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ASSIGNMENT-2 Q2 (Course Name- Artificial Intelligence) (Course Code - PGS-AI-205)

Assignment Submission

Course: Artificial Intelligence (Course Code - PGS-AI-205)

Topic: Question 2 — Knowledge Representation and Reasoning (KRR)

1. Overview of Knowledge Representation and Reasoning (KRR)

Knowledge Representation and Reasoning (KRR) is a fundamental area of Artificial Intelligence dedicated to representing information about the real world in a structured format that a computer system can process to solve complex problems. An intelligent AI agent cannot rely solely on raw data or hardcoded algorithms; it requires a structured internal model of its domain to make sound decisions.

A typical KRR system consists of two primary components:

  • Knowledge Base (KB): A centralized repository of facts, rules, assertions, and relationships expressed in a formal logic language.
  • Inference Engine: A reasoning mechanism that applies logical rules to the Knowledge Base to derive new facts, verify hypotheses, and answer queries.

For a knowledge representation system to be effective, it should possess four key properties:

  • Representational Adequacy: The ability to express all necessary knowledge in a given domain.
  • Inferential Adequacy: The ability to manipulate structures to yield new knowledge from existing facts.
  • Inferential Efficiency: The ability to guide reasoning mechanisms quickly toward a solution.
  • Acquisition Efficiency: The ease with which new knowledge can be acquired and integrated into the system.

2. Propositional Logic vs. First-Order Logic

A. Propositional Logic (PL)

Propositional Logic is the simplest form of logic in AI. It deals with complete declarative statements called propositions, which can be evaluated as either True or False.

Syntax & Connectives:

  • Variables: Represented by uppercase letters (P, Q, R).
  • Negation (¬): ¬P ("Not P")
  • Conjunction (∧): P ∧ Q ("P and Q")
  • Disjunction (∨): P ∨ Q ("P or Q")
  • Implication (→): P → Q ("If P, then Q")
  • Biconditional (↔): P ↔ Q ("P if and only if Q")

Example: Let P = "It is raining" and Q = "The ground is wet." The statement P → Q represents: "If it is raining, then the ground is wet."

Limitations: Propositional logic treats sentences as indivisible units. It cannot analyze individual objects, properties, or general rules. To express "All humans are mortal," propositional logic would require a separate symbol for every human on Earth, making general statements impossible to write efficiently.

B. First-Order Logic (FOL) / Predicate Logic

First-Order Logic extends propositional logic by introducing objects, relations, and quantifiers, making it far more expressive for complex real-world domains.

Key Building Blocks:

  • Objects: Real-world entities (e.g., John, Apple, Earth).
  • Predicates: Properties or relations between objects (e.g., IsMortal(x), Loves(x, y)).
  • Functions: Mappings returning an object based on input (e.g., FatherOf(x)).
  • Universal Quantifier (∀): "For all" or "Every" (∀x (Human(x) → Mortal(x))).
  • Existential Quantifier (&exists;): "There exists at least one" (&exists;x (Doctor(x) ∧ Kind(x))).

Example: "Every student who studies passes the exam" is formally represented as:
∀x (Student(x) ∧ Studies(x) → Passes(x, Exam))

3. Core Inference Techniques

Inference is the mechanical process of deriving new logical conclusions from existing facts in the Knowledge Base. There are three primary modes of reasoning:

1. Deductive Reasoning (Top-Down / Truth-Preserving)

Moves from general, universally accepted rules to a specific conclusion. If the premises are true, the conclusion is guaranteed to be true.

Structure: Rule: ∀x (P(x) → Q(x)), Premise: P(A) → Conclusion: Q(A)

Example: All birds lay eggs → A parrot is a bird → Therefore, a parrot lays eggs.

2. Inductive Reasoning (Bottom-Up / Probabilistic)

Generalizes broad rules from specific observed instances. The conclusion is probable or plausible, but not logically guaranteed.

Structure: Specific Observations → General Rule

Example: The sun has risen in the east every morning in recorded history → Therefore, the sun will always rise in the east.

3. Abductive Reasoning (Diagnostic / Best Explanation)

Starts with an observation and works backward to infer the most likely hypothesis or cause behind it.

Structure: Observation (Q) + Rule (P → Q) → Hypothesis (P is likely)

Example: The grass outside is wet → Known rule: Rain makes grass wet → Hypothesis: It likely rained last night.

4. Automated Theorem Proving Methods

A. Forward Chaining (Data-Driven)

Forward chaining begins with known facts in the Knowledge Base and continuously applies inference rules (like Modus Ponens) to derive new facts until a target goal is satisfied. It is ideal for real-time monitoring and event-driven processing systems.

B. Backward Chaining (Goal-Driven)

Backward chaining starts from the target query and works backward through conditional rules to determine if matching base facts exist in the Knowledge Base. It is widely used in diagnostic expert systems and logic programming languages like Prolog.

C. Resolution Principle (Refutation Proof)

Developed by Alan Robinson, the Resolution method is a complete and sound inference technique operating on Conjunctive Normal Form (CNF):

  1. Convert all Knowledge Base sentences into CNF (conjunctions of disjunctions).
  2. Negate the target query statement Q and add ¬Q to the Knowledge Base.
  3. Repeatedly apply the resolution rule (A ∨ B) ∧ (¬B ∨ C) → (A ∨ C) to resolve complementary literals.
  4. If an empty clause (■ / Contradiction) is derived, the negated query is proven false, meaning the original query Q is mathematically proven True.

5. Applications in Expert Systems and Intelligent Decision-Making

A. Expert Systems Architecture

An Expert System is an AI software program that emulates the decision-making ability of a human specialist using rule bases (If-Then statements) combined with an inference engine.

  • MYCIN: A historical medical expert system that used backward chaining and certainty factors to identify bacterial infections and recommend suitable antibiotic dosages.
  • DENDRAL: An expert system used in organic chemistry to infer unknown chemical structures based on mass spectrometry data.

B. Intelligent Decision-Making Applications

  • Credit Approval & Financial Underwriting: Rule-based automated engines evaluate applicant risk profiles against regulatory and organizational policies to grant loans instantly.
  • Medical Diagnostic Support: Modern clinical decision support systems combine First-Order Logic and probabilistic reasoning to suggest medical diagnoses based on patient symptoms, blood panels, and genetic markers.
  • Autonomous Systems and Safety Rules: Self-driving vehicles enforce non-negotiable safety constraints (e.g., "If pedestrian detected in lane → apply immediate emergency brakes") represented as high-priority logical rules inside their decision controllers.

Conclusion

Knowledge Representation and Reasoning forms the backbone of symbolic Artificial Intelligence. While Propositional Logic offers a simple foundation for true/false assertions, First-Order Logic expands this to model complex entities and relationships. By combining structured inference techniques (deduction, induction, abduction) with algorithmic theorem provers (resolution, forward/backward chaining), AI systems can build expert knowledge bases capable of explainable, intelligent decision-making in real-world scenarios.