interrogator's state
[1, 1] [1, 2] [1, 3] [1, 4] [1, 5]
[2, 1] [2, 2] [2, 3] [2, 4] [2, 5]
[3, 1] [3, 2] [3, 3] [3, 4] [3, 5]
[4, 1] [4, 2] [4, 3] [4, 4] [4, 5]
[5, 1] [5, 2] [5, 3] [5, 4] [5, 5]
witness's state
[4, 4]
intensional model
number →
a → { 1, 2, 3, 4, 5 }
b → { 1, 2 }
c → { 1, 2, 3 }
black →
a → { 1, 3 }
b → { 1, 2, 4 }
c → { 2, 3 }
red →
a → { 2, 4, 5 }
b → { 3, 5 }
c → { 1, 4, 5 }
face →
a → { }
b → { 3, 4, 5 }
c → { 4, 5 }
beats →
[a, b] → { }
[a, c] → { }
[b, a] → { 3, 4, 5 }
[b, b] → { }
[c, a] → { 4, 5 }
[c, b] → { }
[c, c] → { }
[a, a] → { }
[b, c] → { 3 }
|
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.
|