Conformant.Planning.via.Symbolic.Model.Checking.and.Heuristi

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Knowledge subgoals. For every knowledge formula φx considered by KACMBP, C OMPUTE KS S computes a belief state representing the associated KS. The computation focuses on the states for which Kφx holds both before and after a given action α is performed; if some of such states may originate (via α) from a state where φx does not hold, then a KS is found: we obtain the KS by collecting all the states for which Kφx holds both before and after α is performed. More in detail, for every knowledge formula φx , KACMBP considers singularly each disjoint K(x = v), denoted with φ(x,v) , in the selected knowledge formulae, building an associated subgoal for each of them, and finally making the union the results.

Basically HSCP performs a backward search in belief space based on the symbolic machinery presented in this paper, which provides an efficient way to expand and store belief states. The main difference from the present work concerns the way in which the search is guided. HSCP is driven by a simple selection criterion, based on the cardinality of the belief state. This turns out to be ineffective in many cases, since reachability information and knowledge acquisition information are both disregarded.

Xn : Bs. The “knowledge bound”, used to prevent useless knowledge-level searches, is also represented as a vector whose components refer to the considered knowledge formulae. This vector is initialized by S ELECT TARGET K NOWLEDGE , and indicates the maximal knowledge achievable during the search for each φx . Its initial value indicates that perfect knowledge might be reached over each φx ; the values for each active component are updated during the search, when a knowledge-level search attempt fails, by S ET TARGET K NOWL EDGE L IMIT R EACHED .

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