CSE630	
Homework 4
Jason Kim

1. (9.4)
a. {x/A,y/B,z/B}
b. fail
c. {Father(x)/Father(y),y/John} 
d. {x/y,y/x}


2. (9.18)
a. V Horse(x) /\ Animal(x) /\ HeadOf(h,x) --> Horse(h) /\ Animal(h)
b. E(there exists) Horse(x) /\ Animal (x) /\ HeadOf(h,x) st, ~Horse(h)\/ ~Animal(h)
c. The negation creates an Inverse Error, thus the statement is true.

3. (11.4)
a. Init: (At(Monkey ,A , Low) /\ At(Bananas,B,High) /\ At(Box,C,Low))
b. 
Action(Go(Monkey,A))
PRECOND: ~At(Monkey,A) 
Effect: ~At(Monkey,B)/\~At(Monkey,C)
Action(Go(Monkey,B))
PRECOND: ~At(Monkey,B) 
Effect: ~At(Monkey,A)/\~At(Monkey,C)
Action(Go(Monkey,C))
PRECOND: ~At(Monkey,C) 
Effect: ~At(Monkey,A)/\~At(Monkey,B)

Action(Push(Box,A))
PRECOND:At(Monkey,Box)
Effect: ~At(Box,B) /\ ~At(Box,C)
Action(Push(Box,B)
PRECOND:At(Monkey,Box)
Effect: ~At(Box,A) /\ ~At(Box,C)
Action(Push(Box,C)
PRECOND:At(Monkey,Box)
Effect: ~At(Box,A) /\ ~At(Box,B)

Action(ClimbUp(Monkey,Box))
PRECOND: At(Monkey,Box)
Effect: At(Monkey,Box,High)

Action(ClimbDown(Monkey,Box))
PRECOND: At(Monkey,Box)
Effect: At(Monkey,Box,Low)

Action(Grasp(Monkey,Object))
PRECOND: At(Monkey,Object)
Effect: At(Object,Monkey)

Action(UnGrasp(Monkey,Object))
PRECOND: Object(At(Monkey))
Effect: ~At(Monkey,Object)

c.
At(Bananas,Monkey,Low) /\ At(Box,C,Low)

No.

d. 
Action(Push(Box,to,Weight)
PRECOND: Weight is not Heavy

4. (11.7)
a. Yes
b. No
c. Yes pretty much the same as forward state search, because you're making the next state a precond for a new action.
d. yes



5. (11.11)
Init: At(BlockB(Left,Low)) /\ At(BlockA(Middle,Low)) /\ At(BlockC(Middle,Medium)) 
Goal: At(BlockA(Right,High)) /\ At(BlockB(Right,Medium)) /\ At(BlockC(Right,Low))
Action: Move(BlockA,Position,Height)
PRECOND: ~At(BlockB,Position,Height) V ~At(BlockC,Position,Height)
Effect: At(BlockA,Position,Height)
Action: Move(BlockB,Position,Height)
PRECOND: ~At(BlockA,Position,Height) V ~At(BlockC,Position,Height)
Effect: At(BlockB,Position,Height)
Action: Move(BlockC,Position,Height)
PRECOND: ~At(BlockA,Position,Height) V ~At(BlockB,Position,Height)
Effect: At(BlockC,Position,Height)
noninterleaved planner cannot solve this problem because it can't move one block back

6. (11.13)
action: go(x,y)
Precond: At(Shakey,x)
Effect: At(Shakey,y)
action: Push(b,x,y)
Precond: At(Shakey,x)
Effect: At(Box,y)
action: Climb(b)
Precond: At(Shakey,Box)
Effect: Floor(On) V Floor(Off)
action: Turn(s)
Precond: At(Shakey,Switch)
Effect: Light(On) or Light(off)

Plan: 
Go(Room3,Box2)
Push(Box2,Room1,Room2)