Rules
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A Kripke frame with 4 worlds is generated:
, where .
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The game tells you how many accessibility relations are in the frame , but not the exact shape of it.
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You have a total of 10 moves ().
In each move you can do one of the following:
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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:
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Guess the Kripke frame.
If your frame is equal or isomorphic to the secret frame , you win.
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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
- falsum:
⊥, F, 0, \bot
- negation:
¬, ~, \neg, \lnot
- box modality:
□, [], !, L, \Box
- diamond modality:
⋄, <>, ?, M, \Diamond
- conjunction:
∧, ^, &, \wedge, \land
- disjunction:
∨, v, |, \vee, \lor
- implication:
→, ->, >, \rightarrow, \to
- equivalence:
↔, <->, =, \leftrightarrow, \equiv
- parentheses:
(, )