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Understanding First-Order Logic and Knowledge-Based Agents in Computer Science

This supplemental material offers a comprehensive overview of first-order logic syntax, atomic sentences, and logical connectives. It discusses quantifiers, variables, and predicates with practical examples, including kinship relations and the Minesweeper game. The document also describes the functioning of a knowledge-based agent that utilizes perception to return actions. Key axioms and predicates for the Minesweeper game illustrate the relationship between the environment and actions, providing foundational knowledge for CSE 327 students under Prof. Jeff Heflin.

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Understanding First-Order Logic and Knowledge-Based Agents in Computer Science

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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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