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-AGENT(percept) returns an action
persistent: KB, a knowledge base
t, a counter, initially 0 indicating time
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. 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
• 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
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)