Table 2 The standard inference rules for predicate logic
From: Predicting protein functions by applying predicate logic to biomedical literature
Rule of inference | Name |
|---|---|
¬ q p → q --------- ∴¬p | Modus Tollens |
p p → q --------- ∴q | Modus Ponens |
p ∧ q --------- ∴p | Simplification |
p q ------- ∴p ∧ q | Conjunction |
p ∨ q ¬p ------- ∴q | Disjunctive Syllogism |
p ---------- ∴p ∨ q | Disjunctive Amplification |
¬p → False ----------- ∴p | Contradiction |
p ∧ q p → (q → r) ---------------- ∴r | Conditional Proof |
p → r q → r --------- ∴ (p ∨ q) → r | Proof by Cases |
p → q q → r --------- ∴ p → r | Law of Syllogism |