Derivations in Sentential Logic: Validating Arguments with Modus Ponens and Modus Tollens , Study notes of Reasoning

Download Derivations in Sentential Logic: Validating Arguments with Modus Ponens and Modus Tollens and more Study notes Reasoning in PDF only on Docsity! 1 1 INTRO LOGIC DAY 09 2 UNIT 2 DERIVATIONS IN SENTENTIAL LOGIC 3 Basic Idea We start with a few argument forms, which we presume are valid, and we use these to demonstrate that other argument forms are valid. We demonstrate (show) that a given argument form is valid by deriving (deducing) its conclusion from its premises using a few fundamental modes of reasoning. 4 Example 1 – Modus Ponens (MP) A → C A –––––– C we can employ modus ponens (MP) to derive the conclusion from the premises. if A then C A –––––––––– C P P → Q Q → R R → S –––––– S Example Argument Form 2 5 Example 1 (continued) / S; R→S; Q→R ; P→QP MP Q MP R MP S 6 Example 2 – Modus Tollens (MT) we can employ modus tollens (MT) to derive the conclusion from the premises. Example Argument Form if A then C not C –––––––––– not A ∼S R → S Q → R P → Q –––––– ∼P A → C ~C –––––– ~A 7 Example 2 (continued) / ~P; P→Q; Q→R ; R→S~S MT ~R MT ~Q MT ~P 8 Example 3 – using both MP and MT we can employ a combination of MP and MT to derive the conclusion from the premises. A → C A ––––––– C A → C ~C ––––––– ~A ∼S R → S ∼R → ∼T P → T ∼P → ∼Q ––––––––– ∼Q Example Argument Form