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Unit II
Logical Reasoning
V.Saranya
AP/CSE
Sri Vidya College of Engineering and
Technology,
Virudhunagar

Logical Agents
Knowledge based Agents
The Wumpus World
Logic

February 20, 2006 AI: Chapter 7: Logical Agents 3
Logical Agents
• Humans can know “things” and “reason”
– Representation: How are the things stored?
– Reasoning: How is the knowledge used?
• To solve a problem…
• To generate more knowledge…
• Knowledge and reasoning are important to artificial agents
because they enable successful behaviors difficult to achieve
otherwise
– Useful in partially observable environments
• Can benefit from knowledge in very general forms,
combining and recombining information

Knowledge-Based Agents
• Central component of a Knowledge-Based Agent is
a Knowledge-Base
– A set of sentences in a formal language
• Sentences are expressed using a knowledge representation
language
• Two generic functions:
– TELL - add new sentences (facts) to the KB
• “Tell it what it needs to know”
– ASK - query what is known from the KB
• “Ask what to do next”

• The agent must be able to:
– Represent states and actions
– Incorporate new percepts
– Update internal
representations of the world
– Deduce hidden properties of
the world
– Deduce appropriate actions
Inference Engine
Knowledge-Base
Domain-
Independent
Algorithms
Domain-
Specific
Content

• Declarative
– You can build a knowledge-based agent simply by
“TELLing” it what it needs to know
• Procedural
– Encode desired behaviors directly as program
code
• Minimizing the role of explicit representation and
reasoning can result in a much more efficient system

Wumpus World
• Performance Measure
– Gold +1000, Death – 1000
– Step -1, Use arrow -10
• Environment
– Square adjacent to the Wumpus are smelly
– Squares adjacent to the pit are breezy
– Glitter iff gold is in the same square
– Shooting kills Wumpus if you are facing it
– Shooting uses up the only arrow
– Grabbing picks up the gold if in the same square
– Releasing drops the gold in the same square
• Actuators
– Left turn, right turn, forward, grab, release,
shoot
• Sensors
– Breeze, glitter, and smell

Wumpus World
• Characterization of Wumpus World
– Observable
• partial, only local perception
– Deterministic
• Yes, outcomes are specified
– Episodic
• No, sequential at the level of actions
– Static
• Yes, Wumpus and pits do not move
– Discrete
• Yes
– Single Agent
• Yes

Wumpus World

LOGIC
Syntax:
– Knowledge base consists of sentences
– These sentences are expressed according to the
syntax.
Ex: “x + y=4” is a well formed sentence.
Semantic:
• Meaning of the sentence.
• Mention the truth of each sentence.

Logic
• Entailment means that one thing follows logically
from another
a |= b
• a |= b iff in every model in which a is true, b is also
true
• if a is true, then b must be true
• the truth of b is “contained” in the truth of a

Example
• “X+Y=4” is true where X is 2
– And Y is 2
• But false where x is 1 and y is 1.
• (every sentence must be true or false in each
possible world.)

Entailment
• Relation of logical element.
• A sentence follows logically from another
sentence.
• Notation : αl= β
– Means sentence a entails(require, need, improve,
demand) β
– If every word of α is true and β is also true.
– (simply if α is true then β must be true)

Logic in Wumpus world
• The agent detecting nothing in
[1,1]
• The agent is interested in
whether the adjacent squares
[1,2] & [2,2] and [3,1].
• Each of these squares may or
may not contain a pit.
• So 23 = 8 possible models.

Conclusion
• α1 : there is no pit in [1,2]
• α2 : there is no pit in [2,2]
• KB is false in any model in which [1,2]
contains pit ,because there is no breeze in
[1,1]
We know if KB is true α1 is also true.
Hence KB is not equal to α1
in some models, if KB is true α2 is false
KB V α2 so the agent cannot conclude that
there is no pit in [2,2]

Inference (assumption or conclusion)
• The inference algorithm I can be derive from
KB, then
•KB |-i a
• a is derived from KB by i” (or)
• “ i derives a from KB”

Sound
• An inference algorithm derives only entailed sentences is called
“Sound or Truth Preserving”.
• Soundness is highly desirable property.
Correspondence between world and
representation
entailssentences sentence
Representation
World
Aspects of the
real world
Aspects of the
real world
semantics
semantics

Illustration
Sentences are physical configuration of the
agent.
Reasoning is the process of constructing new
physical configurations from old ones.
If any connection between logical reasoning
process and the real environment in which
the agent exists is called “grounding”

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Logical reasoning 21.1.13

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