KRiPkE

Daily Challenge!

• The answer of the game changes every day.
• The progress of the game persists until the next day (14:31:51 from now).
• You can also play Random Challenge.

Rules

• A Kripke frame with 4 worlds and 4 relation(s) is generated: $\footnotesize \mathcal{F} = \left<W, R\right>$, where $\footnotesize |W| = 4$ and $\footnotesize |R| = 4$.
• You have a total of 10 moves (). In each move you can do one of the following:
  • Enter a modal formula. The game tells you in how many worlds the formula is valid. In other words, it tells you the following natural number:
    $\footnotesize \mathrm{N}(\varphi) = \bigl| \Set{ w \in W | \forall \mathop{\Vdash}\, (w \Vdash \varphi) } \bigr|$
  • Guess the Kripke frame. If your frame is equal or isomorphic to $\footnotesize \mathcal{F}$, you win.
• You lose when you run out of moves.

Syntax

You may use the following symbols:

• propositional variables: p, q, r, s
• verum: ⊤, T, 1, \top, top
• falsum: ⊥, F, 0, \bot, bot
• negation: ¬, ~, \neg, \lnot, not
• box: □, ◻, [], !, L, \Box, box
• diamond: ◇, ◊, ♢, ⋄, <>, ?, M, \Diamond, dia
• conjunction: ∧, ^, &, \wedge, \land, and
• disjunction: ∨, v, |, \vee, \lor, or
• implication: →, ->, ⊃, >, \rightarrow, \to, to
• equivalence: ↔, <->, ≡, =, \leftrightarrow, \equiv, eq
• parentheses: (, \left, ), \right