1. Logical Agents Prof. Dr. Widodo Budiharto 2018
Course : Artificial Intelligence
Logical Agents Prof. Dr. Widodo Budiharto 2018

2. Outline Knowledge-Based Agents The Wumpus World Logic
Propositional Logic

3. Knowledge-Based Agents
The central component of knowledge-based agent is knowledge base (KB)
Knowledge base is set of “sentences”
Each “sentence” expressed in a language called a knowledge representation language and represent about the world
Axiom: sentence is taken as given without being derived from other sentences
TELL and ASK: standard name for add new sentences to the KB and a way to query what is known

4. Knowledge-Based Agents
TELL and ASK may involve inference
Inference: deriving new sentence from old sentences
Obey the requirement when one ASK a question of KB
Answer should follow from what has been told (TELLED) to the KB previously

5. Knowledge-Based Agents
Knowledge-based agent takes a percept as input and return an action
3 steps when an agent program is called:
TELLs the knowledge base what is perceives
ASKs the knowledge base what action it should perform
TELLs the knowledge base which action was chosen and the agent executes the action
Agents can be viewed at the knowledge level
i.e., what they know, regardless of how it implemented

6. Knowledge-Based Agents
A simple knowledge-based agent

7. Knowledge-Based Agents
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. Knowledge-Based Agents
Building a Knowledge-Based Agent
Declarative approach:
TELLing it what it need to know, starting with an empty knowledge base then the agent designer can TELL sentences one by one until agent knows how to operate in its environment
Procedural approach:
Encodes desired behaviors directly as program code

9. Knowledge-Based Agents
A successful agent often combines both declarative and procedural elements in its design
The declarative knowledge can often be compiled into more efficient procedural code

10. The Wumpus World

11. The Wumpus World Performance measure Environment
gold +1000, death -1000
-1 per step, -10 for using the arrow
Environment
A 4 x 4 grid rooms
Agent always starts in [1,1] facing to the right
The location of gold Wumpus are chosen randomly
Uniform distribution
Each square can be a pit with a probability 0.2

12. The Wumpus World Actuators: Sensors: (Perceive it)
Turn Left by 90˚, Turn Right by 90˚, Forward, Grab, Climb, Shoot
Sensors: (Perceive it)
Stench: when the agent in the adjacent squares of Wumpus
Breeze: when the agent in the adjacent squares of Pit
Glitter: when the agent in the square of Gold
Bump: When the agent walks into a wall
Scream: When the Wumpus is killed

13. The Wumpus World A = Agent B = Breeze G = Glitter, Gold
OK = Safe square
P = Pit
S = Stench
V = Visited
W = Wumpus

14. The Wumpus World A = Agent B = Breeze G = Glitter, Gold
OK = Safe square
P = Pit
S = Stench
V = Visited
W = Wumpus

15. The Wumpus World A = Agent B = Breeze G = Glitter, Gold
OK = Safe square
P = Pit
S = Stench
V = Visited
W = Wumpus

16. The Wumpus World A = Agent B = Breeze G = Glitter, Gold
OK = Safe square
P = Pit
S = Stench
V = Visited
W = Wumpus

17. Logic
In standard logics, every sentence must be either true or false in each possible world—there is no “in between.”
Logics
formal languages for representing information such that conclusions can be drawn
Syntax
defines the sentences in the language
Semantics
define the "meaning" of sentences

18. Logic Example of KRL: the language in arithmetic Syntax:
x + y = 4 is a valid sentence;
x4y+=is not a valid sentence
Semantics:
x + y = 4 is true in a world where x is 2 and y is 2
x + y = 4 is false in a world where x is 1 and y is 1

19. Logic Possible world = model
Informally, we may think of a possible world as, for example, having x men and y women sitting at a table playing bridge, and the sentence x + y = 4 is true when
There are four people in total
Formally, the possible models are just all possible assignments of real numbers to the variables are x and y
If a sentence A is true in model m, we say that m satisfies A or sometimes m is a model of A
We use the notation of M(A) to mean the set of all models of A

20. Logic
Entailment means that one thing follows from another (a fact can be drawn from (collection) other fact
KB ╞ α : Knowledge base KB entails sentence α if and only if α is true in all worlds where KB is true
KB ╞ α iff M(KB)  M(α)

21. Logic
Example:
KB containing sentences “the Giants won” and “the Reds won” entails “Either the Giants won or the Reds won”
x+y = 4 entails 4 = x+y
Entailment is a relationship between sentences (syntax) that is based on semantics

22. Logic Entailment in Wumpus World After [1, 1] OK, [2,1] Breeze:
Entrapment model in [1, 2], [2, 2], [3, 1]: 3 choices of Boolean  8 possible models

23. Logic
Entailment in Wumpus World

24. Logic
Entailment in Wumpus World

25. Logic
Entailment in Wumpus World

26. Logic
Entailment in Wumpus World

27. Logic
Entailment in Wumpus World

28. Inference in Logic
KB ├i α = sentence α can be derived from KB by procedure i
Consequences of KB are a haystack; α is a needle.
Entailment = needle in haystack; inference = finding it
Soundness: i is sound if whenever KB ├i α, it is also true that KB╞ α
Completeness: i is complete if whenever KB╞ α, it is also true that KB ├i α

29. Propositional Logic Propositional logic is the simplest logic
The syntax of propositional logic defines the allowable sentences
The atomic sentences consists of a single proposition symbol
Complex sentences are constructed from simpler sentences, using parentheses and logical connectives

30. Propositional Logic There are five connectives in common use
 (not). If S is a sentence, S is a sentence (negation)
 (and). If S1 and S2 are sentences, S1  S2 is a sentence (conjunction)
 (or). If S1 and S2 are sentences, S1  S2 is a sentence (disjunction)
 (implies). If S1 and S2 are sentences, S1  S2 is a sentence (implication)
 (if and only if). If S1 and S2 are sentences, S1  S2 is a sentence (biconditional)

31. Propositional Logic
The semantic defines the rules for determining the truth of a sentence with respect to a particular model
In propositional logic, a model simply fixes the truth value for every proposition symbol, I.e. P1,2 = true
For complex sentences, there are five rules for any sub sentences in any model m :
S1
true iff S1
false
S1  S2
true and S2
true
S1  S2
true or
S1  S2
true unless
S1  S2
S1 and S2

32. Propositional Logic
The rules can also be expressed with truth tables that specify the truth value of a complex sentence for each possible assignment of truth values to its components.
Simple recursive process evaluates an arbitrary sentence, e.g., P1,2  (P2,2  P3,1) = true  (true  false) = true  true = true

33. Wumpus World Sentences
Let Pi,j be true if there is a pit in [i, j].
Let Bi,j be true if there is a breeze in [i, j].
P1,1
B1,1
B2,1
“Pits cause breezes in adjacent squares”
B1,1  (P1,2  P2,1 )
B2,1  (P1,1  P2,2  P3,1 )
“A square is breezy if and only if there is an adjacent pit”

34. Wumpus World Sentences

35. References
Widodo Budiharto. (2015). Artificial Intelligence, Andi Offset Publisher.
Stuart Russell, Peter Norvig Artificial Intelligence : A Modern Approach. Pearson Education. New Jersey. ISBN: