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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
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