Gremlins and Goblins - PowerPoint PPT Presentation

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Gremlins and Goblins

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Gremlins and Goblins. Gremlins always tell the truth. Goblins sometimes lie. ... You are in a dungeon with two gremlins and a goblin (but you don't know which is ... – PowerPoint PPT presentation

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Title: Gremlins and Goblins


1
Gremlins and Goblins
  • Gremlins always tell the truth. Goblins sometimes
    lie. Unfortunately, their appearance is
    identical.
  • You are in a dungeon with two gremlins and a
    goblin (but you dont know which is which). There
    is a red door and a blue door. One door leads to
    the exit. The other door leads to a pit of deadly
    venomous snakes.

2
The Query
  • Your objective is to find the exit. Your
    companions give you some advice
  • Gorbnitz (G1) The red door is the way out. I am
    telling the truth!
  • Grovnack (G2) The blue door is the way out.
    Gorbnitz is lying!!
  • Glidnoph (G3) I dont know which door is the way
    out, but Gorbnitz is telling the truth.

3
Solving the Problem
  • Express the problem in first-order logic.
  • Express the negated goal in first-order logic and
    add it to the KB.
  • Translate all of the knowledge into standard form
    (clausal normal form).
  • Apply resolution to derive a contradiction.
  • The answer is in the bindings.

4
Describing the Problem
  • Goblins /gremlins mutually exclusive
  • ?x Gob(x) ? ?Grem(x)
  • ?x Grem(x) ? ?Gob(x)
  • One goblin
  • Gob(G1) ? Gob(G2) ? Gob(G3)
  • Two gremlins
  • (Grem(G1) ? Grem(G2)) ? (Grem(G1) ? Grem(G3)) ?
    (Grem(G1) ? Grem(G3))

5
The Problem II
  • Exactly one door is the exit
  • Exit(Red) ? Exit(Blue)
  • ?(Exit(Red) ? Exit(Blue)
  • The creatures statements
  • Grem(G1) ? Exit(Red) ? Grem(G1)
  • Grem(G2) ? Exit(Blue) ? Grem(G2)
  • Grem(G3) ? Grem(G1)

6
Describing the Negated Goal
  • Goal ?e Exit(e)
  • Negated goal ?e ?Exit(e)

7
Clausal Normal Form
  • ?Gob(x) ? ?Grem(x)
  • ?Grem(y) ? ?Gob(y) redundant
  • Gob(G1) ? Gob(G2) ? Gob(G3)
  • Grem(G1) ? Grem(G2)
  • Grem(G2) ? Grem(G3)
  • Grem(G1) ? Grem(G3)
  • ?Grem(G1) ? Exit(Red)
  • ?Grem(G1) ? Grem(G1) tautology
  • ?Grem(G2) ? Exit(Blue)
  • ?Grem(G2) ? Grem(G2) tautology
  • ?Grem(G3) ? Grem(G1)
  • ?Exit(e) negated goal

8
Think about the proof!
  • Both G1 and G3 say that G1 is telling the truth,
    so this must be true (since they cant both be
    lying)
  • If G1 is telling the truth, then the red door is
    the exit!
  • Now all we have to do is construct the resolution
    proof tree that demonstrates this line of
    reasoning

9
Resolution Proof Tree
?Grem(G3) ? Grem(G1)
Grem(G3) ? Grem(G1)
?Grem(G1) ? Exit(Red)
Grem(G1)
Exit(Red)
?Exit(e)
e/Red
FALSE
10
The Answer
  • The exit is red!
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