lect10 - INTRO LOGIC DAY 10 1 DERIVATIONS IN SENTENTIAL...

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1 1 INTRO LOGIC DAY 10 2 DERIVATIONS IN SENTENTIAL LOGIC 2 nd day

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2 3 Review We demonstrate (show) that an argument is valid by deriving ( deducing ) its conclusion from its premises using a few fundamental modes of reasoning . 4 Initial Modes of Reasoning Modus (Tollendo) Tollens (denying by denying) –––––– Modus (Ponendo) Ponens (affirming by affirming) –––––– Modus Tollendo Ponens (1) (affirming by denying) –––––– Modus Tollendo Ponens (2) (affirming by denying) ––––––
3 5 (10) (9) (8) (7) (6) (5) (4) (3) (2) (1) Example 1 5,9, Q 4,8, P 3,7, T 1,2, R DD : Q Pr P Q Pr P T Pr R T Pr R S Pr S S ; R S ; R  T ; P T ; P  Q / Q MP MTP2 MTP1 MT 1.write all premises 3.apply rules to available lines 4.box and cancel ( high-five! ) 2.write ‘show’ conclusion 6 Rules for Today &I &O & & –––––– –––––– –––––– –––––– & & I O –––––– ––––––   –––––– –––––– I see CD O  ––––––– –––––––  DN DN  ––––– ––––– 

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4 7 Rules of Inference – Basic Scheme every connective has an
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