First-order logic in Artificial Intelligence

First-Order Logic (FOL), or Predicate Logic, is used in AI for representing knowledge and reasoning. It extends Propositional Logic by adding quantifiers, variables, predicates, and functions, making it more expressive.

Key Components:

• Constants: Specific objects (e.g., John, Paris).
• Variables: Generic objects (e.g., x, y).
• Predicates: Properties or relationships (e.g., Loves(John, Mary)).
• Quantifiers:
  • Universal (∀): “For all.”
  • Existential (∃): “There exists.”
• Logical Connectives: AND (∧), OR (∨), NOT (¬), IMPLIES (→).

Example Sentences:

• Atomic: Loves(John, Mary).
• Complex: ∀x (Human(x) → Mortal(x)).

Use in AI:

1. Knowledge Representation: Represent facts and rules.
2. Reasoning: Derive new facts using logic.
3. Planning: Encode actions and goals.
4. NLP: Interpret language as logical statements.

Advantages:

• Expressive: Models complex relationships.
• Logical: Supports reasoning and proofs.

Limitations:

• Complexity: Inference can be computationally expensive.
• Decidability: Some problems may not terminate.

FOL is powerful for structured reasoning and formal knowledge representation in AI.