Get Representing Plans Under Uncertainty: A Logic of Time, PDF

By Peter Haddawy (eds.)

ISBN-10: 3540576975

ISBN-13: 9783540576976

This monograph integrates AI and decision-theoretic ways to the illustration of making plans difficulties via constructing a first-order good judgment of time, likelihood, and motion for representing and reasoning approximately plans. The semantics of the good judgment accommodates intuitive houses of time, probability, and motion principal to the making plans challenge. The logical language integrates either modal and probabilistic constructs and permits quantification through the years issues, chance values, and area members. The language can symbolize the opportunity that proof carry and occasions take place at a variety of instances and that activities and different occasions have an effect on the long run. An set of rules for the matter of creating development making plans is constructed and the good judgment is used to end up the set of rules correct.

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Extra info for Representing Plans Under Uncertainty: A Logic of Time, Chance, and Action

Example text

4. From r ---+lb infer Ore ---+Dtlb. r --* lb Hypothesis Ot(r --+ lb) NEC Ot(r --+ lb) --+ ( o r e ~ O:lb) I2 O,r ~ O t bl MoPo: 2,3 T h e o r e m 7. Ot(r -+ lb) --+ (<>re -+ <>:lb) 1. 2. 3. 4. o , ( r --, r ~ O,(-~lb --, -,r o,(-,r162 ~ o~-,r o,-1r O,-~lb -~ O,-~r -+ <>re ~ <>tlb O:(r ---, r ~ (<>,r ---, <>tlb) Theorem8. Def of I2 Def of -* and <> Theorem 4:1-3 From r ---+lb infer <>re --+ <>:lb. 1. r ---, lb Hypothesis 2. Q:(r NEC 3. <>:r ---, <>,lb Theorem 7 and MoPo Theorem9. 1. 2. 3. 4. 5.

Present and past possibility is certain. (tl 0 ~ Pt2( 9162 = 1) T h e o r e m 3 7. Present and past chance is certain. (tl__ c~) > 0 ~ Pt~(P,~(r > ~) = 1) M o d a l O p e r a t o r s a n d Q u a n t i f i e r s . The following theorems capture the relationships between the quantifiers and the modal operators. These theorems hold because the domain of individuals does not vary from world to world. Theorem38. VXl'qtr ---* 1. 2. 3. 4. 5. 6. 7. 8. 9. Barcan formula.

3. 4. 5. (tlt,r - - * (tltl r --+ --* <>t2<>t,r --* --* <>t,<>tlr ~ ntl~tlr --+ f'lt,~t,q~ --+ ---, (Ot~<>tlr <>tl r ) <>tl<>txr <>t,r I"lt2~taq~ Ot~<>tlr Theorem 30 Theorem 26 I4 IT1 Theorem g: 1-g 41 Theorem33. (t~<_t2) ~ Present and past chance are inevitable. (~t~P,,(r >_ a ---, Dt~P,x(r _> a) 1. ( t l < t 2 ) ---* <>t~Pt,(r > a ---* ~ t l P t , ( r > cr Theorem 30 2. ~ t x P t , ( r > a ---+ Dt~Pt~(r > ~ IF2 3. (tl_ ce ---+ ot2Pt~(r ) _> cr IT1 4.

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Representing Plans Under Uncertainty: A Logic of Time, Chance, and Action by Peter Haddawy (eds.)


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