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Logic Programs and Classical Planning with LTL Constraints. Ravi Palla Advisor:J Benton. Disjunctive Logic Programs (DLP). Consist of rules of the form A_1;A_2;…;A_k :- B_1,B_2,…,B_m,not B_{m+1},…,not B_n. A_i and B_i are atoms. Why LP encodings ?.
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Logic Programs and Classical Planning with LTL Constraints Ravi Palla Advisor:J Benton
Disjunctive Logic Programs (DLP) • Consist of rules of the form A_1;A_2;…;A_k :- B_1,B_2,…,B_m,not B_{m+1},…,not B_n. A_i and B_i are atoms.
Why LP encodings ? • Smaller Ground Instances compared to SAT encodings. • Answer Sets of DLP without negation are exactly the minimal models of the corresponding SAT encoding. This implies less redundant actions in the plans generated.
Why LP encodings ? • Re-use of SAT encoding principles. • Linear time transformation to a logic program whose answer sets correspond to models – Answer set solvers just ground the program and use SAT solvers to compute answer sets.
LP Encoding of the Domain • The complete initial state holds at level 0 and the end goals hold at the highest level. • Each fact can be transformed to a DLP rule by just re-writing all negative literals ~f as “ :- f. ”.
LP Encoding of the Domain • Actions imply their preconditions and effects. a(T) -> precond(T) & effects(T+1) • Straight-forward translation to DLP rules. • Just Eliminate Conjunction in the consequent and move negative literals to the antecedent.
LP Encoding of the Domain • Conflicting actions are mutually exclusive. ~a_1(T) v ~a_2(T) • Can be turned to :- a_1(T), a_2(T).
LP Encoding of the Domain • Explanatory Frame Axioms f(T) & ~f(T+1) -> V_{a deletes f} a ~f(T) & f(T+1) -> V_{a adds f} a • Can be turned to DLP rules by just moving the negative literals to the consequent.
LP Encoding of the PDDL 3.0 Constraints • Two different translations defined. • Naive but exponential. • Compact but uses new predicates.
Compact Encoding for “always” • always F. • Turn F to DNF – F_1 v F_2 v … v F_k. • Add the following set of rules p(T) :- F_i(T) for all i. :- not p(T). • p is the new predicate introduced.
