Probabilistic Projection in Planning



Automated planners need to do temporal reasoning— that is, to decide what will be true at various times if their plans are executed, in support of planning operations (such as reordering plan steps) that depend on when various facts become true or false during plan execution. The main line of research in this area is to represent a plan as a partially ordered list of events, and to attempt to infer what must be true before or after each event. In many such efforts, it is assumed that the events’ effects are all known and context-independent, so that the fact P is true after event e if and only if there is some event e′ preceding or coinciding with e that has P as an effect, and such that for every event e″ with ¬P as an effect, e″ precedes e′ or follows e (McAllester and Rosenblitt, 1991; Dean and McDermott, 1987; Chapman, 1987; Allen, 1984; van Beek, 1992).


Atomic Formula Recursive Call Plan Execution Execution Trace Exogenous Event 
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  1. 60.
    In (Dean and McDermott, 1987), these were called time tokens.“ The implementation of occasions is not quite faithful to this formal definition, as we see in Section 8.3.Google Scholar
  2. 61.
    In the actual implementation, formulas and rules are expressed in a Lispish notation, which is described in Section 8.3.Google Scholar
  3. 62.
    There are more flexible ways in the actual implementation, described in Section 8.3.Google Scholar
  4. 63.
    An alternative way to state the condition is to take the consequent of a rule, and generate all possible combinations of “signs” for the atomic formulas in it. Every combination except the one given must have probability zero. For the case at hand, the second rule would assign conditional probability zero to B A -’C, -4B A C, and -+B A -.C.Google Scholar
  5. 64.
    Of course, by making additional assumptions, it is possible to assign probabilities in cases like these. One such approach is explored by Thiébaux and Hertzberg (Thiébaux and Hertzberg, 1992). In my experience, it is usually preferable to rewrite rules to avoid inconsistencies.Google Scholar
  6. 65.
    and, in the actual implementation, timeline initializers, described in Section 8.3.Google Scholar
  7. 66.
    An alternative idea would be to keep a “used rule instance” table in addition to the established-queries table.Google Scholar
  8. 67.
    The only reason to use d instead of A in the rule is that in the implementation, it is occasionally useful to set d = O.Google Scholar
  9. 68.
    There are execution traces in which an infinite number of events happen after A becomes true (in fact, there are some in which A changes truth value infinitely often just before t),but the set of all such execution traces is of measure 0, and TL-RETRIEVE will run forever in such cases, never concluding that A is true at t.Google Scholar
  10. 69.
    This negation-as-failure operator was originally named by Sussman et al. in (Sussman et al., 1971).Google Scholar
  11. 70.
    One simplication is that in the actual system, an initializer must also return a “justification” for its answer. The justification system is not mature enough to talk about in this chapter.Google Scholar

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© Springer Science+Business Media Dordrecht 1997

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