Ch. 8

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
Knowledge-Based Agent

• function KB-AGENT(percept) returns an
  action static KB, counter t0
• TELL(KB, MAKE-PERCEPT-SENTENCE(percept,
  t)) action ? ASK(KB, MAKE-ACTION-QUERY(t)) TELL(
  KB, MAKE-ACTION-SENTENCE(action, t)) t ? t
  1 return action
• From Figure 7.1, p. 196

4
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

5
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 (didnt uncover a mine)

6
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) ? rt)
• also need 6 other rules for 1ltklt8
• ?s,r NearbyMines(s,8) ? Adjacent(s,r) ? Mine(r)
• ?x,y,a,b Adjacent(x,y,a,b) ? (ax1 ? ax ?
  ax-1) ? (by ? by1 ? by-1) ? (a?x ? a?y) ?
  Legal(x,y) ? Legal(a,b)
• ?x,y Legal(x,y) ? x gt 0 ? y gt 0 ? x ? N ? y ?
  M

7
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)