Tag: Smullyan

  • Boolean and Heyting islands

    Raymond Smullyan‘s logic puzzles frequently involve Knights (who always tell the truth) and Knaves (who always lie). In his book Logical Labyrinths (really a first course in propositional logic) he introduced islands where the lying or truth-telling habits can vary from day to day—that is, an inhabitant might lie on some days and tell the […]

  • The strange logic of subways

    “A subway is just a hole in the ground, and that hole is a maze.” “The map is the last vestige of the old system. If you can’t read the map, you can’t use the subway.” Eddie Jabbour in Can he get there from here? (NYT) Sometimes, lines between adjacent stations can be uni-directional (as…

  • Heyting Smullyanesque problems

    Raymond Smullyan brought Knights and Knaves puzzles to a high art in his books. Here’s the setting: On Smullyan’s islands there are Knights, who always tell true statements, Knaves, who always lie, and sometimes also Normals, who sometimes tell the truth and sometimes lie. (image credit MikeKlein) Problems of this sort can be solved by…

  • Knights and Knaves, the Heyting way

    (image credit: Joe Blitzstein via Twitter) Smullyan’s Knights and Knaves problems are classics. On an island all inhabitants are either Knights (who only tell true things) and Knaves (who always lie). You have to determine their nature from a few statements. Here’s a very simple problem: “Abercrombie met just two inhabitants, A and B. A…

  • Smullyan and the President’s sanity

    Smullyan found himself in a very strange country indeed! All the inhabitants of this country are completely truthful – they always tell you honestly what they believe, but the trouble is that about half of the population are totally mad, and all their beliefs are wrong! The other half are totally sane and accurate in…