1. Artificial Intelligence Knowledge Representation Logical Agents
Chapter 7
Instructor : Miss Mahreen Nasir

2. Outline Knowledge-based agents Logic in general
Propositional (Boolean) logic
Equivalence, validity, satisfiability
Predicate Logic
Sememtic Networks
Frames

3. Logical Agents
Knowledge-based agents – agents that have an explicit representation of knowledge that can be reasoned with.
These agents can manipulate this knowledge to infer new things at the “knowledge level”

4. Knowledge Based Agent
The central component a knowledge-based agent is its Knowledge base (KB) : set of sentences in a formal language (i.e. a list of facts that are known to the agent).
Each sentence is expressed in a language called a knowledge representation language, and represent some assertion about the world

5. Knowledge Bases Knowledge base = set of sentences in a formal language
Declarative approach to building an agent (or other system):
Tell it what it needs to know
Then it can Ask itself what to do - answers should follow from the KB
Agents can be viewed at :
Knowledge level - i.e., what they know, what its goals are, in order to fix its behavior, regardless of how implemented
Implementation level
i.e., data structures in KB and algorithms that manipulate them

6. Each time the agent program is called:
It TELLs the KB what it perceive.
It ASKs the KB what action it should perform (query).
The agent program TELLs the knowledge base which action was chosen and the agent executes the action.

7. A Simple knowledge based Agent
The agent must be able to:
Represent states, actions, etc.
Incorporate new percepts
Update internal representations of the world
Deduce hidden properties of the world
Deduce appropriate actions

8. What is a Logic?
Logics are formal languages for representing information such that conclusions can be drawn.
Have a syntax and semantics
Syntax
How to make sentences, valid strings of sentences
Rules for constructing legal sentences in the logic
Semantics
Define the meaning of the sentences
How we interpret sentences in the logic

9. Logic-Syntax & Semantics
Example: Arithmatic language
Syntax: x+y=4 a well formed sentence
X2y+= not a well formed sentence
x + 2 >= y is true if and only if the number of x + 2 is no less than the number y
x +2 >= y is true in a world (or model) where x = 7, y = 1
x +2 >= y is false in a world (or model) where x = 0, y = 6

10. Propositional Logic
Propositions: assertions about an aspect of a world that can be assigned either a true or false value.
e.g. Sky is cloudy, Sarah is happy, Is morning, P1, ..
True, False are propositions meaning true and false
Atoms/atomic sentences:
composed of a single propositional symbol
e.g. Sky is cloudy

11. Propositional Logic Complex Sentences:
constructed of simpler sentences using logical connectives (disjunction, implication, equivalence, negation),
e.g. Sky is cloudy ∧ Sarah is happy.
Sentences Literals:
Either an atomic sentence (P1, positive literal) or a negated atomic sentence (¬P1, negative literal)

12. Propositional Logic -Syntax
The proposition symbols P1, P2 etc are (atomic) sentences
If S is a sentence, (S) is a sentence (negation)
If S1 and S2 are sentences, (S1  S2) is a sentence (conjunction)
If S1 and S2 are sentences, (S1  S2) is a sentence (disjunction)
If S1 and S2 are sentences, (S1  S2) is a sentence (implication)
If S1 and S2 are sentences, (S1  S2) is a sentence (biconditional)

13. Propositional Logic -Sementics
Each model specifies true/false for each proposition symbol
E.g. P1,2 P2,2 P3,1
false true false
With these symbols, 8 possible models, can be enumerated automatically.
S is true iff S is false
S1  S2 is true iff S1 is true and S2 is true
S1  S2 is true iff S1is true or S2 is true
S1  S2 is true iff S1 is false or S2 is true
i.e., is false iff S1 is true and S2 is false
S1  S2 is true iff S1S2 is true and S2S1 is true
Simple recursive process evaluates an arbitrary sentence, e.g.,
P1,2  (P2,2  P3,1) = true  (true  false) = true  true = true

14. Truth Table for Connectives

15. English to Propositional Formulae
Example 1 :
“It is not the case that the Sky is Blue ” :¬ B
( alternatively teh sky is not blue )
“The Sky is Blue and the Grass is Green ” :B ∧ G
“ Either teh sky is Blue or the Grass is Green ” :B ∨ G
“ If the Sky is Blue, then the Grass is not Green” :B→ ¬ G
“ The Sky is Blue if anf only if the Grass is Green ” :B↔ G
“ If the sky is blue,then if the Grass is not Green,the Plants will not Grow ” :B→ ( ¬ G→ ¬ P )

