Propositional Logic

Propositional Logic, a.k.a. Zero-Order Logic, or the Propositional Calculus, is a logistic system for reasoning about propositions (statements which are exclusively true or false).

Syntax

The formulas of propositional logic are given by:

    FORMULA  →  VAR  |  "F"  |  "(" FORMULA "⇒" FORMULA ")"
    VAR      →  p  |  q  |  r  ...

For arbitrary formulas A and B

    ~A is an abbreviation for (A ⇒ F)
    T  is an abbreviation for ~F
    (A ∨ B) is an abbreviation for (~A ⇒ B)
    (A ∧ B) is an abbreviation for ~(~A ∨ ~B)
    (A ≡ B) is an abbreviation for (A ⇒ B) ∧ (B ⇒ A)

Semantics

Rules of Inference

Properties of Propositional Logic

Soundness

Consistency

Completeness

Decidability

What Propositional Logic Cannot Express