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Discrete mathematics: reasoning rules
2022-07-05 00:58:00 【Xiaobai Xiaozheng】
Rules of reasoning | interpretative statement |
---|---|
Premise introduction rules | Premise can be introduced at any time of proof |
Conclusion introduction rules | At any time of proof , The proved conclusion can be used as the premise of subsequent proof |
Replacement rule | At any time of proof , Any sub propositional formula in a propositional formula can be replaced by an equivalent propositional formula |
Hypothetical reasoning rules | P ∧ (P→Q) ⇒ Q |
Additional rules | P ⇒ P∨Q |
Simplify the rules | P ∧ Q ⇒ P |
Rejection rule | ¬Q∧(P→Q) ⇒ ¬P |
Hypothetical syllogism rule | (P→Q)∧(Q→R) ⇒ P→R |
Disjunctive syllogism rule | ¬P∧(P∨Q) ⇒ Q |
Constructive dilemma rule | (P∨Q)∧(P→R)∧(Q→S) ⇒ (S∨R) |
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