Representing Simple Facts in Logic

Predicate logic (first-order logic) extends propositional logic with objects, properties, relations, and quantifiers, making it expressive enough to represent most facts needed by an AI system.

From Propositional to Predicate Logic

Building Blocks

Representing Simple Facts

Classic Example: Marcus the Pompeian

Man(Marcus)
Pompeian(Marcus)
For all x: Pompeian(x) implies Roman(x)
ruler(Caesar)
For all x: Roman(x) implies loyalto(x, Caesar) OR hate(x, Caesar)
For all x, there exists y: loyalto(x, y)
For all x, y: man(x) AND ruler(y) AND tryassassinate(x, y) implies NOT loyalto(x, y)
tryassassinate(Marcus, Caesar)

From these facts, an inference procedure (e.g., resolution) can derive NOT loyalto(Marcus, Caesar) and then hate(Marcus, Caesar) — a textbook demonstration of how predicate logic supports automated reasoning, not just fact storage.

Well-Formed Formulas (WFFs)

A predicate logic sentence must be built following strict syntax rules (a well-formed formula) so that an inference engine can parse and manipulate it mechanically — this precision is predicate logic's biggest advantage over informal representations like plain English or ad-hoc semantic nets.