1. Logic Programs and Classical Planning with LTL Constraints Ravi Palla Advisor:J Benton

2. 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.

3. 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.

4. 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.

5. 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. ”.

6. 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.

7. 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).

8. 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.

9. LP Encoding of the PDDL 3.0 Constraints  Two different translations defined.  Naive but exponential.  Compact but uses new predicates.

10. 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.

11. Questions ?