CS Artificial Intelligence 2007 Semester 2. CompSci 366. Classical Planning: Regression Planning. Part II: Lecture 5 1 of 20

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1 CS Artifiil Intelligene 2007 Semester 2 CompSi 366 Clssil Plnning: Regression Plnning Prt II: Leture 5 1 of 20

2 CS Artifiil Intelligene 2007 Semester 2 Outline Review of Progression Plnning(PP) Regression Plnning Overview Regression Plnning in Prolog Prt II: Leture 5 2 of 20

3 CS Artifiil Intelligene 2007 Semester 2 Review of Progression Plnning(PP) PP: Cheks whether the new urrent stte stisfies the gol (if it is then done!). Finds ll the ops pplile in urrent stte. Selets one of those ops nd progresses the stte thru tht op to get the new urrent stte. Reurse with the new stte nd the old gol. Prt II: Leture 5 3 of 20

4 CS Artifiil Intelligene 2007 Semester 2 RP: Preview of Regression Plnning (RP) Cheks whether the urrent gol set is stisfied y the initil sitution (if it is then done!). Find ops tht n stisfy some of the gols. Selets one of the ops nd regresses the gol set thru tht op to get the new urrent gol set. Reurse with the new gol set nd the old initil sitution. Prt II: Leture 5 4 of 20

5 CS Artifiil Intelligene 2007 Semester 2 Wht is regression? Wht does it men to regress logi epression, L, thru n tion desription, A? It mens omputing nother logi epression, P, suh tht if P is true in stte S then if A is pplied to S then L must e true in tht new stte. Prt II: Leture 5 5 of 20

6 CS Artifiil Intelligene 2007 Semester 2 Regression Emple Emple Prolem Initil Sitution Gol Prt II: Leture 5 6 of 20

7 CS Artifiil Intelligene 2007 Semester 2 Regression Emple ont d Domin Opertors: MBB(X,,Z): X Z X Z Note: = ler MBT(X,): X X MTB(X,): X X Prt II: Leture 5 7 of 20

8 CS Artifiil Intelligene 2007 Semester 2 Find Some Ops tht Stisfy Some Gols X Z Gol X MBB(X,,Z) MTB(X,) MBB(,,) MBB(,,) MTB(,) MTB(,) Prt II: Leture 5 8 of 20

9 CS Artifiil Intelligene 2007 Semester 2 Selet Op & Regress Gol Regressed Gol Set MTB(,) Gol Prt II: Leture 5 9 of 20

10 CS Artifiil Intelligene 2007 Semester 2 Does Initil Stte Stisfy Regressed Gol Set? Initil Sitution Regressed Gol Set Prt II: Leture 5 10 of 20

11 Find Some Ops tht Stisfy Some Gols Regressed Gol Set CS Artifiil Intelligene 2007 Semester 2 X Z MBB(X,,Z) MBB(,,) X MTB(X,) MTB(,) MBT(X,) X MBT(,) Prt II: Leture 5 11 of 20

12 CS Artifiil Intelligene 2007 Semester 2 Selet Op & Regress Gol Regressed Gol Set MTB(,) Regressed Gol Set MTB(,) Gol Prt II: Leture 5 12 of 20

13 CS Artifiil Intelligene 2007 Semester 2 Initil Sitution Stisfies Regressed Gol Set Initil Sitution Finl Regressed Gol Set MBT(,) Regressed Gol Set MTB(,) Regressed Gol Set MTB(,) Gol Prt II: Leture 5 13 of 20

14 CS Artifiil Intelligene 2007 Semester 2 Progrmming Regression Plnning in Prolog We now hve proedurl understnding of regression plnning. How do we go out implementing RP in Prolog? Prt II: Leture 5 14 of 20

15 CS Artifiil Intelligene 2007 Semester 2 Progrmming Regression Plnning in Prolog ont d Think delrtively: i.e., define wht prolem eing solved y pln mens. Wnt definition tht uses regression of gol sets rther thn progression of sttes. Wnt simple definition - use divide & onquer pproh. Speifilly, indution/reursion! Prt II: Leture 5 15 of 20

16 CS Artifiil Intelligene 2007 Semester 2 Progrmming Regression Plnning in Prolog ont d Bse se: wht would e the simplest se where pln solved prolem? The solutely simplest se would e where the initil sitution lredy stisfied the gol nd we hd the empty pln. We ould sy this in Prolog y: solvedby(prolem(init, Gols), [ ]) :- stisfiedby(gols, Init). Prt II: Leture 5 16 of 20

17 CS Artifiil Intelligene 2007 Semester 2 Progrmming Regression Plnning in Prolog ont d Indutive se: sine the simplest se used the empty pln, perhps we should do the indution on the length of the pln. We ould do this in Prolog y: solvedby(prolem(init, Gols), Pln) :- ppend(rest, [Step], Pln), hievessome(step, Gols), regressesthruto(gols, Step, NewGols), solvedby(prolem(init, NewGols), Rest). Prt II: Leture 5 17 of 20

18 CS Artifiil Intelligene 2007 Semester 2 Progrmming Regression Plnning in Prolog ont d hievessome(step, Gols) s definition should e rther ovious. regressesthruto(gols, Step, NewGols) s definition is proly less so. The gol of regression is to ompute the wekest preondition, NewGols, for when it is gurnteed tht Gols will e hieved fter eeuting Step. However, this is too epensive nd so we ompute suffiient ondition for gurnteeing tht Gols will e hieved fter eeuting Step. Prt II: Leture 5 18 of 20

19 CS Artifiil Intelligene 2007 Semester 2 Progrmming Regression Plnning in Prolog ont d Regression should fil if resulting gol desription is inonsistent (ssume initil sitution onsistent then no vlid pln should e le to hieve n inonsistent sitution). Inonsistenies our if there is gol, G, nd not(g) is either n effet or preondition of the step. Why??? Prt II: Leture 5 19 of 20

20 CS Artifiil Intelligene 2007 Semester 2 Progrmming Regression Plnning in Prolog ont d Regressed gols = Gols - Effets(Step) + Preonditions(Step), where - is set differene. Prt II: Leture 5 20 of 20