First-order predicate calculus (or first-order logic, predicate-logic) goes beyond describing how propositions relate to each other, which is the subject of propositional calculus by examining how predicates relate to the subjects they specify.

The calculus of first order logic analyzes sentences like the following:

  • "Objects exists, which have the attribute P."
  • "All X have the attribute Y."

In order to analyze sentences and the predicates they contain, we "formalize" the sentences so that they look like this:

  • ∃x ( P(x) )
  • ∀x ( P(x) )

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