16. English to Propositional Formulae
p = “It is below freezing”
q = “It is snowing”
It is below freezing and it is snowing
It is below freezing but not snowing
It is not below freezing and it is not snowing
It is either snowing or below freezing (or both)
If it is below freezing, it is also snowing
It is either below freezing or it is snowing, but it is not snowing if it is below freezing
That it is below freezing is necessary and
sufficient for it to be snowing
pq
p¬q
¬p¬q
pq
p→q
((pq)¬(pq))
p↔q

17. Truth Table Truth tables can be used to test sentences for validity
One row for each possible combination of truth values for the symbols in the sentence
Given n symbols,2^n possible
combinations of truth value assignments.
Here each row is an interpretation

18. Truth Tables-Implications
Does A⇒B is equivalent to ¬A ∨ B?
A⇒B is true iff A is false or B is true
is false iff A is true and B is false
Implication is used in propositional logic and predicate logic to describe a relationship between two propositions or sentences.

19. Truth Tables-Validity

20. Truth Tables -Satisfiability

21. Truth Tables-Unsatisfiability

22. Predicate Logic Propositional logic combines atoms
An atom contains no propositional connectives
Have no structure (today_is_wet, john_likes_apples)
Predicates allow us to talk about objects
Properties: is_wet(today),is _a_bird(x)
Relations: likes(john, apples)
True or false
In predicate logic each atom is a predicate
e.g. first order logic, higher-order logic

23. First Order Logic More expressive logic than propositional
Constants are objects: john, apples
Predicates are properties and relations:
likes(john, apples)
Functions transform objects:
likes(john,
Variables represenfruit_of(apple_tree))t any object: likes(X, apples)
Quantifiers qualify values of variables
True for all objects (Universal): X. likes(X, apples)
Exists at least one object (Existential): X. likes(X, apples)

24. Example: FOL Sentence “Every rose has a thorn” For all X
if (X is a rose)
then there exists Y
(X has Y) and (Y is a thorn)

25. Example: FOL Sentence Note the change from “and” to “or”
“On Mondays and Wednesdays I go to John’s house for dinner”
Note the change from “and” to “or”
Translating is problematic

26. Non-Logical Representations
Production rules
Semantic networks
Conceptual graphs
Frames
Logic representations have restricitions and can be hard to work with

27. Production Rules Rule set of <condition,action> pairs
“if condition then action”
Match-resolve-act cycle
Match: Agent checks if each rule’s condition holds
Resolve:
Multiple production rules may fire at once (conflict set)
Agent must choose rule from set (conflict resolution)
Act: If so, rule “fires” and the action is carried out
Working memory:
rule can write knowledge to working memory
knowledge may match and fire other rules
قاعدة تعيين من أزواج <condition،action> "اذا كان الشرط ثم العمل" مباريات لحل-ACT دورة المباراة: وكيل الشيكات اذا كان الشرط يحمل كل قاعدة في حل: قد قواعد إنتاج متعددة اطلاق النار في وقت واحد (مجموعة النزاع) يجب اختيار وكيل حكم من مجموعة (حل النزاعات) القانون: إذا كان الأمر كذلك، حكم "حرائق" ويتم تنفيذ الإجراء من الذاكرة العاملة: يمكن كتابة قاعدة المعرفة لالذاكرة العاملة قد تطابق المعرفة وإطلاق قواعد أخرى

28. Production Rules Example
IF (at bus stop AND bus arrives) THEN action(get on the bus)
IF (on bus AND not paid AND have oyster card) THEN action(pay with oyster) AND add(paid)
IF (on bus AND paid AND empty seat) THEN sit down
conditions and actions must be clearly defined
can easily be expressed in first order logic!

29. Graphical Representation
Graphs easy to store in a computer
To be of any use must impose a formalism
Jason is 15, Bryan is 40, Arthur is 70, Jim is 74
How old is Julia?

30. Semantic Networks Because the syntax is the same
We can guess that Julia’s age is similar to Bryan’s

31. Semantic Networks
Used as an alternative to predicate logic for knowledge representation
Knowledge is stored in the form of Graph
Nodes represent objects in the world
Arcs represent relationships between the objects

32. Semantic Networks

33. Conceptual Graphs
Semantic network where each graph represents a single proposition
Concept nodes can be
Concrete (visualisable) such as restaurant, my dog Spot
Abstract (not easily visualisable) such as anger
Edges do not have labels
Instead, conceptual relation nodes
Easy to represent relations between multiple objects

34. Frame Representations
Semantic networks where nodes have structure
Frame with a number of slots (age, height, ...)
Each slot stores specific item of information
When agent faces a new situation
Slots can be filled in (value may be another frame)
Filling in may trigger actions
May trigger retrieval of other frames
Inheritance of properties between frames
Very similar to objects in OOP

35. Example: Frame Representation