1 Write the basic algorithm for learning sets of First-Order Rules.

In machine learning, First-Order Rules are logical rules that use First-Order Logic (FOL) to represent concepts with
variables and relations (e.g., Parent(x, y), Student(x)). Learning such rules is useful in domains like natural language
processing, robotics, and expert systems.

We aim to learn a set of rules that together describe a target concept from examples.
Goal:

Learn a set of if-then rules (hypotheses) that classify examples into positive and negative, based on relational and
structured data.

Basic Algorithm Steps:

Input:
 A set of positive examples (P)
 A set of negative examples (N)
 A set of background knowledge (B) (optional)

Output:
 A set of first-order rules that covers most or all positive examples, and no negative examples

Algorithm: Learn-First-Order-Rules
Initialize H = ∅ (empty set of rules)

While there are positive examples left:

1. Create an empty rule R
2. While R covers any negative examples:
a. Specialize R by adding conditions (literals)
to exclude negative examples
3. Add R to H
4. Remove all positive examples covered by R from P

Return H

Explanation:
 The algorithm greedily learns one rule at a time.
 Each rule is refined so that it excludes all negative examples.
 This process repeats until all positive examples are covered.
 It builds a hypothesis set H that consists of rules like:
Student(x) ∧ Studies(x, y) → Passes(x)

Example:
Suppose we want to learn a rule for who is a good student.

Positive examples:
 GoodStudent(Alice)
 GoodStudent(Bob)

Features:
 StudiesHard(x), AttendsClass(x), SubmitsHomework(x)

The algorithm may learn rules like:

IF AttendsClass(x) ∧ SubmitsHomework(x) THEN GoodStudent(x)
Advantages:
 Handles relational data and structured input
 Very expressive (can represent complex relationships)

Disadvantages:
 Learning is computationally expensive
 Can overfit if not carefully controlled
 May require background knowledge to be effective

Learning first-order rule sets is a powerful but complex approach to machine learning. It allows for expressive and
human-readable models, especially useful in domains where relationships between entities matter.

2 Explain the explanation-based learning algorithm Prolog-EBG with a suitable example.

Explanation-Based Learning (EBL) is a form of machine learning where the system generalizes from a single example by
using domain knowledge. Instead of learning from many examples, it explains why a single example is an instance of a
concept and then generalizes that explanation.

Prolog-EBG is an EBL system based on the Prolog programming language and logic programming.

Key Idea of Prolog-EBG:

 Given a specific example and a domain theory (in Prolog form), the algorithm:
1. Explains the example using the domain theory (builds a proof tree).
2. Generalizes the explanation to form a rule that applies to other similar cases.

Steps of the Prolog-EBG Algorithm:

1. Input:
o A training example E
o A domain theory D (set of Prolog rules)
o A goal concept G (target predicate)
2. Construct Proof:
o Use Prolog to prove that E satisfies G using the domain theory.
o Build a proof tree from this explanation.
3. Generalize the Explanation:
o Replace constants (like specific names) with variables.
o Remove irrelevant parts of the explanation.
4. Output:
o A general rule (Horn clause) that covers the example and can apply to others.

Example:
Let’s say we want to learn what makes someone a good student.

Domain Theory in Prolog:

good_student(X) :- studies(X), attends_class(X).
studies(alice).
attends_class(alice).
Example:
 Goal: Prove that good_student(alice) is true.

Step 1: Explanation (Proof)

Prolog proves:
 studies(alice) is true
  attends_class(alice) is true
→ Therefore, good_student(alice) is true

Step 2: Generalization
 Replace alice with a variable X
 Get a general rule:
good_student(X) :- studies(X), attends_class(X).

This is the general rule learned using Prolog-EBG.

Advantages:
 Learns from a single example
Produces human-readable rules
Fast once domain theory is available

Disadvantages:
 Requires a correct and complete domain theory
Not suitable when domain knowledge is missing
 Generalization may fail if explanation is incorrect

Prolog-EBG is an effective explanation-based learning method that uses logic programming to generalize examples into
rules. It’s best suited for domains where strong background knowledge is available and interpretability is important.

3 Discuss the Inverse Resolution rule for first order logic.

Inverse Resolution is a machine learning technique used in Inductive Logic Programming (ILP). Unlike traditional
resolution (used to derive new facts), inverse resolution reconstructs hypotheses (rules) that can explain observed
examples.

It is called inverse because it reverses the process of deductive reasoning, moving from conclusions back to possible
rules that could have produced them.

Basic Concept
 Traditional resolution starts with facts and rules to derive conclusions.
 Inverse resolution starts with a conclusion (example) and infers possible rules that could have led to it.

