Situation Calculus. Dr. Neil T. Dantam. Spring CSCI-498/598 RPM, Colorado School of Mines
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1 Situation alculus Dr. Neil T. Dantam SI-498/598 RPM, olorado School of Mines Spring 2018 Dantam (Mines SI, RPM) Situation alculus Spring / 24
2 Logic and Planning Outline Logic and Planning locksworld Domain Planning Domain Definition Language (PDDL) Operators Facts Planning pproaches Heuristic Search onstraint-ased Planning Dantam (Mines SI, RPM) Situation alculus Spring / 24
3 Logic and Planning Logical alculi Propositional alculus: oolean variables (propositions) Logical Operators (,,, =,, ) Predicate alculus: Extends the propositional calculus with: Objects Predicates Functions Quantifiers Situation alculus: Extends the predicate calculus to model actions that change state: Fluents ctions Dantam (Mines SI, RPM) Situation alculus Spring / 24
4 Logic and Planning Situation alculus Predicate alculus + changing state: Fluents ctions Synonym for state variables of the system Example: closed (suitcase) contains (suitcase, laptop) From Latin fluere meaning to flow. Elements: Label: Name / arguments Precondition: States where the action is valid Effect: Result of the action Example: Label: open (suitcase) Precondition: closed (suitcase) Effect: closed (suitcase) Dantam (Mines SI, RPM) Situation alculus Spring / 24
5 Logic and Planning Illustration State/ction Sequence open (suitcase) insert (suitcase, banana) closed (suitcase) contains (suitcase, laptop) contains (suitcase, banana) remove (suitcase, laptop) close (suitcase) Dantam (Mines SI, RPM) Situation alculus Spring / 24
6 Logic and Planning Illustration utomaton open (suitcase) closed (suitcase) contains (suitcase, laptop) contains (suitcase, banana) closed (suitcase) contains (suitcase, laptop) contains (suitcase, banana) close (suitcase) remove (suitcase, laptop) closed (suitcase) contains (suitcase, laptop) contains (suitcase, banana)... Dantam (Mines SI, RPM) Situation alculus Spring / 24
7 Logic and Planning Exercise: State Space Size Objects: = {suitcase, backpack} = {laptop, banana, book} Predicate: contains : Fluents: Dantam (Mines SI, RPM) Situation alculus Spring / 24
8 Logic and Planning Transition System State Space: Q = f 0 f 1... f m, for each fluent f i ctions: U = {a 0,..., a n } Transitions: δ : Q U Q, where for δ(q 0, a) = q 1, q 0 satisfies the precondition of a q 1 is the effect of a applied to q 0 Start: q 0 Q is the initial state Goal: G Q is the set of goal states Dantam (Mines SI, RPM) Situation alculus Spring / 24
9 locksworld Domain Outline Logic and Planning locksworld Domain Planning Domain Definition Language (PDDL) Operators Facts Planning pproaches Heuristic Search onstraint-ased Planning Dantam (Mines SI, RPM) Situation alculus Spring / 24
10 locksworld Domain Planning Problem Start Goal Dantam (Mines SI, RPM) Situation alculus Spring / 24
11 locksworld Domain First-Order Logic Description onstants:,, Predicates: on (?x,?y) clear (?x) ontable (?x) handempty () Fluents: clear () clear () ontable () ontable () handempty () Dantam (Mines SI, RPM) Situation alculus Spring / 24
12 locksworld Domain Task Language pick-up () put-down () unstack (, ) pick-up () stack (, ) put-down () pick-up () put-down ()... Dantam (Mines SI, RPM) Situation alculus Spring / 24
13 locksworld Domain Example: pick-up (?x) Precondition: ontable (?x) clear (?x) handempty () Effect: ontable (?x) clear (?x) handempty () holding (?x) pick-up () ontable () ontable () on (, ) clear () clear () handempty () ontable () ontable () on (, ) clear () clear () handempty () holding () Dantam (Mines SI, RPM) Situation alculus Spring / 24
14 locksworld Domain Exercise: unstack (?x,?y) Precondition: on (?x,?y) clear (?x) handempty () Effect: on (?x,?y) clear (?x) handempty () holding (?x) clear (?y) unstack (, ) ontable () ontable () on (, ) clear () clear () handempty () Dantam (Mines SI, RPM) Situation alculus Spring / 24
15 Planning Domain Definition Language (PDDL) Outline Logic and Planning locksworld Domain Planning Domain Definition Language (PDDL) Operators Facts Planning pproaches Heuristic Search onstraint-ased Planning Dantam (Mines SI, RPM) Situation alculus Spring / 24
16 Planning Domain Definition Language (PDDL) Operators Example: pick-up (?x) pick-up (?x) PDDL Precondition: ontable (?x) clear (?x) handempty () Effect: ontable (?x) clear (?x) handempty () holding (?x) ( : a c t i o n pick up : parameters (? x ) : p r e c o n d i t i o n ( and ( o n t a b l e? x ) ( c l e a r? x ) ( handempty ) ) : e f f e c t ( and ( not ( o n t a b l e? x ) ) ( not ( c l e a r? x ) ) ( not ( handempty ) ) ( h o l d i n g? x ) ) ) Dantam (Mines SI, RPM) Situation alculus Spring / 24
17 Planning Domain Definition Language (PDDL) Operators Exercise: unstack (?x,?y) unstack (?x,?y) PDDL Precondition: on (?x,?y) clear (?x) handempty () Effect: on (?x,?y) clear (?x) handempty () holding (?x) clear (?y) ( : a c t i o n u n s t a c k : parameters (? x? y ) : p r e c o n d i t i o n ( and ( on? x? y ) ( c l e a r? x ) ( handempty ) ) : e f f e c t ( and ( not ( on? x? y ) ) ( not ( c l e a r? x ) ) ( not ( handempty ) ) ( h o l d i n g? x ) ( c l e a r? y ) ) ) Dantam (Mines SI, RPM) Situation alculus Spring / 24
18 Planning Domain Definition Language (PDDL) Operators Full Operators File Dantam (Mines SI, RPM) Situation alculus Spring / 24
19 Planning Domain Definition Language (PDDL) Facts Example: PDDL Facts Start PDDL Goal ( d e f i n e ( problem sussman anomaly ) ( : domain b l o c k s ) ( : o b j e c t s a b c ) ( : i n i t ( on c a ) ( o n t a b l e a ) ( o n t a b l e b ) ( c l e a r c ) ( c l e a r b ) ( handempty ) ) ( : g o a l ( and ( on b c ) ( on a b ) ) ) ) Dantam (Mines SI, RPM) Situation alculus Spring / 24
20 Planning Domain Definition Language (PDDL) Facts Exercise: PDDL Facts Start PDDL Goal Dantam (Mines SI, RPM) Situation alculus Spring / 24
21 Planning pproaches Outline Logic and Planning locksworld Domain Planning Domain Definition Language (PDDL) Operators Facts Planning pproaches Heuristic Search onstraint-ased Planning Dantam (Mines SI, RPM) Situation alculus Spring / 24
22 Planning pproaches Heuristic Search Heuristic Search pick-up () unstack (, ) stack (, ) put-down () Dantam (Mines SI, RPM) Situation alculus Spring / 24
23 Planning pproaches onstraint-ased Planning onstraint-ased Planning aka STPlan pick-up (, s 0 ) pick-up (, s 0 ) = precondition at step i {}}{ ontable (?x, s 0 ) clear (?x, s 0 ) handempty (s 0 ) ontable (?x, s 1 ) clear (?x, s 1 ) handempty (s 1 ) holding (?x, s 1 ) }{{} effect at step i+1 Dantam (Mines SI, RPM) Situation alculus Spring / 24
24 Planning pproaches onstraint-ased Planning Summary Logic and Planning locksworld Domain Planning Domain Definition Language (PDDL) Operators Facts Planning pproaches Heuristic Search onstraint-ased Planning Dantam (Mines SI, RPM) Situation alculus Spring / 24
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