Abstract
In this paper, we use commonsense reasoning and graph representation to study logical puzzles with three types of people. Strong Truth-Tellers say only true atomic statements, Strong Liars say only false atomic statements, and Strong Crazy people say only self-contradicting statements. Self-contradicting statements are connected to the Liar paradox, i.e., no Truth-Teller or a Liar could say “I am a Liar”. A puzzle is clear if it only contains its given statements to solve it, and a puzzle is good if it has exactly one solution. It is known that there is no clear and good Strong Truth-Teller–Strong Liar (also called SS) puzzle. However, as we prove here, there are good and clear Strong Truth-Teller, Strong Liar and Strong Crazy puzzles (SSS-puzzles). The newly investigated type ‘Crazy’ drastically changes the scenario. Some properties of the new types of puzzles are analyzed, and some statistics are also given.
Highlights
Logical puzzles have various roles in our life
We present a new type of puzzle
T is the set of Strong Truth-Tellers, L is the set of Strong Liars, and C is the set of Strong Crazy people in the puzzle
Summary
Logical puzzles have various roles in our life. They are helpful for training our brains, to learn logical thinking, and for recreation. We investigate the new type, the Crazy persons, instead of Mutes (see Table 2) This is a new approach in puzzles to deal with sentences that have a third truth-value; Crazy people can say self-contradictory statements that are not true and not false if a Truth-Teller or a Liar, respectively, would say them. In the solution of the puzzle in the previous example, if we assume that Anne is a Truth-Teller, Bale is a Truth-Teller and Suzan is a Liar; Bale (who has the same type as Anne) said that. A function N → {Truth-Teller, Liar, Crazy} is a solution of the puzzle if the following holds for each person Ak who said anything in the puzzle: Ak is Truth-Teller exactly as in Definition 5. Person Ak is a Crazy person if Ak said only self-contradictory statements
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