interrogator's state
[1, 1] [1, 2] [1, 3] [1, 4] [1, 5] [1, 6] [1, 7] [1, 8]
[2, 1] [2, 2] [2, 3] [2, 4] [2, 5] [2, 6] [2, 7] [2, 8]
[3, 1] [3, 2] [3, 3] [3, 4] [3, 5] [3, 6] [3, 7] [3, 8]
[4, 1] [4, 2] [4, 3] [4, 4] [4, 5] [4, 6] [4, 7] [4, 8]
[5, 1] [5, 2] [5, 3] [5, 4] [5, 5] [5, 6] [5, 7] [5, 8]
[6, 1] [6, 2] [6, 3] [6, 4] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 1] [7, 2] [7, 3] [7, 4] [7, 5] [7, 6] [7, 7] [7, 8]
[8, 1] [8, 2] [8, 3] [8, 4] [8, 5] [8, 6] [8, 7] [8, 8]
witness's state
[4, 4]
intensional model
face →
a → { 4, 7 }
b → { 1, 6, 7 }
c → { 1, 4 }
beats →
[a, b] → { 4 }
[a, c] → { 7 }
[b, a] → { 1, 6 }
[b, b] → { }
[c, a] → { 1 }
[c, b] → { 4 }
[c, c] → { }
[a, a] → { }
[b, c] → { 6, 7 }
black →
a → { 3, 5, 6, 8 }
b → { 1, 2, 4, 7 }
c → { 2, 3 }
number →
a → { 1, 2, 3, 5, 6, 8 }
b → { 2, 3, 4, 5, 8 }
c → { 2, 3, 5, 6, 7, 8 }
red →
a → { 1, 2, 4, 7 }
b → { 3, 5, 6, 8 }
c → { 1, 4, 5, 6, 7, 8 }
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formulae
| predn(arg1,...,argn) | atomic |
| (c = c') | equality |
| (A & B) | conjunction |
| (A | B) | disjunction |
| (A > B) | if ... then |
| (A < B) | if |
| (A <> B) | iff |
| EX A | existential |
| ^X A | universal |
| ?A | yes/no |
| ?X1...Xn A | wh- |
notes
- Equality statements have parentheses. pred(arg) statements do not.
- Variables must be in capital letters.
- No free variables.
- The existential binds exactly one variable. The question operator can bind any number of variables.
- White space in formulae is ignored.
- The system gives strongly exhaustive answers. This is not hard-wired into Groenendijk's logic.
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