Knowledge & Reasoning for Students study

UNIT-III
Knowledge & Reasoning
7 Hours
Statistical Reasoning: Probability and Bays’ Theorem, Certainty Factors and
Rule-Base Systems, Bayesian Networks, Dempster-Shafer Theory, Fuzzy
Logic. AI for knowledge representation, rulebased knowledge
representation, procedural and declarative knowledge, Logic programming,
Forward and backward reasoning.

Dr. Rohit D. Ghulanavar 2
• Statistical Reasoning
• Statistical reasoning involves the use of statistical methods to
analyze and interpret data, draw conclusions, and make decisions
under uncertainty.
• Bayes' Theorem in Artificial Intelligence
• Bayes' theorem is a fundamental concept in probability and
statistics.
• It often referred to as Bayes' rule or Bayes' law, Bayesian
reasoning, which determines the probability of an event with
uncertain knowledge.
• Bayes' theorem was named after the British mathematician
Thomas Bayes.

• What is Bayes' Theorem?
• In probability theory, Bayes' theorem relates the conditional probabilities of two random events and their
marginal probabilities. It helps calculate the probability of one event occurring given that another event has
already occurred.
• It is a way to calculate the value of P(B|A) with the knowledge of P(A|B).
The above equation (a) is called as Bayes' rule or Bayes' theorem. This equation is basic of most modern
AI systems for probabilistic inference.
Bayes' theorem can be derived using product rule and conditional probability of event A with known event B:
As from product rule we can write:
P(A ⋀ B)= P(A|B) P(B) or
Similarly, the probability of event B with known event A:
P(A ⋀ B)= P(B|A) P(A)
Equating right hand side of both the equations, we will get:

Key Terms in Bayes' Theorem
• Bayes' theorem consists of four main components:
• Prior Probability (P(A))
• Likelihood (P(B|A))
• Evidence/Marginal Probability (P(B))
• Posterior Probability (P(A|B))

Example-1:
Suppose you have a bag containing the following marbles:3 red marbles ,2 blue marbles,5 green marbles
In total, there are 3+2+5=10 marbles.
Step 1: Define Events
Let A be the event "drawing a red marble."
Let B be the event "drawing a marble that is not blue."
Step 2: Determine Probabilities
Calculate P(B):
The marbles that are not blue are 3 red + 5 green = 8 marbles.
Calculate P(A∩B):
The only red marbles are also not blue. So, if you draw a red marble, it satisfies both conditions.
Calculate P(A B)
∣ :
To find P(A B), we can use the formula:
∣
Substituting the values we found:

Example-2:
Question: From a standard deck of playing cards, a single card is drawn.
The probability that the card is king is 4/52, then calculate posterior
probability P(King|Face), which means the drawn face card is a king
card.
P(king): probability that the card is King= 4/52= 1/13
P(face): probability that a card is a face card= 3/13
P(Face|King): probability of face card when we
assume it is a king = 1
Putting all values in equation (i) we will get:

Uses of Bayes' Rule in Artificial Intelligence
• Naive Bayes Classification-Widely used in natural language processing
and text classification.
• Spam Email Filtering-Determines whether incoming emails are spam.
• Anomaly Detection-Identifies anomalies or outliers in datasets.
• Personalization-Updates user preferences in recommendation
systems.
• Medical Diagnosis-Updates the likelihood of various diagnoses based
on patient symptoms, test results, and medical history.

What is a rule-based system in AI?-
• Rule based system in AI require a set of facts or source of data, and a set of
rules for manipulating that data. These rules are sometimes referred to as ‘If
statements’ as they tend to follow the line of ‘IF X happens THEN do Y’.
A rule-based system is a type of artificial intelligence that uses a set of “if-then”
rules to derive conclusions or take actions based on given facts.
Components:
Knowledge Base: Stores all the known facts and rules.
Inference Engine: Applies the rules to the facts to derive new information or make
decisions.
Working Memory: Holds temporary information that the system is currently
processing.
Functionality: The system checks the facts in the working memory against the rules
in the knowledge base. When a rule’s conditions are met, the inference engine
executes the corresponding action or conclusion.
These systems are commonly used in expert systems, decision support systems, and
various AI applications.

