Inference Rules

Abstract

A B –––––– A&B A&B –––––– A A&B –––––– B ~(A&B) =========== A → ~B vI vO ∼ ∼ ∼ ∼vI/O A –––––– A∨B B –––––– A∨B A∨B ∼A –––––– B A∨B ∼B –––––– A ~(A∨B) ∼A –––––– A→B B –––––– A→B A→B A –––––– B A→B ∼B –––––– ∼A ~(A→B) =========== A & ~B ↔ ↔ ↔ ↔I ↔ ↔ ↔ ↔O ∼ ∼ ∼ ∼↔ ↔ ↔ ↔I/O A→B B→A –––––– A↔B A↔B –––––– A→B A↔B –––––– B→A ~(A↔B) =========== ∼A↔B I O DN A ∼A –––– ––– A ~∼A ===== A Note: The ~O and ~I rules are combined, using a long equals sign '==='. Henceforth, any rule that is displayed with '===' is a bi-directional rule, which can be used both as an in-rule and as an out-rule.