Goal:
Given:
 A set of background knowledge B
 A set of positive examples E
Find:
 A hypothesis (H) such that:
𝐵∪𝐻⊨𝐸

That is, E can be logically derived from 𝐵 ∪ 𝐻

Inverse Resolution Rule:

The general inverse resolution step is:
𝑖𝑛𝑣
𝐵∪𝐶 ⇒ 𝐶→ 𝐵
Which means:
 If using a rule B, we can deduce a clause C,
 Then, we can reverse this and say: if C is observed, BB might be the rule used to derive it.
Example:
Let’s say the system observes:
 Example (E): grandparent(alice, bob)
 Background knowledge (B):
parent(alice, charlie).
parent(charlie, bob).

We want to learn a hypothesis H that connects parent and grandparent.

Using inverse resolution, we can hypothesize:
grandparent(X, Z) :- parent(X, Y), parent(Y, Z).

Now, B ∪ H ⊢ E — the example can be explained by the new hypothesis and existing background facts.

Advantages:
 Works well in relational and structured domains
Learns logical rules instead of just patterns
Supports multi-step reasoning

Disadvantages:
 Computationally expensive
 Can generate many irrelevant rules
 Needs careful search to avoid incorrect generalizations

Applications:
 Natural Language Understanding
 Knowledge Base Completion
 Bioinformatics and Relational Data Mining

Inverse resolution is a powerful rule-learning approach in First-Order Logic. By reversing logical deduction, it helps
machines learn interpretable and logical rules that explain how conclusions are derived from data and background
knowledge.

4 Define the following i) Generalization ii) ϴ-Subsumption iii) Entailment

i) Generalization

Generalization is the process of creating a more abstract or broader concept from specific examples or instances.

In machine learning, a hypothesis H1 is said to be more general than hypothesis H2 if H1 covers all examples that H2
covers, and possibly more.

Example:
 H1: Animal(x)
 H2: Dog(x)
Here, H1 is a generalization of H2 because all dogs are animals, but not all animals are dogs.

ii) ϴ-Subsumption (Theta-Subsumption)

Theta-subsumption is a logical relation between two first-order logic clauses. A clause C1 theta-subsumes clause C2 if
there exists a substitution θ (theta) such that:
𝐶10 ⊆ 𝐶2

It is used in Inductive Logic Programming to determine if one clause is more general than another.
Example:
 C1: parent(X, Y)
 C2: parent(alice, bob)
Here, C1 theta-subsumes C2 with substitution θ = {X/alice, Y/bob}.

iii) Entailment

Entailment is a logical relationship where a set of statements (or rules) logically implies another statement.
In symbols:
𝐵⊨ℎ
Means: background knowledge B entails hypothesis h, i.e., if B is true, then h must also be true.

Example:
If:
 parent(alice, bob)
 parent(bob, charlie)
 grandparent(X, Z) :- parent(X, Y), parent(Y, Z)
Then:
 B ⊨ grandparent(alice, charlie)

These three concepts - generalization, theta-subsumption, and entailment - are core to logical learning and reasoning
in machine learning, especially in inductive logic programming and symbolic AI. They help machines derive, compare,
and validate logical rules.

5 What is Knowledge-Level learning? Explain.

Knowledge-Level Learning refers to learning that happens at the knowledge level, focusing on what is represented
rather than how it is represented or the specific implementation details.

Introduced by Allen Newell, it means learning based on understanding the meaning and structure of knowledge in a
problem domain, rather than low-level data or sensory inputs.

Explanation:
 At the knowledge level, learning is about acquiring concepts, rules, and strategies that help solve problems.
 It involves forming, modifying, and organizing knowledge structures like facts, rules, and heuristics.
 The system builds or refines its knowledge base to improve performance on tasks.

Key Points:
 Focus on ‘What’ not ‘How’: The emphasis is on what knowledge is needed rather than how the system
executes or processes information.
 Helps the system to generalize across different problems by understanding concepts.
 Enables explanation and reasoning at a high level.

Example:
Suppose a robot is learning how to navigate rooms:
 Data level: learns raw sensor inputs (like distance measurements).
 Knowledge level: learns concepts like "door," "hallway," and "obstacle" and rules like "If door ahead, turn right."
The robot at the knowledge level understands meaningful concepts and uses them to make decisions, not just raw data.

Importance in AI:
 Helps build systems that can transfer learning between tasks.
 Facilitates explainable AI by focusing on interpretable knowledge.
  Bridges the gap between low-level data processing and high-level reasoning.

Knowledge-Level Learning is a powerful approach that emphasizes learning meaningful, abstract knowledge about a
domain. It allows AI systems to reason, generalize, and explain their behavior effectively.