What are advantages and Disadvantages of the rule-based system in AI?

Examples of Rule-based Systems
Healthcare, finance, and engineering are just a few examples of the sectors and
applications that use rule-based systems.
Medical Diagnosis
Fraud Detection
Quality Control
Decision support systems

Rule-based System vs. Learning-based System
Rule-Based Systems Learning-Based Systems
Uses a set of predetermined rules to
make decisions
Learns from data to make decisions
Rules are created by human experts
Knowledge is acquired through machine
learning algorithms
Limited ability to adapt to new situations
Can adapt to new situations by learning
from data
Transparent decision-making process
Decision-making process may not be
transparent
Scalable by adding or modifying rules Scalable by retraining the model
Consistent in decision-making
Decision-making may not always be
consistent
Fast decision-making
May require significant time for training
the model

Certainty Factors in Artificial Intelligence

1.Components of Certainty Factors:
•Belief: The degree of confidence in the truth of a proposition(something
offered for consideration or acceptance).
•Disbelief: The degree of confidence that a proposition is false.
•Uncertainty: The lack of confidence in either belief or disbelief.
2.Calculation:
•Certainty factors can be combined from multiple sources of evidence. When
two or more rules lead to a conclusion, their certainty factors can be merged to
produce an overall certainty factor for that conclusion.
•The formula for combining certainty factors CF1and CF2is:

The combined certainty factor
(CFcombined that the patient has
either the flu or a cold based on the
symptoms of fever and cough is
+0.92. This indicates a very high level
of certainty that the patient is likely to
have an illness based on the provided
rules.

Bayesian Belief Network in artificial intelligence
It is also called a
Bayes network,
belief network,
decision network,
or Bayesian model.

Directed Acyclic Graph
A Bayesian network graph is made up of nodes and Arcs (directed links)-
In the above diagram, A, B, C, and D are
random variables represented by the nodes of
the network graph.
If we are considering node B, which is
connected with node A by a directed arrow, then
node A is called the parent of Node B.
Node C is independent of node A.
Note: The Bayesian network graph does not contain any cyclic graph. Hence, it is known
as a directed acyclic graph or DAG.

Example-1

Example-2

Real-World Applications of Bayesian Networks
• Prediction: Customer behavior in marketing by analyzing purchase patterns.
• Anomaly Detection: In security systems, identify unusual patterns or behaviors that may
indicate fraud or breaches.
• Diagnostics: Diseases based on symptoms and patient history.
• Automated Insight: Businesses, helping them make data-driven decisions.
• Reasoning: Allowing systems to infer conclusions from incomplete or uncertain
information.
• Time Series Prediction: In finance and economics,to predict future trends based on
historical data.

Disadvantage
• In Bayesian theory, probabilities are assigned to all possible outcomes,
which can be limiting when there is a lack of information.
• DST, on the other hand, allows for the representation of uncertainty by
assigning beliefs to sets of possibilities rather than single outcomes.
• This means it can express partial belief in multiple outcomes
simultaneously, which is useful when dealing with incomplete or
ambiguous information.

Dempster-Shafer Theory (DST)
Dempster-Shafer Theory (DST), developed by Arthur P.
Dempster in 1967 and Glenn Shafer in 1976.
•Purpose: DST was created to address limitations in
Bayesian theory, particularly its inability to describe
ignorance.
•Evidence Combination: Unlike Bayesian theory, which
focuses on single pieces of evidence, DST combines all
possible outcomes of a problem.

Dempster-Shafer theory, which is used to combine
multiple pieces of evidence to form a single belief
function. This belief function represents an overall
degree of belief in a hypothesis or outcome. The
process involves:
•Belief Combination: Combining belief functions from
each piece of evidence to create a new belief function.
•Overall Degree of Belief: The new belief function
represents the overall degree of belief in the
hypothesis or outcome.

