1. Explain Planning in the Unification Process. Select anyone design problem and provide solution with example.

Unification is a fundamental operation in AI that supports logical planning and automated reasoning. In planning systems based on first-order logic, unification is used to match goals with available actions or rules by finding suitable substitutions. It enables the inference engine to apply relevant rules whose preconditions match the current state.

Unification in Planning
In logic-based planning:
  • Goals are expressed as predicates.
  • Actions are defined with preconditions and effects.
  • The planning system uses unification to match action preconditions with current facts.
  • If unification succeeds, the action is applied.
Unification ensures that variable substitutions are consistent, constants match, function symbols match, and cyclic substitutions are avoided.
Design Problem: Medical Diagnosis Rule-Based Planning
Problem Statement
Design a simple AI planning system for disease diagnosis.

Knowledge Base (Rules)
  1. Fever(X) ∧ Cough(X) → Flu(X)
  2. Flu(X) → Prescribe(Medicine, X)
Given Facts
Fever(John)
Cough(John)

Goal
Prescribe(Medicine, John)
Step-by-Step Solution Using Unification
Step 1: Match Goal with Rule

Goal: Prescribe(Medicine, John)

Compare with Rule 2:
Flu(X) → Prescribe(Medicine, X)

Unification gives:
X = John

New Subgoal: Flu(John)

Step 2: Match Subgoal with Rule

Subgoal: Flu(John)

Compare with Rule 1:
Fever(X) ∧ Cough(X) → Flu(X)

Unification gives:
X = John

New Subgoals:
Fever(John), Cough(John)

Step 3: Check Facts

Given Facts:
Fever(John) ✔
Cough(John) ✔

Both preconditions satisfied.
Final Plan
Fever(John) ∧ Cough(John)
→ Flu(John)
→ Prescribe(Medicine, John)
Role of Unification in this Planning
  • Matches goal with rule head.
  • Substitutes variable X with John.
  • Ensures logical consistency.
  • Enables automated reasoning and rule chaining.
Thus, unification acts as the core mechanism for logical planning, theorem proving, and expert systems in AI.
2. Describe State-Space Search with Suitable Examples such as the Water Jug Problem.

State space search is a problem-solving technique in AI where a problem is represented as a collection of states and transitions between them. The objective is to find a sequence of actions that transforms the initial state into the goal state.
Components of State-Space Search
  • State
  • Initial State
  • Goal State
  • Operators (Actions)
  • Path
  • Search Strategy
Example: Water Jug Problem
Problem Definition

Two jugs:
3-liter jug
5-liter jug

Goal: Measure 4 liters of water.
State Representation
State = (x, y)
x → water in 3L jug
y → water in 5L jug

Initial State: (0, 0)
Goal State: (0, 4)
Possible Actions
  • Fill a jug
  • Empty a jug
  • Pour from one jug to another
State-Space Search Using BFS
Step 1: Start
(0, 0)

Step 2: Fill 5L Jug
(0, 5)

Step 3: Pour 5L → 3L
(3, 2)

Step 4: Empty 3L
(0, 2)

Step 5: Pour 5L → 3L
(2, 0)

Step 6: Fill 5L
(2, 5)

Step 7: Pour 5L → 3L
(3, 4)

Step 8: Empty 3L
(0, 4) ✔ Goal Reached
Search Strategies Used
1. Breadth-First Search (BFS)
Explores level by level.
Complete and optimal for uniform cost problems.

2. Depth-First Search (DFS)
Explores deep before backtracking.
Less memory usage but not always optimal.
Properties of State-Space Search
  • Branching Factor
  • Depth
  • Completeness
  • Optimality
  • Time Complexity
  • Space Complexity
Working Mechanism
  1. Define initial state.
  2. Generate successor states using operators.
  3. Add new states to frontier.
  4. Check goal condition.
  5. Avoid repeated states.
  6. Continue until goal is found or search fails.

State-space search systematically explores all possible configurations and guarantees solution discovery when a valid path exists, making it fundamental in puzzles, robotics, navigation, and AI planning systems.