6 Discuss the drawbacks of Explanation-based learning.

Explanation-Based Learning (EBL) is a method where a system generalizes knowledge by explaining a single example
using existing domain knowledge. While powerful, it has several limitations:

1. Dependence on Strong Domain Knowledge

 EBL needs a complete and correct domain theory to work effectively.
 If the background knowledge is incomplete, wrong, or missing, EBL cannot generate useful generalizations.

2. Overgeneralization
 The system may create rules that are too broad, leading to incorrect predictions.
 It lacks statistical validation across multiple examples, increasing the risk of poor generalizations.

3. Inflexibility
 EBL focuses on deductive reasoning, not learning from data.
 It does not improve with more data, unlike statistical learning models.

4. Ignores Noise and Exceptions

 EBL assumes the data and background theory are perfect and noise-free.
 It struggles in real-world environments where data can be noisy or contradictory.

5. Limited to Deterministic Domains

 Works best where causes and effects are clearly defined.
 Not suitable for probabilistic or uncertain domains.

6. Computational Complexity
 Building and generalizing explanation trees can be computationally expensive.
 Especially hard when the domain theory is large and complex.

7. Poor Learning from Multiple Examples

 EBL typically learns from only one or few examples, unlike statistical learning that improves with more
examples.
 Doesn’t naturally support learning from experience or updating over time.

While EBL is useful in structured domains with rich background knowledge, it has major drawbacks such as overreliance
on domain theory, lack of flexibility, and difficulty handling real-world uncertainty. It is best suited for well-defined,
logical tasks, not for general-purpose or data-driven learning.

7 Write about Temporal Difference Learning

Temporal Difference (TD) Learning is a reinforcement learning method used to predict future outcomes and improve
decision-making based on experience. It combines ideas from Monte Carlo methods and Dynamic Programming.
It is widely used in areas like game playing, robotics, and control systems.

Key Idea
TD learning learns directly from raw experience (sequences of states and rewards), without needing a model of the
environment.
It updates value estimates based on the difference (error) between:
 The current estimate and
 A new estimate from the next observed state.

This difference is called the Temporal Difference error.

TD Learning Equation
For a state , the value is updated as:

𝑉(𝑆𝑡 ) ← 𝑉(𝑆𝑡 ) + 𝛼[𝑅𝑡+1 + 𝛾𝑉(𝑆𝑡+1 ) − 𝑉(𝑆𝑡 )]

Where:
 α = learning rate (0 < α ≤ 1)
 𝛾 = discount factor (0 ≤ γ ≤ 1)
 𝑅𝑡+1 = reward received after moving from 𝑆𝑡 to 𝑆𝑡+1

Example
Suppose a robot moves through rooms to reach a goal:
 It learns to assign higher value to rooms closer to the goal.
 Every time it moves and sees a reward or next room’s value, it updates the value of the current room.

This helps it improve behavior over time, even before reaching the final goal.

Types of TD Learning
1. TD(0) – Updates based on one-step prediction.
2. TD(λ) – Combines many-step predictions using eligibility traces.

Advantages
 Learns online and incrementally
 No need for a model of the environment
 Works in stochastic (random) environments
 Efficient for real-time systems

Disadvantages
 Convergence depends on learning rate
 Needs many iterations for large state spaces
 May not perform well if reward signals are too sparse

Applications
 TD-Gammon (famous backgammon-playing program)
 Robotics
 Autonomous systems
 Reinforcement learning agents

Temporal Difference Learning is a powerful and flexible method in reinforcement learning that allows agents to learn
from experience by comparing predicted values over time. It balances between immediate feedback and long-term
prediction, making it suitable for dynamic environments.

8 Write about Inverted deduction approach to inductive logic programming.

In Inductive Logic Programming (ILP), the goal is to learn logical rules or hypotheses from examples and background
knowledge. The inverted deduction approach is one such method used to construct hypotheses that explain the given
examples.
What is Inverted Deduction?
 Inverted deduction is a reverse process of logical deduction.
 While deduction applies known rules to derive facts, inverted deduction starts from facts (examples) and works
backward to discover the rules that could have generated them.
 It tries to find a hypothesis H such that:
𝐵∪𝐻⊨𝐸

where:
o B is the background knowledge
o E is the positive example
o H is the hypothesis to be learned

How it Works
1. Given:
o Background knowledge B
o Positive example E
2. Goal:
o Find a hypothesis H that, when added to B, allows deduction of E
3. Steps:
o Use backward chaining to trace back from the example
o Identify intermediate predicates or conditions needed
o Construct rules (hypotheses) that fill in the gap between B and E

Example
Suppose:
 E: grandparent(alice, bob)
 B: parent(alice, charlie), parent(charlie, bob)

Inverted Deduction works backward from the example to find:

grandparent(X,Z):−parent(X,Y),parent(Y,Z)

This rule (hypothesis) explains how the background facts lead to the example.

