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Ch. 8 – First Order Logic

Ch. 8 – First Order Logic. Supplemental slides for CSE 327 Prof. Jeff Heflin. Syntax of First-Order Logic. Sentence  AtomicSentence | (Sentence Connective Sentence) | Quantifier Variable,… Sentence |  Sentence AtomicSentence  Predicate(Term,…) | Term = Term

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Ch. 8 – First Order Logic

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

  2. Syntax of First-Order Logic Sentence  AtomicSentence | (Sentence Connective Sentence) | Quantifier Variable,… Sentence |  Sentence AtomicSentence  Predicate(Term,…) | Term = Term Term  Function(Term,…) | Constant | Variable Connective  | |  |  Quantifier   |  From Figure 8.3, p. 247

  3. Kinship Domain A1: x Male(x) Female(x) A2: w,h Husband(h,w)  Male(h)  Spouse(h,w) A3: x,y Spouse(x,y)  Spouse(y,x) A4: p,c Parent(p,c)  Child(c,p) A5: x,y Parent(x,y)  Ancestor(x,y) A6: x,y,z Ancestor(x,y)  Parent(y,z)  Ancestor(x,z) A7: x,y Sibling(x,y) xyp Parent(p,x)  Parent(p,y)

  4. Knowledge-Based Agent function KB-AGENT(percept) returns an actionstatic: KB, counter t=0 TELL(KB, MAKE-PERCEPT-SENTENCE(percept, t)) action ASK(KB, MAKE-ACTION-QUERY(t)) TELL(KB, MAKE-ACTION-SENTENCE(action, t))t t + 1return action From Figure 7.1, p. 196

  5. 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

  6. 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)

  7. Minesweeper Axioms • 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

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