1. Artificial Intelligence and Lisp Lecture 9 Reasoning about Actions and Planning, II LiU Course TDDC65 Autumn Semester,

2. Schemas for characterizing actions
State transition schema (in earlier lecture): one prestate, one poststate
Extended state transition schema: allow conditional and nondeterministic actions. Set of prestate/poststate pairs
State transition with immediate causation (STIC): direct effects of actions are followed by indirect effects, but still with sequential execution. Indirect effects are “instantaneous”
Trajectory set schema (TSS): Actions are characterized by a set of trajectories consisting of two or more partial states. Trajectory of length 2 corresponds to the above. This allows for concurrent actions and actions with extended duration.

3. Schemas for characterizing actions
State transition schema (in earlier lecture): one prestate, one poststate
Extended state transition schema: allow conditional and nondeterministic actions. Set of prestate/poststate pairs. This will be considered integrated with STIC (next item).
State transition with immediate causation (STIC): direct effects of actions are followed by indirect effects, but still with sequential execution. Indirect effects are “instantaneous”
Trajectory set schema (TSS): Actions are characterized by a set of trajectories consisting of two or more partial states. Trajectory of length 2 corresponds to the above. This allows for concurrent actions and actions with extended duration.

4. State transition with immediate causation (STIC)
Replace the use of prest and post functions by atrans function.
Example: from {[: agent-has 22]} to
{<{[: agent-has 22]} {[: agent-has 21]}>
<{[: agent-has 22]} {[: agent-has 23]}>
<{[: agent-has 23]} {[: agent-has 22]}>
<{[: agent-has 23]} {[: agent-has 24]}> ... }
Replace function apply by Apply
(Apply play (Apply play {[: agent-has 22]} )) =
{{[: agent-has 20]}{[: agent-has 22]}{[: agent-has 24]}}
Introduce ficticious action called causation
Consider actions to be atomic (no arguments or parameters)

5. Convergence and stable state
Consider .S
(Apply causation .S)
(Apply causation (Apply causation .S))
(Apply causation (Apply causation (Apply causation .S)))
... and so on
If two successive expressions have equal value then we have obtained convergence in a stable state set, written as.
(Apply* causation .S)
This is the only case that is of interest here.
Specify total effects of an action .a as
(Apply* causation (Apply .a .s))

6. Regressive planning with conditional and nondeterministic actions
Point of nondeterminism: (atrans a) contains both
<s, s'> and <s , s”> where s' and s” are not equal
For every combination of a and s that is a point of nondeterminism, select one of the s', s”, etc as the primary one
Find a solution to the planning problem using only the primary outcomes in every such point
Identify all points in the solution that relies on a primary outcome. Make additional planning in order to have plans for the other outcome(s).
If different outcomes have different probability, then choose the most likely one as primary, and consider the other ones in order
Some (esp. unlikely) cases may be postponed to execution time.

7. Progressive planning and conditional plans
Progressive planning: start with initial state; build sequences of actions forward until goal state is reached (simple case)
More general case requires conditional plans, formed as
[soares a1 a2 ... an R]
[if c at af]
Must R = (Apply an (Apply an-1 (Apply ... (Apply a1 start)...)))
Start with [soares start] containing no actions
Add actions to soares expression, obtaining
[soares a1 a2 ... an an+1 (Apply an+1 R)]
Add conditional expression obtaining instead
[soares a1 a2 ... an [if c [soares Rt] [soares Rf]] R]
where Rt and Rf are complementary subsets of R where the condition c is true or false, respectively

8. Example of conditional plan
[soares a1 a2 ... an
[if [= has-money true]
[soares buy-food
{{[: hungry false][: have-money true]}
{[: hungry false][: have-money false]} }]
[soares beg-food
{{[: hungry false][: have-money false]}} ]]
R ]
where R is the set of two states above

9. Progressive planning with immediate causation
Regressive planning: may be possible to generalize the use of primary outcome
Progressive planning: straightforward

10. Middle-out planning using islands
Method uses the following steps:
1. Choose main action(s) and an order on them
2. Identify likely enabling actions for the first main action, and insert them into the plan
3. Find plan from starting state to first main action, directly or via the chosen enabling actions
4. Repeat 2-3 for steps to later main actions, and to goal
Backup: if step 3 fails, then return to an earlier cycle and find another plan.

11. Logic for characterizing actions
Earlier effect rule:
(imp (and [existsroad .fr .to]
[D .s .t [moveto .o .fr .to]]
[H .s (the position of .r) .fr] )
[H .t (the position of .r) .to] )
Easy to use for conditional effects:
(imp (and [D .s .t toggle][H .s light on])
[H .t light off] )
(imp (and [D .s .t toggle][H .s light off])
[H .t light on] )

12. Frame problem and occlusion
In order to avoid frame axioms, use PMON axiom:
(imp (and [H .s .f .v]
[H (succ .s .a) .f .w]
[/= .v .w] )
[X .s (succ .s .a) .f] )
together with axioms that imply X for specific actions and specific features. Example.
(imp [D .s .t toggle]
(and [X .s .t light]
(imp [H .s light on][H .t light off])
(imp [H .s light off][H .t light on]) ))

13. Immediate Causation Rules in Logic
Example
(imp [D .s .t [toggle .sw]]
(and [X .s .t (state .sw)]
(imp [H .s (state .sw) on][H .t (state .sw) off])
(imp [H .s (state .sw) off][H .t (state .sw) on]) ))
(imp (and [H .s (state .sw) on][controls .sw .lmp])
[H .s (light .lmp) on])
(imp (and [H .s (state .sw) off][controls .sw .lmp])
[H .s (light .lmp) off])
[connected myswitch mylamp]

14. Occlusion in Causation Rules
(imp (and [controls .sw .lmp][X .s .t (state .sw)])
[X .s .t (light .lmp)] )
or - consider (light .lmp) as always occluded, technically speaking

15. Causation Sequences A:T, B:T -> A:F, B:F A:F, B:F -> A:T, B:F
A:T, B:F -> A:F, B:T
A:F, B:T -> A:F, B:T
This is an example of a back-and-forth sequence
The simple translation to causation axiom in logic does not work for such causation structures.

16. Endstate Description of Causation
Basic idea: Characterize the stable states using stable-state axioms; combine them with indirect effect axioms that specify some of the indirect effects.
Combine this with a principle of finding the “closest” stable state from the state capturing the stated indirect effects
Often define “closest” as “minimal additional change” (called “minimization of change”)