Advantages
 Works well in structured logical domains
 Produces interpretable rules
 Based on sound logical inference principles

Disadvantages
 Can be computationally intensive
 Assumes complete and correct background knowledge
 Not ideal in noisy or uncertain environments

Applications
 Knowledge base construction
 Expert systems
 Natural language understanding
 Bioinformatics

The Inverted Deduction Approach in ILP helps systems learn rules by reversing the reasoning process, making it a
useful method for learning in logic-based AI systems. However, it requires a solid foundation of domain knowledge and
is best suited for clean, logical domains.
9 Write the sequential covering algorithm for learning disjunctive set of rules.

The Sequential Covering Algorithm is used to learn a set of if-then rules (a disjunctive rule set) from training data. It is
commonly used in rule-based machine learning and inductive logic programming.

Each rule covers a subset of the positive examples, and together the rules cover the entire set.

Purpose
 Learn a disjunctive hypothesis:
e.g.,
If A then positive OR If B then positive OR If C then positive
 The algorithm learns one rule at a time that covers some positive examples while avoiding negatives.

Pseudocode: Sequential Covering Algorithm

Input:
- Training examples (positive and negative)
- Target concept (goal)
- Rule learning algorithm (Learn-One-Rule)

Output:
- A set of rules (disjunctive)

Algorithm:
1. Initialize RuleSet = {}
2. While there are still uncovered positive examples:
a. Learn a rule R using Learn-One-Rule that covers some uncovered positives and few (or no) negatives
b. Add R to RuleSet
c. Remove examples covered by R from the training set
3. Return RuleSet

Example
Let’s say we are learning the concept "PlayTennis".
 Examples include attributes like Outlook, Humidity, Wind, etc.
 Rule 1: If Outlook = Sunny and Humidity = Normal then PlayTennis = Yes
 Rule 2: If Outlook = Overcast then PlayTennis = Yes

Each rule is learned one by one, covering part of the positive examples until all are covered.

Advantages
 Produces interpretable rules
 Easy to understand and implement
 Good for classification problems

Disadvantages
 Might overfit if rules are too specific
 Needs careful handling of noise and exceptions

The Sequential Covering Algorithm is a powerful method for building rule-based classifiers. It learns a series of rules
that together define a complete classification system by covering all positive examples step-by-step. It is especially
useful in domains where explanatory rules are important.
10 Illustrate Task Q-Learning

Q-Learning is a popular reinforcement learning (RL) algorithm that helps an agent learn how to act in an environment to
maximize cumulative reward. It is a model-free method, meaning the agent doesn't need to know the environment’s
dynamics in advance.

It can be applied to various tasks, including robot navigation, game playing, and automated decision-making.

Key Concepts
 Agent: Learns and acts in the environment.
 Environment: Where the agent operates.
 State (S): A situation the agent is in.
 Action (A): What the agent can do.
 Reward (R): Feedback from the environment.
 Q-value (Q(S, A)): Expected future reward of taking action A in state S.

Q-Learning Formula
𝑄(𝑆𝑡 , 𝐴𝑡 ) ← 𝑄(𝑆𝑡 , 𝐴𝑡 ) + 𝛼 [𝑅𝑡+1 + max 𝑄(𝑆𝑡+1 , 𝑎) − 𝑄 (𝑆𝑡 , 𝐴𝑡 )
𝑎
Where:
 α = learning rate
 𝛾 = discount factor
 𝑄(𝑆𝑡 , 𝐴𝑡 ) = reward after taking action
 max 𝑄 = maximum estimated future reward

Task Illustration: Robot Grid Navigation

Task: A robot needs to reach a goal cell in a grid.

 States: Grid positions (e.g., (1,1), (2,3))
 Actions: Move up, down, left, right
 Rewards:
o +10 for reaching the goal
o -1 for each move
o -10 for hitting a wall

How Q-Learning Works:

1. The robot starts in a random cell.
2. It picks actions and explores the environment.
3. It receives rewards and updates its Q-table using the Q-learning formula.
4. Over time, it learns the best action for each state to reach the goal efficiently.

Sample Q-Table (Partial)

State Up Down Left Right

(1,1) -1.2 0.5 -1.0 1.8
(1,2) 1.0 0.8 -0.5 2.5
Goal 0 0 0 0

Bold values indicate the best action in that state.

Advantages
 Learns optimal policy without needing a model
 Works in stochastic environments
  Can handle delayed rewards

Disadvantages
 Needs many exploration episodes to learn
 Q-table grows large with big state spaces
 Needs tuning of α and γ for good performance

Q-Learning helps an agent learn optimal behavior in a task through trial and error. It is widely used in various tasks like
robot control, game AI, and real-time decision systems, making it a core method in reinforcement learning.