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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL

[basic rules used in proofs of propositional logic]

14 ideas
A: we may assume any proposition at any stage [Lemmon]
MPP: Given A and A→B, we may derive B [Lemmon]
MTT: Given B and A→B, we derive A [Lemmon]
DN: Given A, we may derive A [Lemmon]
CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon]
∧I: Given A and B, we may derive A∧B [Lemmon]
∧E: Given A∧B, we may derive either A or B separately [Lemmon]
∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon]
∨I: Given either A or B separately, we may derive A∨B [Lemmon]
RAA: If assuming A will prove B∧B, then derive A [Lemmon]
Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD]
Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington]
Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read]
Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS]