1. Introduction to Knowledge-bases
Knowledge-base Agent
Representation, Reasoning and Logic
Propositional Logic
Syntax & Semantics
Inferencing
Example:
Wumpus World
A Propositional logic Knowledge-based Agent for the Wupus World
CPSC 533 AI - Knowledge-bases

2. Knowledge-base Agent Sentences Knowledge Representation Language
Background Knowledge KB
tell
ask/result
agent
percept
Describing a KB...
What it knows
Knowledge level
Logical level
How it knows
Implementation level
Knowledge implementation
CPSC 533 AI - Knowledge-bases

3. Knowledge-base Agent Sentences Knowledge Representation Language
Background Knowledge KB
sentences
inference
engine
tell
ask/result
agent
percept
Describing a KB...
What it knows
Knowledge level
Logical level
How it knows
Implementation level
Knowledge implementation
CPSC 533 AI - Knowledge-bases

4. Representation, Reasoning & Logic
Knowledge Representation Languages
Express knowledge in a computer-tractable manner.
Are described in terms of:
Syntax: Configurations to represent sentences.
Semantics: Determines sentences meaning.
Logic: Language with well-defined syntax and semantics.
Inferencing
inferencing a
agent
x sentences
x+a sentences
world
y facts
y+d facts
CPSC 533 AI - Knowledge-bases

5. Representation, Reasoning & Logic
Inferencing (cont)
Process where true sentences are generated, based on existing ones.
Characteristics:
Process: Truth-preserving / Sound.
Sentences: Entailed.
sentences
entailed
sentence
Proof
Completeness
For an Inference Process to be “sound”, it has to comply with the
inferencing semantical rules of a language (a.k.a. proof theory)
CPSC 533 AI - Knowledge-bases

6. Representation, Reasoning & Logic
Semantics
Sentences do not have a meaning: they need to be interpreted.
“The sky is blue” vs. “The bird is in the cage”.
Characteristics of sentences:
Valid: True under all interpretations.
Satisfiable: True under some interpretations.
Un-satisfiable: False in all worlds.
Logics
CPSC 533 AI - Knowledge-bases

7. Propositional Logic Syntax Constants: True, False Symbols: P, Q, ...()
Connectives:
BNF
sentence à atomic_sentence | complex_sentence
atomic_sentence à TRUE | FALSE | P | Q | ...
complex_sentence à ( sentence ) | sentence connective sentence | Øsentence
connective à Ù | Ú | Þ | Û
CPSC 533 AI - Knowledge-bases

8. “A sentence has a meaning derived from its parts.”
Propositional Logic
Semantics
Constants: True = True, False = False
Symbols: Not valid, but satisfiable.
“A sentence has a meaning derived from its parts.”
Truth tables
CPSC 533 AI - Knowledge-bases

9. Propositional Logic Inference Rules a entails b a Modus-Ponens b
And-Elimination
And-Introduction
Or-Introduction
Double-Negation Elimination
Unit Resolution
Resolution a b
a Þ b, a b
a1 Ù a2 Ù ... Ù an ai
a1 , a2 , ... , an
a1 Ù a2 Ù ... Ù an ai
a1 Ú a2 Ú ... Ú an
ØØa a
a Ú b, Øb a
Ø a Þ b, b Þ g
Ø a Þ g
CPSC 533 AI - Knowledge-bases

10. Propositional Logic (example)
Wumpus World 1 2 3 4
òòò Stench
Wumpus
» Breeze
Pit
Gold
Gold Hunter D
start
CPSC 533 AI - Knowledge-bases

11. Propositional Logic (example)
Wumpus World 1 2 3 4 1 2 3 4
òòò
òòò
òòò OK D OK
p - Pit
w - Wumpus
CPSC 533 AI - Knowledge-bases

12. Propositional Logic (example)
Wumpus World 1 2 3 4 1 2 3 4
òòò
òòò
òòò p? OK p?
p - Pit
w - Wumpus
CPSC 533 AI - Knowledge-bases

13. Propositional Logic (example)
Wumpus World 1 2 3 4 1 2 3 4
òòò
òòò
òòò p? OK p?
p - Pit
w - Wumpus
CPSC 533 AI - Knowledge-bases

14. Propositional Logic (example)
Wumpus World 1 2 3 4 1 2 3 4
òòò
òòò w!
òòò OK D p!
p - Pit
w - Wumpus
CPSC 533 AI - Knowledge-bases

15. Propositional Logic (example)
Wumpus World 1 2 3 4 1 2 3 4
òòò
òòò w! OK
òòò OK D p!
p - Pit
w - Wumpus
CPSC 533 AI - Knowledge-bases

16. Propositional Logic (example)
Wumpus World 1 2 3 4 1 2 3 4
òòò p?
òòò w! p?
òòò OK D p!
p - Pit
w - Wumpus
CPSC 533 AI - Knowledge-bases

17. Propositional Logic (example)
A Propositional logic KB Agent for the Wumpus World 1 2 3 4
òòò
ØS1,1 ØS2,1 S1,2 ØB1,1 B2,1 ØB1,2
R1 : ØS1,1 Þ ØW1,1 Ù ØW1,2 Ù ØW2,1
R2 : ØS2,1 Þ ØW1,1 Ù ØW2,1 Ù ØW2,2 Ù ØW3,1
R3 : ØS1,2 Þ ØW1,1 Ù ØW1,2 Ù ØW2,2 Ù ØW1,3
R4 : S1,2 Þ W1,1 Ú W1,2 Ú W2,2 Ú W1,3
òòò
1,3
òòò
1,2
1,1
2,1
3,1
CPSC 533 AI - Knowledge-bases

18. Propositional Logic (example)
A Propositional logic KB Agent for the Wumpus World
1) Modus Ponens on ØS1,1 and R1
ØW1,1 Ù ØW1,2 Ù ØW2,1
2) And-Elimination
ØW1, ØW1, ØW2,1
3) Modus Ponens on ØS2,1 and R2
ØW1,1 Ù ØW2,1 Ù ØW2,2 Ù ØW3,1
4) And-Elimination
ØW1, ØW2, ØW2, ØW3,1
5) Modus Ponens on S1,2 and R4
W1,1 Ú W1,2 Ú W2,2 Ú W1,3
6) Unit Resolution
W1,2 Ú W2,2 Ú W1,3
7) Unit Resolution
W2,2 Ú W1,3
8) Unit Resolution
W1,3
ØS1,1 ØS2,1 S1,2 ØB1,1 B2,1 ØB1,2
R1 : ØS1,1 Þ ØW1,1 Ù ØW1,2 Ù ØW2,1
R2 : ØS2,1 Þ ØW1,1 Ù ØW2,1 Ù ØW2,2 Ù ØW3,1
R3 : ØS1,2 Þ ØW1,1 Ù ØW1,2 Ù ØW2,2 Ù ØW1,3
R4 : S1,2 Þ W1,1 Ú W1,2 Ú W2,2 Ú W1,3
Goal: W1,3
CPSC 533 AI - Knowledge-bases