Ch. 9 – FOL Inference

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 substitutionslocalanswers, a set of substitutions, initially empty if goals is empty then return { }q’ SUBST( ,FIRST(goals))for each sentence rin KB where STANDARDIZE-APART(r) = (p1… pn  q) and ’ UNIFY(q,q’) succeedsnew_goals  PREPEND([p1,…,pn],REST(goals))answers  FOL-BC-ASK(KB, new_goals, COMPOSE(’, ))  answersreturnanswers From Figure 9.6, p. 288

3. Backward Chaining Example Set of sentences: S1: x1,y1 child(x1,y1)  parent(y1,x1) S2: x2,y2 parent(x2,y2)  female(x2)  mother(x2,y2) S3: child(Lisa,Homer) S4: child(Lisa,Marge) S5: female(Marge) Note: variables have already been standardized apart using subscripts Query: x mother(x,Lisa)

4. Backward Chaining Search Tree mother(x0,Lisa) match rule S2’={x2/x0, y2/Lisa} parent(x0,Lisa), female(x0) match rule S1’={y1/x0, x1/Lisa} child(Lisa,x0), female(x0) match S4 ’={x0/Marge} match S3 ’={x0/Homer} female(homer) female(marge) no matches answers={} (FAIL!) matches S5 answers={x0/Marge}

5. Forward Chaining function FOL-FC-ASK (KB,) returns a substitution or falselocalnew, the new sentences inferred on each iteration repeat until new is emptynew  {}for each sentence rin KBdo (p1… pn  q )  STANDARDIZE-APART(r)for each  such that SUBST( , p1… pn)= SUBST( , p1’ … pn’) for some p1’ ,…, pn’ in KBq’ SUBST( ,q)if q’ is not a renaming of some sentence already in KB or newthen do add q’ to new UNIFY(q’, ) if  is not failthen return add new to KBreturnanswers From Figure 9.3, p. 282