✅ Proof (logic) §

= a proof (in a calculus) is a concrete and finite configuration of symbols, which adheres to the rules of a given calculus

Requirements §

It must be possible to check:

• If the configuration of symbols adheres to the rules of a given calculus
• What the premises and the conclusion are

Notation §

• $M⊢A$
  • “it exists a proof for $A$ out of the premises $M$
• $⊢A$
  • -> a proof with no premises
  • = theorem

!IMPORTANT §

• • $M⊢A$ does NOT mean ”$A$ follows logically from the premises $M$”
    • that would be: $M\models A$

Types §

• ⬆️ Inductive proof

How to proof: §

• 📏 Calculus (logic)

📖 Example: §

• premises: {¬p}
• conclusion: ¬(p∧q).