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Open AccessArticle

Truth-Teller–Liar Puzzles with Self-Reference

Department of Mathematics, Eastern Mediterranean University, Famagusta, North Cyprus, via Mersin 10, Gazimağusa 99450, Turkey
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 190;
Received: 30 December 2019 / Revised: 22 January 2020 / Accepted: 26 January 2020 / Published: 4 February 2020
(This article belongs to the Special Issue Mathematical Methods in Artificial Intelligence)
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.
Keywords: SS-puzzles; SSS-puzzles; Crazy people; self-contradictory statements; puzzle-graphs SS-puzzles; SSS-puzzles; Crazy people; self-contradictory statements; puzzle-graphs
MDPI and ACS Style

Alzboon, L.; Nagy, B. Truth-Teller–Liar Puzzles with Self-Reference. Mathematics 2020, 8, 190.

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