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

2. Goal-Based Agent Environment Agent sensors State
What the world is like now
How the world evolves
Environment
What it will be like if I do action A
What my actions do
What action I should do now
Goals
actuators
Agent
From Fig. 2.13, p. 52

3. 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

4. Example KB Sentences For an adventure game AI, specified informally:
State of the world
I am healthy
A wall is in front of me
Effects of actions
If I fall in a pit, I will die
If I shoot something, I will injure it
Changing goals
If I see an enemy, then attack
If I am injured, then retreat

5. 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

6. Semantics of Complex Sentences
s1  s2
s1  s2
s1  s2
s1  s2 F T
If s1 and s2 are sentences (atomic or complex) whose truth with respect to an interpretation are given by the first two columns, the truth of complex sentences formed from these sentences is given by the appropriate column.

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

8. 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

9. 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)

10. 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