The Dempster-Shafer Theory (DST) is a way to handle uncertainty when
making decisions. Here’s how it works:
1.Combining Evidence: Imagine you have different clues or pieces of evidence
about something. DST helps you combine all these clues to figure out how
likely something is.
2.Belief and Plausibility:
1.Belief: This is how much you trust a certain outcome based on the clues
you have.
2.Plausibility: This is how possible an outcome is, considering the clues
don’t completely rule it out.
3.Handling Uncertainty: DST is useful because it can deal with situations
where you don’t have all the information or where the clues might point to
different outcomes.
Think of it like solving a mystery with different hints. DST helps you put all the

What is Fuzzy Logic?
• Fuzzy Logic is a computational approach used to handle uncertainty and
vagueness in decision-making processes.
• The term "fuzzy" refers to situations where information is unclear.
• Fuzzy logic contains the multiple logical values and these values are the
truth values of a variable or problem between 0 and 1. This concept was
introduced by Lofti Zadeh in 1965 based on the Fuzzy Set Theory.
• This concept provides the possibilities which are not given by computers,
but similar to the range of possibilities generated by humans.
• In the Boolean system, only two possibilities (0 and 1) exist, where 1
denotes the absolute truth value and 0 denotes the absolute false value.
• But in the fuzzy system, there are multiple possibilities present between
the 0 and 1, which are partially false and partially true.

Key Features
• Degrees of Truth:
• fuzzy logic introduces a range of values between
0 and 1. This means that a statement can be
partially true to varying degrees.
• Handling Uncertainty:
• Fuzzy logic effectively addresses scenarios where
clear-cut answers are not possible. It allows us to
make informed decisions based on imprecise
information.
• Fuzzy Sets:
• Instead of using traditional sets where an
element either belongs or does not belong, fuzzy
logic uses fuzzy sets. For example, a person might
belong to the fuzzy set of "tall people" with a
membership value of 0.8, indicating they are quite
tall but not definitively so.
• Linguistic Variables:
• These are variables described using natural
language terms like "hot," "cold," "young," or
"old." This makes fuzzy logic more relatable and
easier to implement in human-centered applications.
• Rule-Based Systems:
• Fuzzy logic operates on rules expressed in "IF-
THEN" format. For instance, "IF the temperature
is warm THEN set the fan speed to medium" allows
systems to make decisions that resemble human
reasoning.
Membership Function
The membership function is a function which represents the
graph of fuzzy sets, It is a graph which is used for mapping each
element of x to the value between 0 and 1.
This function is also known as indicator or characteristics
function.

Architecture of a Fuzzy Logic System

• Applications of Fuzzy Logic
• It is used in Businesses for decision-making support system.
• This concept is also used in the Defence in various areas. Defence mainly uses the Fuzzy logic systems
for underwater target recognition and the automatic target recognition of thermal infrared images.
• It is also widely used in the Pattern Recognition and Classification in the form of Fuzzy logic-based
recognition and handwriting recognition. It is also used in the searching of fuzzy images.
• Fuzzy logic systems also used in Securities.
• It is also used in microwave oven for setting the lunes power and cooking strategy.
• This technique is also used in the area of modern control systems such as expert systems.
• Finance is also another application where this concept is used for predicting the stock market, and for
managing the funds.
• It is also used for controlling the brakes.
• It is also used in the industries of chemicals for controlling the ph, and chemical distillation process.
• It is also used in the industries of manufacturing for the optimization of milk and cheese production.
• It is also used in the vacuum cleaners, and the timings of washing machines.
• It is also used in heaters, air conditioners, and humidifiers.

