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SL5 Day 13 Exam Format: Constructing Derivations in Sentential Logic

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This document outlines the format for Exam 2 in SL5, focusing on the construction of derivations from premises to conclusions using symbolic argument forms. The exam consists of 6 argument forms with 15 points each, plus an additional 10 free points. Students will solve problems from several designated problem sets and apply inference and derivation strategies. The provided rule sheet will help guide students in constructing valid arguments and utilizing key inference rules effectively.

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SL5 Day 13 Exam Format: Constructing Derivations in Sentential Logic

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  1. INTRO LOGIC Derivations in SL5 DAY 13

  2. Exam 2 Format • 6 argument forms, 15 points each, plus 10 free points • Symbolic argument forms (no translations) • For each one, you will be asked to construct a derivation of the conclusion from the premises. • The rule sheet will be provided. • 1 problem from Set D • 2 problem from Set E • 2 problems from Set F • 1 problem from Set G (91-96)

  3. Inference Rules (so far) &O (&) ––––––––   &O & ––––––  & ––––––  &I   –––––– &   –––––– & O   ––––––    ––––––  I  ––––––   ––––––  O () ––––––––   O   ––––––    ––––––  O () –––––––– & DN  –––––   –––––  I   –––– 

  4.  Rules (so far) DD : DD     CD : CDAs:    D : DAs:     ID : IDAs:    

  5. SHOW-STRATEGIES • There are 6 kinds of formulas in Sentential Logic: 1. atomic formulas P, Q, etc. 2. negations  3. conjunctions & 4. conditionals  5. disjunctions  6. biconditionals  For each of these, there is a suggested show-strategy.

  6. Show-Conditional Strategy • :  •  As • :  • ° • ° • ° CD ??

  7. Show-Negation Strategy • :  •  As • :  • ° • ° •  D DD

  8. Show-Atomic Strategy • :  •  As • :  • ° • ° •  ID DD  is atomic (P,Q,R, etc.)

  9. Show-Disjunction Strategy • :  • [] As • :  • ° • ° •  ID DD

  10. Show-Conjunction Strategy &D • : & • :  • ° • ° • ° • :  • ° • ° • ° ?? ?? NEW RULENEW STRATEGY

  11. Example 1 (1) P  (Q & R) Pr (2) : (P  Q) & (P  R) &D (3) : P  Q CD (4) P As (5) : Q DD (6) Q & R 1,4, O (7) Q 6, &O (8) : P  R CD (9) P As (10) : R DD (11) Q & R 1,9, O (12) R 11, &O

  12. Example 2 (1) P  Q Pr (2) Q  P Pr (3) Q P Pr (4) : P & Q &D (5) : P D (6) P As (7) :  DD (8) Q 1,6, O (9) P 3,8, O (10)  6,9, I (11) : Q D (12) Q As (13) :  DD (14) P 2,12, O (15) P 3,12, O (16)  14,15, I

  13. Example 3 (1) P  Q Pr (2) P Q Pr (3) : (P  Q)  (Q & P) CD (4) P  Q As (5) : Q & P &D (6) : Q ID (7) Q As (8) :  DD (9) P 1,7, O (10) Q 4,9, O (11)  7,10, I (12) : P ID (13) P As (14) :  DD (15) Q 2,13, O (16) P 4,15, O (17)  13,16, I

  14. THE END

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