Computing LOI

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

number → 
	a → { 1, 2, 3, 5, 6, 8 }
	b → { 2, 3, 4, 5, 8 }
	c → { 2, 3, 5, 6, 7, 8 }
black → 
	a → { 3, 5, 6, 8 }
	b → { 1, 2, 4, 7 }
	c → { 2, 3 }
red → 
	a → { 1, 2, 4, 7 }
	b → { 3, 5, 6, 8 }
	c → { 1, 4, 5, 6, 7, 8 }
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 }

formulae

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.