On the Island of Logical Robots
Suppose you are a maintenance tech who works on an island with many different robots, in three different models. (1) Truthinator 9000, (2) D-Seevr 4.0, and (3) Benders. All three kinds of robots look exactly alike, so you can’t tell them apart based on what they look like. They all know everything there is to know. But Truthinators are programmed always to tell the truth; D-Seevrs are programmed always to tell lies. Benders mostly lie, of course, but they can choose to say false things and they also can choose to say true things. All of them only output intelligible declarative sentences with definite consistent truth values.
Now suppose that a robot needs a repair and wants to identify its model to you. Truthinator 9000 would say “I am Truthinator 9000.” But then, D-Seevr might also say that, and so might Bender, if he chooses to lie, which he often does. Bender could truthfully say “I’m a Bender, bub” but a D-Seevr might say that too.
Is there one sentence that a Bender could say that would allow you, as a sufficiently logical maintenance tech, to identify the robot as a Bender rather than a Truthinator or a D-Seevr? If so, what?
Is there one sentence that a Truthinator could say that would allow you to definitely identify the robot as a Truthinator and not as a Bender or a D-Seevr? If so, what?
Is there anything that a D-Seevr could say in one sentence that would allow you to definitely identify the robot as a D-Seevr, and not as a Truthinator or a Bender?
- This is of course a modified Knights and Knaves problem, of the sort popularized by Raymond Smullyan. But the presence of Benders on the island should significantly change the sort of strategies available.↩