white wine and a beer.
After learning who ordered the red wine and the white wine, the water can infer that Carla ordered a beer.
R
W
B
Ann ordered red wine
Bob ordered white wine
Carla ordered beer
Ann
R
B
W
Bob
Bob
Bob
Carla
Carla
Carla
Carla
Carla
Carla
W
R
R
W
B
B
R\, W B
R\,B\,W
W R\,B
W B\,R
B\,R\ W
B\, W R
B
W
B
R
W
R
R\, W B
R\,B\,W
W R\,B
W B\,R
B\,R\ W
B\, W R
R\, W B
R\,B\,W
R\, W B
Ann ordered red wine
Bob ordered white wine
After learning that Ann ordered red wine and Bob ordered white wine,
Carla must have ordered Beer.
R\text{ or } W \text{ or } B, \text{ not } R, \text{ not } W\Rightarrow B
R\,WB
That is, the only possibility is: