Extensions: Concurrency, Interrupts, Sensing

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1 IIc. Procedural action programs 1 Extensions: Concurrency, Interrupts, Sensing Exogenous actions Concurrency and interrupts in GOLOG A transitional semantics for GOLOG Sensing actions

2 Mailbot in a Constantly Changing World IIc. Procedural action programs 2

3 IIc. Procedural action programs 3 Example: Exogenous Actions Symbol AddRequest CancelRequest Idle Type PACKAGE ROOM ROOM # ACTION PACKAGE # ACTION # ACTION proc Interaction p. r 1. r 2. AddRequest(p, r 1 ) p. CancelRequest(p) endproc;

4 IIc. Procedural action programs 4 Precondition Axioms Poss(AddRequest(p, r 1 ), s, t) t = Do(AddRequest(p, r 1 ), s) ( r' 1, r' 2 ) Holds(Request(p, r' 1, r' 2 ), s) ( b, r') Holds(Carries(b, p, r'), s) r 1 r 2 Poss(CancelRequest(p), s, t) t = Do(CancelRequest(p), s) ( r 1 ) Holds(Request(p, r 1 ), s) Poss(Idle, s, t) t = Do(Idle, s)

5 IIc. Procedural action programs 5 Effect Axioms Poss(AddRequest(p, r 1 ), s, t) ( f)[f = Request(p, r 1 ) Holds(f, s) Holds(f, t)] ( f)[f Request(p, r 1 ) Holds(f, s) Holds(f, t)] Poss(CancelRequest(p), s, t) ( r 1 )(Holds(Request(p, r 1 ), s) ( f)[holds(f, s) f Request(p, r 1 ) Holds(f, t)] ( f)[f = Request(p, r 1 ) Holds(f, s) Holds(f, t)]) Poss(Idle s, t) ( f)[holds(f, s) Holds(f, t)] ( f)[ Holds(f, s) Holds(f, t)]

6 IIc. Procedural action programs 6 Concurrency and Interrupts in GOLOG Command Meaning concurrent execution concurrent execution with priority concurrent iteration interrupt

7 IIc. Procedural action programs 7 Modified GOLOG Program for Mail Delivery proc Deliver... endproc;... proc Interaction... endproc; Interaction* (while ( p, r 1 ) Request(p, r 1 ) do Idle endwhile; Control)

8 IIc. Procedural action programs 8 A Transitional Semantics for GOLOG The transitional semantics for GOLOG is given by formulas meaning that Trans(, s, ', s') Final(, s) executing one step of in s may result in s', and ' is what remains of after this step; can be considered completed in s.

9 IIc. Procedural action programs 9 Transitional Semantics for GOLOG Constructs Trans(nil, s, ', s') False Trans(a, s, ', s') Poss(a, s, s') ' = nil s' = Do(a, s) Trans(?, s, ', s') [s] ' = nil s' = s Trans( 1 ; 2, s, ', s') ( 1 ') (Trans( 1, s, 1 ', s') ' = ( 1 '; 2 )) Final( 1, s) Trans( 2, s, ', s') Trans( 1 2, s, ', s') Trans( 1, s, ', s') Trans( 2, s, ', s') Trans( x. (x), s, ', s') ( x) Trans( (x), s, ', s') Trans( *, s, ', s') ( '') (Trans(, s, '', s') ' = ( ''; *))

10 IIc. Procedural action programs 10 Transitional Semantics for GOLOG Macros Trans(if then 1 else 2 endif, s, ', s') [ s] Trans( 1, s, ', s') [ s] Trans( 2, s, ', s') Trans(while do endwhile, s, ', s') ( '') ( [ s] Trans(, s, '', s') ' = ( ''; while do endwhile))

11 IIc. Procedural action programs 11 Transitional Semantics for Concurrency Trans( 1 2, s, ', s') ( ) (Trans( 1, s,, s') ' = ( 2 )) ( ) (Trans( 2, s,, s') ' = ( 1 )) Trans( 1 2, s, ', s') ( ) (Trans( 1, s,, s') ' = ( 2 )) ( ) ( Trans( 2, s,, s') ' = ( 1 )) ( '', s'') Trans( 1, s, '', s'') Trans(, s, ', s') ( '') ( Trans(, s, '', s') ' = ( '' ))

12 IIc. Procedural action programs 12 Transitional Semantics for Interrupts while True do if then else False? endif endwhile To terminate the interrupt after one execution, use an arbitrary fluent that is true initially and set to false by.

13 IIc. Procedural action programs 13 Transitional Semantics: Final Configurations (1) Final(nil, s) True Final(a, s) False Final(?, s) False Final( 1 ; 2, s) Final( 1, s) Final( 2, s) Final( 1 2, s) Final( 1, s) Final( 2, s) Final( x. (x), s) ( x) Final( (x), s) Final( *, s) True

14 IIc. Procedural action programs 14 Transitional Semantics: Final Configurations (2) Final( 1 2, s) Final( 1, s) Final( 2, s) Final( 1 2, s) Final( 1, s) Final( 2, s) Final(, s) True Final(if then 1 else 2 endif, s) [ s] Final( 1, s) [ s] Final( 2, s) Final(while do endwhile, s) [ s] Final(, s)

15 IIc. Procedural action programs 15 The Overall Transitional Semantics DO(, s, s') :<=> ( ')(Trans*(, s, ', s') Final( ', s')) where Trans*(, s, ', s') :<=> ( P)([( 1, s 1 )P( 1, s 1, 1, s 1 ) ( 1,..., s 3 )(P( 1, s 1, 2, s 2 ) Trans( 2, s 2, 3, s 3 ) P( 1, s 1, 3, s 3 ))] P(, s, ', s'))

16 IIc. Procedural action programs 16 Example Suppose Holds(f, S 0 ) f = At(1) f = Empty(B 1 ) f = Empty(B 2 ) f = Empty(B 3 ) Then DO( mail, S 0, S) is true for, e.g., S = Do(Drop(B 1 ), Do(Go(Up), Do(Pick(P 2, B 1 ), Do(Go(Down), Do(CancelRequest(P 1 ), Do(AddRequest(P 2, 1, 2), Do(Go(Up), Do(AddRequest(P 1, 2, 1), Do(Idle, S 0 )))))))))

17 Programs with Sensing IIc. Procedural action programs 17

18 Example: Having a Robot Negotiate a Maze IIc. Procedural action programs 18

19 IIc. Procedural action programs 19 A High-Level Control Program for the Robot proc TakeNextStep TurnRight; SenseBlocked; while Blocked do TurnLeft; SenseBlocked endwhile; GoForward endproc; while At(Exit) do TakeNextStep endwhile

20 IIc. Procedural action programs 20 Recap: Online- vs. Offline-Execution Online-execution Agent commits immediately to every non-deterministic choice Program may not be completed althoug s exists s.th. DO(, S 0, s) Example: [Go(Up); ( b) Empty(b)?] Go(Down) Offline-execution Agent searches for s s.th. DO(, S 0, s) before executing any action

21 IIc. Procedural action programs 21 Offline vs. Online Execution in the Presence of Sensing Without sufficient knowledge, GOLOG programs with sensing cannot be executed offline. Without sufficient knowledge of fluent Blocked, there is no provably successful run of maze. Online execution provides sufficient information about initially unknown fluents when needed. But the advantages of offline execution (to enable search) are lost.

22 IIc. Procedural action programs 22 The Search Operator Only subprograms in the scope of the search operator are executed offline. Example: {(PlanA PlanB); SubGoal?}; (ActC ActD); Test? Action PlanA or action PlanB is chosen, depending on which achieves goal SubGoal. Action ActC or action ActD is chosen, and the agent commits to this choice prior to testing Test.

23 IIc. Procedural action programs 23 Axiomatizing Sensing Actions The special predicate SF(a, s) is true if what is sensed by action a holds in situation s. SF(SenseBlocked, s) Holds(Blocked, s) SF(TurnLeft, s) True SF(TurnRight, s) True SF(GoForward, s) True

24 IIc. Procedural action programs 24 Histories A history h is a sequence of (action, sensing result)-pairs (a 1, v 1 ), (a 2, v 2 ),..., (a n, v n ) (n 0) End[h, s] :<=> Do(a n,..., Do(a 2, Do(a 1, s))...) Sensed[h, s] :<=> { } SF(a 1, Do(a 1, s))... { }SF(a n, End[h, s]) where is placed wrt. a i iff v i = false

25 IIc. Procedural action programs 25 Example The history h = (TurnRight, true), (SenseBlocked, false), (GoForward, true) determines this formula as Sensed[h, S 0 ]: True Holds(Blocked, Do(SenseBlocked, Do(TurnRight, S 0 ))) True...

26 IIc. Procedural action programs 26 Transitional Semantics in the Presence of Sensing Given a history h and domain axiomatization Ax A transition is possible if Ax Sensed[h, s] Trans(, End[h, s], ', s') A program may terminate if Ax Sensed[h, s] Final(, End[h, s])

27 IIc. Procedural action programs 27 Semantics of Search Operator Trans(, s, ', s') ( '') (Trans(, s, '', s') ' = '' Final(, s) Final(, s) ( e, s e )(Trans*( '', s', e, s e ) Final( e, s e )))

Continuing the KRR Journey

1 Weeks 1 3 Week 4 Week 5 Week 6 Continuing the KRR Journey Propositional and first-order logic (FOL) Expressiveness and Decidability: Propositional logic is decidable, FOL is not. Classical planning problems: