1. Ch. 9 – FOL Inference Supplemental slides for CSE 327 Prof. Jeff Heflin

2. Backward Chaining function FOL-BC-ASK (KB, goals,  ) returns a set of substitutions local answers, a set of substitutions, initially empty if goals is empty then return {  } q’  SUBST( ,FIRST(goals)) for each sentence r in KB where STANDARDIZE-APART(r) = (p 1  …  p n  q) and  ’  UNIFY(q,q’) succeeds new_goals  PREPEND([p 1,…,p n ], REST(goals)) answers  FOL-BC-ASK(KB, new_goals, COMPOSE(  ’,  ))  answers return answers From Figure 9.6, p. 288

3. Backward Chaining Example Set of sentences: S 1 :  x 1,y 1 child(x 1,y 1 )  parent(y 1,x 1 ) S 2 :  x 2,y 2 parent(x 2,y 2 )  female(x 2 )  mother(x 2,y 2 ) S 3 : child(Lisa,Homer) S 4 : child(Lisa,Marge) S 5 : female(Marge) Note: variables have already been standardized apart using subscripts Query:  x mother(x,Lisa)

4. Backward Chaining Search Tree mother(x 0,Lisa) parent(x 0,Lisa), female(x 0 ) child(Lisa,x 0 ), female(x 0 ) female(homer)female(marge) match S 4  ’={x 0 /Marge} match rule S 2  ’={x 2 /x 0, y 2 /Lisa} match rule S 1  ’={y 1 /x 0, x 1 /Lisa} match S 3  ’={x 0 /Homer} no matches answers={} (FAIL!) matches S 5  ’={ x 0 /Marge}  answers= { x 0 /Marge}

5. Forward Chaining function FOL-FC-ASK (KB,  ) returns a substitution or false local new, the new sentences inferred on each iteration repeat until new is empty new  {} for each sentence r in KB do (p 1  …  p n  q )  STANDARDIZE-APART(r) for each  such that SUBST( , p 1  …  p n )= SUBST( , p 1 ’  …  p n ’) for some p 1 ’,…, p n ’ in KB q’  SUBST( ,q) if q’  is not a renaming of some sentence already in KB or new then do add q’ to new   UNIFY(q’,  ) if  is not fail then return  add new to KB return answers From Figure 9.3, p. 282