Ch. 8 – First Order Logic Supplemental slides for CSE 327 Prof. Jeff Heflin.

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Ch. 8 – First Order Logic Supplemental slides for CSE 327 Prof. Jeff Heflin

Syntax of First-Order Logic Sentence  AtomicSentence | ComplexSentence AtomicSentence  Predicate(Term,…) | Term = Term ComplexSentence  (Sentence) |  Sentence | Sentence  Sentence | Sentence  Sentence | Sentence  Sentence | Sentence  Sentence | Quantifier Variable,… Sentence Term  Function(Term,…) | Constant | Variable Quantifier   |  From Figure 8.3, p. 293

Knowledge-Based Agent function KB-A GENT (percept) returns an action persistent: KB, a knowledge base t, a counter, initially 0 indicating time TELL(KB, M AKE -P ERCEPT -S ENTENCE (percept, t)) action  ASK(KB, M AKE -A CTION -Q UERY (t)) TELL(KB, M AKE -A CTION -S ENTENCE (action, t)) t  t + 1 return action From Figure 7.1, p. 236

Minesweeper PEAS Description Performance Measure –percentage of mines found Environment –NxM grid with random placement of mines Actuators –choose a square Sensors –chosen square has x adjacent mines –or uncover mine and lose game

Minesweeper Predicates Environment –Mine(s) square s has a mine in it Sensing –NearbyMines(s,k) square s has k adjacent mines –Cleared(s) square s is safe (didn’t uncover a mine)

Minesweeper Axioms  s Cleared(s)   Mine(s)  s,r NearbyMines(s,0)  Adjacent(s,r)   Mine(r)  s NearbyMines(s,1)   r Adjacent(s,r)  Mine(r)  (  t Adjacent(s,t)  Mine(t)  r=t) also need 6 other rules for 1<k<8  s,r NearbyMines(s,8)  Adjacent(s,r)  Mine(r)  x,y,a,b Adjacent([x,y],[a,b])  (a=x+1  a=x  a=x-1)  (b=y  b=y+1  b=y-1)   (a=x  a=y)  Legal([x,y])  Legal([a,b])  x,y Legal([x,y])  x > 0  y > 0  x  N  y  M

Kinship Domain A 1 :  x Male(x)   Female(x) A 7 :  x,y Sibling(x,y)  x  y   p Parent(p,x)  Parent(p,y) A 4 :  p,c Parent(p,c)  Child(c,p) A 3 :  x,y Spouse(x,y)  Spouse(y,x) A 2 :  w,h Husband(h,w)  Male(h)  Spouse(h,w) A 5 :  x,y Parent(x,y)  Ancestor(x,y) A 6 :  x,y,z Ancestor(x,y)  Parent(y,z)  Ancestor(x,z)