Knowledge & Reasoning in AI
Propositional Logic, First-Order Logic (FOL), Inference, and Expert Systems.
Knowledge and Reasoning in AI
Knowledge representation and reasoning are essential for building intelligent agents that can understand the world, draw inferences, and make informed decisions.
Propositional Logic
Propositional logic, or Boolean logic, is a simple form of logic where statements are either true or false.
- Propositions: Statements like "It is raining" (P) or "The ground is wet" (Q).
- Logical Connectives: Operations used to combine propositions.
| Connective | Symbol | Example | Meaning |
|---|---|---|---|
| Negation | Not P | ||
| Conjunction | P and Q | ||
| Disjunction | P or Q | ||
| Implication | If P then Q | ||
| Biconditional | P if and only if Q |
Propositional logic lacks the expressive power to describe relationships between objects generally, which limits its application in complex domains.
First-Order Logic (FOL)
First-Order Logic (FOL), also known as predicate logic, extends propositional logic by introducing objects, predicates, functions, and quantifiers.
- Universal Quantifier (): States that a property holds for all elements in a domain. Example:
- Existential Quantifier (): States that there exists at least one element for which the property holds. Example:
In FOL, a fact is often represented as a predicate. Ensure to properly escape characters like \{Fact\} if writing custom syntax processors.
Inference and Expert Systems
Inference is the process of deriving new sentences from existing ones.
Architecture of an Expert System
- Knowledge Base (KB): Contains domain-specific rules and facts.
- Inference Engine: Applies logical rules to the knowledge base to deduce new information.
Expert systems were among the first successful commercial AI systems, widely used in medical diagnosis and financial forecasting.