CISC 204 Lecture Notes - Lecture 4: Modus Ponens, Sequent, Thq
25 Sep 2017
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Proof by contradiction and the law of excluded middle. The textbook provides four additional rules, each of which can be deduced or derived from the ten basic rules. The proofs are in the textbook so we will simply state the rules and then use them. In this class, we will de ne and use the remaining two derived rules. A proof by contradiction, abbreviated as pbc, is a derived rule that is based on the rule of negation introduction i. To prove a conclusion , the negation is assumed; if this assumption leads to a contradiction then the assumption was false. Suppose that: the truth of p and the falsity of q implies r; that r is false; and that p is true. We can conclude that q is true. p q r, r, p q. Proof strategy: the proof can be performed by writing down the premises of the sequent, then using a single instance of proof by contradiction.
