PlanBench: An Extensible Benchmark for Evaluating Large Language Models on Planning and Reasoning about Change — part 4/5

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A Appendix
A.1 Domain description included in the prompts
A.1.1 Domain included in the prompt
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
I am playing with a set of blocks where I need to arrange the blocks
into stacks . Here are the actions I can do
Pick up a block
Unstack a block from on top of another block
Put down a block
Stack a block on top of another block
I have the f oll ow in g r e s t r i c t i o n s on my actions :
I can only pick up or unstack one block at a time .
I can only pick up or unstack a block if my hand is empty .
I can only pick up a block if the block is on the table and the block
is clear . A block is clear if the block has no other blocks on top
of it and if the block is not picked up .
I can only unstack a block from on top of another block if the block I
am u n s t a c k i n g was really on top of the other block .
I can only unstack a block from on top of another block if the block I
am u n s t a c k i n g is clear .
Once I pick up or unstack a block , I am holding the block .
I can only put down a block that I am holding .
I can only stack a block on top of another block if I am holding the
block being stacked .
I can only stack a block on top of another block if the block onto
which I am stacking the block is clear .
Once I put down or stack a block , my hand becomes empty .
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Listing 1: Blocksworld Domain Description
A.1.2 Domain included in the prompt (for Optimal planning)
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
I am playing with a set of blocks where I need to arrange the blocks
into stacks . Here are the actions I can do :
Pick up a block . It takes 1 minute to pick up a block .
Unstack a block from on top of another block . It takes 1 minute to
unstack a block from on top of another block .
Put down a block . It takes 1 minute to put down a block .
12

Stack a block on top of another block . It takes 1 minute to stack a
block on top of another block .
I have the f oll ow in g r e s t r i c t i o n s on my actions :
I can only pick up or unstack one block at a time .
I can only pick up or unstack a block if my hand is empty .
I can only pick up a block if the block is on the table and the block
is clear . A block is clear if the block has no other blocks on top
of it and if the block is not picked up .
I can only unstack a block from on top of another block if the block I
am u n s t a c k i n g was really on top of the other block .
I can only unstack a block from on top of another block if the block I
am u n s t a c k i n g is clear .
Once I pick up or unstack a block , I am holding the block .
I can only put down a block that I am holding .
I can only stack a block on top of another block if I am holding the
block being stacked .
I can only stack a block on top of another block if the block onto
which I am stacking the block is clear .
Once I put down or stack a block , my hand becomes empty .
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Listing 2: Blocksworld Domain Description
A.2 Example prompts and completion by GPT-3
Below we present the first instance of our 500 instances for each of the tasks and the corresponding
completion by GPT-3 as an example.
A.2.1 Plan generation
[ ST AT EM EN T ]
As initial c o n d i t i o n s I have that , the red block is clear , the blue
block is clear , the yellow block is clear , the hand is empty , the
blue block is on top of the orange block , the red block is on the
table , the orange block is on the table and the yellow block is on
the table .
My goal is to have that the orange block is on top of the blue block .
My plan is as follows :
[ PLAN ]
unstack the blue block from on top of the orange block
put down the blue block
pick up the orange block
stack the orange block on top of the blue block
[ PLAN END ]
[ ST AT EM EN T ]
As initial c o n d i t i o n s I have that , the red block is clear , the yellow
block is clear , the hand is empty , the red block is on top of the
blue block , the yellow block is on top of the orange block , the
blue block is on the table and the orange block is on the table .
My goal is to have that the orange block is on top of the red block .
My plan is as follows :
[ PLAN ]
- - - - - - - - - GPT3 response - - - - - - - - -
unstack the yellow block from on top of the orange block
put down the yellow block
pick up the orange block
stack the orange block on top of the red block
[ PLAN END ]
- - - - - - - - - E xt ra ct ed plan - - - - - - - - -
13