Knowledge Representation in AI
• Knowledge Representation in AI is
the method of structuring and
organizing knowledge so that AI
systems can process and utilize it for
reasoning and decision-making.
• Types of knowledge
• Following are the various types of
knowledge:

Rule-Based Knowledge Representation in AI
• Rule-based knowledge representation is a method used in artificial intelligence (AI) to represent information and
make decisions based on that information. This approach uses rules to encode knowledge and reasoning
processes, allowing AI systems to infer new information and draw conclusions from existing data.
• Rules:
• The fundamental building blocks of rule-based systems are "IF-THEN" statements.
• Knowledge Base:
• This is a collection of rules and facts that the system uses to make decisions.
• Inference Engine:
• It uses two primary methods: forward chaining and backward chaining.
• Forward Chaining:
• This method starts with the known facts and applies rules to infer new information until a goal is reached.
• For example, if you know it’s raining and you have the rule, you can infer that you should take an
umbrella.
• Backward Chaining:
• This approach works backward from a goal or hypothesis to find supporting facts.
• For instance, if the goal is to determine whether to take an umbrella, the system checks if it is raining
using the rules in the knowledge base.

• Advantages of Rule-Based Systems
• Transparency:
• The rules are easy to understand, making it clear how decisions
are made.
• Flexibility:
• New rules can be added easily, allowing the system to adapt to
new information or requirements.
• Modularity:
• Knowledge can be organized into separate rules, making it
easier to manage and update.

• Disadvantages of Rule-Based Systems
• Scalability:
• As the number of rules grows, the complexity of the knowledge base
can make the system slower and harder to maintain.
• Conflict Resolution:
• If multiple rules apply to a situation, the system needs a way to
resolve conflicts, which can complicate decision-making.
• Limited Reasoning:
• Rule-based systems may struggle with situations that require
deeper understanding or reasoning beyond the encoded rules

Procedural and Declarative Knowledge in AI
• In artificial intelligence (AI), knowledge representation is essential for
enabling systems to reason and make decisions.
• Knowledge is typically categorized into two types: procedural
knowledge and declarative knowledge.
• Understanding these types helps in grasping how AI systems learn and
perform tasks.

Feature Declarative Knowledge Procedural Knowledge
Nature Fact-based Skill-based
Expression Easily stated or written
Often implicit, learned
through practice
Example
"Water freezes at 0
degrees Celsius."
"How to swim."
Verification Can be easily verified Harder to articulate
Changeability Static until updated
Dynamic; improves with
experience

Logic Programming in AI
1.Definition: Logic programming is a way to instruct a computer using facts and rules instead of detailed steps.
2.How It Works: You provide information about a problem, and the computer uses logic to figure out the answers.
3.Structure: Programs consist of:
•Facts: Statements that are true (e.g., "All birds can fly").
•Rules: Relationships between facts (e.g., "If something is a bird, then it can fly").
4.Inference: The computer can draw conclusions based on the facts and rules you provide (e.g., deducing that a
penguin, being a bird, can fly).
5.Languages: Common logic programming languages include:
•Prolog: The most well-known, created in the 1970s ,Datalog ,Answer Set Programming (ASP)
6.Applications: Used in various fields such as:
•Databases
•Artificial intelligence
•Natural language processing

Comparison of Forward and Backward Reasoning
Feature Forward Reasoning Backward Reasoning
Direction Data-driven (facts to conclusions)
Goal-driven (conclusions to
facts)
Starting Point Begins with known facts
Begins with a specific goal or
hypothesis
Efficiency
May generate a lot of data; can be
less efficient for complex problems
More efficient for finding specific
conclusions
Usage
Ideal for applications that build
knowledge incrementally
Best for applications needing
verification of hypotheses

Question Bank
• Explain Bayes’ Theorem and provide an example of how it can be applied in real-world
situations.
• Discuss Bayes' rule and find posterior probabilityFrom a standard deck of playing cards,
a single card is drawn. The probability that the card is king is 4/52, then calculate
posterior probability P(King|Face).
• Describe components of rule-based system and explain advantages and disadvantages.
• What are certainty factors discuss with example.
• Explain Bayesian Belief Network in artificial intelligence with suitable example.
• Find the probability of school off given rain, cloud and no humid using Bayesian Belief
Network.
• Explain Dempster-Shafer Theory in detail.
• Explore Architecture of a Fuzzy Logic System.
• Write a short note on knowledge representation.

Knowledge & Reasoning for Students study

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