%% bwplan_disjunction.lp = %% bw.lp + simple planning module using disjunctive rule %% + example initial situation %% + example goal %% where bw.lp is the AL system description of the blocks world %% domain translated into ASP %% Chapter 9 Section 9.1 %% Last Modified: 3/22/2021 %% %% The basic blocks world consists of a robotic arm that can manipulate %% configurations of same-sized cubic blocks on a table. There are %% limitations to what the robotic arm can do. It can move %% unoccupied blocks, one at a time, onto other unoccupied blocks or %% onto the table. (An unoccupied block is one that does not have another %% block stacked on it.) At any given step, a block can be in at most %% one location; in other words, a block can be directly on top of one %% other block, or on the table. We do not impose a limit on how tall %% our towers can be. Our table is big enough to hold all the blocks, %% even if they are not stacked. We do not take into account spatial %% relationships of towers, just which blocks are on top %% of each other and which blocks are on the table. %% UNCOMMENT if using DLV: %% #maxint=10. block(b0). block(b1). block(b2). block(b3). block(b4). block(b5). block(b6). block(b7). location(X) :- block(X). location(t). %% Fluents: fluent(inertial, on(B,L)) :- block(B), location(L). fluent(defined, above(B,L)) :- block(B), location(L). %% Actions: action(put(B,L)) :- block(B), location(L), B != L. #const n = 8. step(0..n). %% Putting block B on location L at step I %% causes B to be on L at step I+1: %% put(B,L) causes on(B,L) holds(on(B,L),J) :- occurs(put(B,L),I), J = I+1, I < n. %% A block cannot be in two locations at once: %% -on(B,L2) if on(B,L1), L1 != L2 -holds(on(B,L2),I) :- holds(on(B,L1),I), location(L2), L1 != L2. %% Only one block can be set directly on top of another: %% -on(B2,B) if on(B1,B), B1 != B2 -holds(on(B2,B),I) :- holds(on(B1,B),I), block(B), block(B2), B1 != B2. %% B is above L if it is directly on top of it or on top of %% another block that is above L: %% above(B,L) if on (B,L) %% above(B,L) if on(B,B1), above(B1,L) holds(above(B2,B1),I) :- holds(on(B2,B1),I). holds(above(B2,B1),I) :- holds(on(B2,B),I), holds(above(B,B1),I). %% It is impossible to move an occupied block: %% impossible put(B,L) if on (B1,B) -occurs(put(B,L),I) :- location(L), holds(on(B1,B),I). %% It is impossible to move a block onto an occupied block: %% impossible put(B1,B) if on(B2,B). -occurs(put(B1,B),I) :- block(B1), block(B), holds(on(B2,B),I). %% CWA for Defined Fluents -holds(F,I) :- fluent(defined,F), step(I), not holds(F,I). %% General Inertia Axiom holds(F,J) :- fluent(inertial,F), holds(F,I), not -holds(F,J), J = I+1, I < n. -holds(F,J) :- fluent(inertial,F), -holds(F,I), not holds(F,J), J = I+1, I < n. %% CWA for Actions -occurs(A,I) :- action(A), step(I), not occurs(A,I). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Simple Planning Module using Disjunctive Rule: success :- goal(I), I <= n. :- not success. occurs(A,I) | -occurs(A,I) :- action(A), step(I), not goal(I), I < n. %% Do not allow concurrent actions: :- action(A1), action(A2), occurs(A1,I), occurs(A2,I), A1 != A2. %% An action occurs at each step before %% the goal is achieved: something_happened(I) :- occurs(A,I). :- step(I), step(J), step(K), goal(I), not goal(K), K = I-1, J < I, not something_happened(J). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Specific initial situation. %% Change at will: %% holds(on(B,L),I): a block B is on location L at step I. holds(on(b0,t),0). holds(on(b3,b0),0). holds(on(b2,b3),0). holds(on(b1,t),0). holds(on(b4,b1),0). holds(on(b5,t),0). holds(on(b6,b5),0). holds(on(b7,b6),0). %% If block B is not known to be on location L at step 0, %% then we assume it is not. -holds(on(B,L),0) :- block(B), location(L), not holds(on(B,L),0). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Specific goal. %% Change at will: goal(I) :- holds(on(b4,t),I), holds(on(b6,t),I), holds(on(b1,t),I), holds(on(b3,b4),I), holds(on(b7,b3),I), holds(on(b2,b6),I), holds(on(b0,b1),I), holds(on(b5,b0),I). %% Alternative Goal: %goal(I) :- holds(on(b3,t),I).