( unstack yellow orange )
( put - down yellow )
( pick - up orange )
( stack orange red )
- - - - - - - - Ground truth plan - - - - - - - - -
( unstack yellow orange )
( put - down yellow )
( pick - up orange )
( stack orange red )
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = SUCCESS = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Listing 3: Plan Generation
A.2.2 Optimal Planning
[ ST AT EM EN T ]
As initial c o n d i t i o n s I have that , the red block is clear , the blue
block is clear , the yellow block is clear , the hand is empty , the
blue block is on top of the orange block , the red block is on the
table , the orange block is on the table and the yellow block is on
the table ..
My goal is to have that the orange block is on top of the blue block .
I want to minimize the time taken to achieve my goal .
My plan is as follows :
[ PLAN ]
unstack the blue block from on top of the orange block
put down the blue block
pick up the orange block
stack the orange block on top of the blue block
[ PLAN END ]
The total time to execute the plan is 4 minutes .
[ ST AT EM EN T ]
As initial c o n d i t i o n s I have that , the red block is clear , the yellow
block is clear , the hand is empty , the red block is on top of the
blue block , the yellow block is on top of the orange block , the
blue block is on the table and the orange block is on the table ..
My goal is to have that the orange block is on top of the red block . I
want to minimize the time taken to achieve my goal .
My plan is as follows :
[ PLAN ]
- - - - - - - - - GPT3 response - - - - - - - - -
unstack the yellow block from on top of the orange block
put down the yellow block
pick up the orange block
stack the orange block on top of the red block
[ PLAN END ]
The total time to execute the plan is 4 minutes .
- - - - - - - - - E xt ra ct ed plan - - - - - - - - -
( unstack yellow orange )
( put - down yellow )
( pick - up orange )
( stack orange red )
- - - - - - - - Ground truth plan - - - - - - - - -
( unstack yellow orange )
( put - down yellow )
( pick - up orange )
( stack orange red )
- - - - - - - - - - - - - - - - Optimal Plan - - - - - - - - - - - - - - - -
14

- - - - - - - - - Correct cost output by LLM - - - - - - - - -
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = SUCCESS = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Listing 4: Optimal planning
A.2.3 Replanning
[ ST AT EM EN T ]
As initial c o n d i t i o n s I have that , the red block is clear , the blue
block is clear , the yellow block is clear , the hand is empty , the
blue block is on top of the orange block , the red block is on the
table , the orange block is on the table and the yellow block is on
the table .
My goal is to have that the orange block is on top of the blue block .
My plan is as follows :
[ PLAN ]
unstack the blue block from on top of the orange block
put down the blue block
pick up the orange block
stack the orange block on top of the blue block
[ PLAN END ]
During execution , an u n e x p e c t e d event has occurred .
After ex ecu ti ng the action " pick up the orange block " at step 3 in the
plan , the fo ll ow ing facts u n e x p e c t e d l y became true :
the orange block is clear ,
the hand is empty ,
the orange block is on top of the red block .
The f ol lo wi ng facts became u n e x p e c t e d l y false :
the red block is clear ,
the hand is cu rr en tly holding orange block .
After re - planning from the new state , the plan is as follows :
[ PLAN ]
unstack the orange block from on top of the red block
stack the orange block on top of the blue block
[ PLAN END ]
[ ST AT EM EN T ]
As initial c o n d i t i o n s I have that , the red block is clear , the yellow
block is clear , the hand is empty , the red block is on top of the
blue block , the yellow block is on top of the orange block , the
blue block is on the table and the orange block is on the table .
My goal is to have that the orange block is on top of the red block .
My plan is as follows :
[ PLAN ]
unstack the yellow block from on top of the orange block
put down the yellow block
pick up the orange block
stack the orange block on top of the red block
[ PLAN END ]
During execution , an u n e x p e c t e d event has occurred .
After ex ecu ti ng the action " pick up the orange block " at step 3 in the
plan , the fo ll ow ing facts u n e x p e c t e d l y became true :
the orange block is clear ,
the hand is empty ,
the orange block is on top of the red block .
The f ol lo wi ng facts became u n e x p e c t e d l y false :
the red block is clear ,
the hand is cu rr en tly holding orange block .
15