Introduction to the Situation Calculus

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Kristian Palmer
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1 Intoduction to the Sitution Clculu Muice Pgnucco School of Compute Sc. & Eng. Univeit of New South Wle NSW 2052, AUSTRALIA Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 2 Reoning About Action One method to eon bout ction i to impl chnge the gent knowledge be Ee ome entence() tht hould no longe be tue nd dd entence tht will now be tue (i.e., fte pefoming ction) Howeve, we cn onl nwe quetion bout the cuent tte It will not be poible to eon bout pt o futue tte On the othe hnd, if ll we wnt to i eon bout which ction to pefom, thi m be vible ppoch NB: Mn emple fom: R. Bchmn nd H. J. Leveque, Knowledge Repeenttion, niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 1 Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 3 Oveview Modelling Domin nd Action Sitution Clculu Stte/Sitution Domin Contint Action The Fme Poblem Solving the Fme Poblem Apect we need to conide: The tte of the wold Action tht chnge tte of the wold nd wht chnge the effect Contint on legl cenio (won t del much with thee in thi lectue) Cn ou think of nthing ele? Summ

2 niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 4 Sitution Clculu Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 6 Action The itution clculu i w of decibing chnge in fit-ode logic In imple tem it m be viewed dilect of FOL Tem ction itution Fluentpedicte o function whoe vlue m v Action e nmed put put object on top of object move z move block fom to z cle cle niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 5 Stte of the Wold Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 7 Sitution Method 1: on C on A on B cle B cle C A S 1 Tble Tble S 1 S 1 Note: we eif tte (i.e., mke them entitie in ou fomlition) Anothe common w uing the itution clculu i follow Method 2: hold on C hold on A hold on B hold cle hold cle A B C Tble Tble Sitution nphot of the wold t pticul point in time Altente view wold hitoie /init initil itution (no ction hve been pefomed) itution eulting fom pefoming ction in itution Fo emple, put A put B Sitution eulting fom putting block B on block C in the initil itution nd then plcing block A on block B B C

3 niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 8 Fluent Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 10 Domin Contint Pedicte nd function whoe vlue m v fom itution to itution Fo emple, Pecondition Boken Specil pedicte Po in tte Fo emple, Po pickup Hev NetTo Boken dop denote tht ction m be pefomed z Holding z Alo known tte contint Tue t ll (legl) tte even though the involve tte-dependent eltion etc. i on the tble iff it i not on top of nothe block on Tble on Tble i cle iff thee i no block on top of it cle on If i block nd thee i nothe block on it, then i not cle on Tble cle niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 9 Effect Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 11 The Fme Poblem Action cn hve poitive effect Fgile Boken dop nd negtive effect Boken epi Action deciption e not complete: The decibe wht chnge BUT not pecif wht t the me! The (fmou) Fme Poblem: The poblem of chcteiing thoe pect of the tte deciption tht e not chnged b n ction One olution Fme Aiom Moving n object e not chnge it colou Colou c Colou c put Fgile thing not bek Boken Fgile Boken dop Since ction often leve mot fluent unchnged, mn fme iom m be equied

4 n, niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 12 Rmifiction Poblem Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 14 Pojection Wht e the mifiction (diect nd indiect effect) of pefoming n ction cle b move c b Recent ppoche hve invetigted the ue of eplicit notion of culit in n ttempt to olve thi poblem efficientl Qulifiction Poblem Detemining wht i tue in the itution eulting fom the pefoming of equence of ction 1 n Suppoe we gthe ll the iom bove in entence F. To detemine whethe fomul φ i tue fte pefoming the equence of ction 1 we need to detemine Γ φ n n 1 1 Wht qulifiction (pecondition) we equie in pecifing ction nd thei effect Ting to pecif ectl unde which condition n ction h pticul effect i ve difficult (in pinciple, the lit of pecondition cn be vt) niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 13 Wht count olution to the fme poblem? Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 15 Leglit Once we hve decibed the ction of tem, we would like temtic method fo utomticll geneting fme iom Pefebl, the epeenttion hould be concie Reon: Requie fme iom fo eoning The e not entiled b othe iom Reduce poibilit of eo in detemining fme iom Cn eil updte fme iom if dditionl effect e pecified cn be pefomed Aitution i legl iff: Legl S 0 ) it i the initil itution Legl Legl Po it eult fom pefoming the ction in legl itution whee it pecondition i tified Adding thee iom to Γ, we cn detemine whethe equence of ction cn be pefomed b howing tht the led to legl itution Γ Legl n n 1 1 n Howeve, we n t know whethe the equence of ction 1

5 niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 16 Noml fom fo effect iom Given poitive effect iom fo fluent Boken: Fgile Boken dop NetTo b Boken eplode b Rewite them: dop Fgile b eplode b NetTob Boken Negtive effect iom: Boken epi Rewite : epi Boken 1 Thee fomule o of the fom: P F 1 F 1 N F n n F n 1 n Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 18 Succeo Stte Aiom Additionl iom: Integit of effect iom P F Unique nme fo ction A 1 A 1 A 1 n n B 1 NF m n 1 1 fo ditinct A nd B n n Togethe, iom on lt thee lide equivlent to ucceo tte iom fo F: F F PF Boken dop Fgile b eplode b NetTob Boken epi NF niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 17 Eplntion Cloue Univeit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 19 Wht we cnnot Aumption: The peviou two fomule chcteie the onl w in which fluent m chnge Eplntion Cloue Aiom F F F F PF NF Diguied fme iom: F PF F F NF F Eplicit time Eogenou ction Concuent ction Continuou ction Comple ction...

6 niveit of São Pulo, Thud 12 Febu, 2004 Into to Sitution Clculu 20 Summ Reoning bout ction i ve inteeting e of tificil intelligence nd often mke ue of nonmonotonic eoning technique We hve een tht numbe of chllenging poblem ie tht we mut del with in ode to eon effectivel One of the poblem, howeve, i the poible polifetion of iom The ech continue fo concie olution to the fme poblem (nd ocited poblem) Othe fomlim include the event clculu, A lnguge, fetue nd fluent, fluent clculu Cuent eech: cul ppoche, cognitive obotic, plnning (n e in it own ight)

Summary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:

Summary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied: Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos