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