1. 2 6 argument forms, 15 points each, plus 10 free points symbolic argument forms (no...

1 INTRO LOGIC INTRO LOGIC DAY 13 DAY 13 Derivations in Derivations in SL SL 5

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Page 1: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

INTRO LOGICINTRO LOGICDAY 13DAY 13

Derivations in SLDerivations in SL55

Exam 2 FormatExam 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 sheetrule sheet will be provided.

1 problem from Set D2 problem from Set E2 problems from Set F1 problem from Set G (91-96)

Page 3: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

Inference Rules (so far)Inference Rules (so far)

––––

––––––

()––––––––

O––––––

––––––

I ––––––

––––––

–––––– &

&I & ––––––

& ––––––

–––––

()––––––––&

(&)––––––––

Page 4: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

Rules (so far)Rules (so far)

D: D As :

CD: CD As:

DD: DD

ID: ID As :

Page 5: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

SHOW-STRATEGIESSHOW-STRATEGIESThere are 6 kinds of formulas in Sentential Logic:

For each of these, there is

a suggested show-strategy.

1. atomic formulas P, Q, etc.

2. negations 3. conjunctions &

4. conditionals 5. disjunctions 6. biconditionals

Page 6: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

Show-Conditional StrategyShow-Conditional Strategy

: As

: °

Page 7: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

Show-Negation StrategyShow-Negation Strategy

: As

: °

Page 8: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

Show-Atomic StrategyShow-Atomic Strategy

: As

: °

is atomic (P,Q,R, etc.)

Page 9: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

Show-Disjunction StrategyShow-Disjunction Strategy

: [] As

: °

Page 10: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

Show-Conjunction StrategyShow-Conjunction Strategy

: &&

: ° ° °

NEW RULENEW RULENEW STRATEGYNEW STRATEGY

11(12)

(11)

(10)

(9)

(8)

(7)

(6)

(5)

(4)

(3)

(2)

(1)

Example 1Example 1

11, R

1,9, Q & R

DD : RAs P

CD : P R6, Q

1,4, Q & R

DD : QAs P

CD : P Q&D: (P Q) & (P R)

PrP (Q & R)

Page 12: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

(12)(13)(14)(15)

(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) Example 2Example 2

As QDD : 2,12, P3,12, P

D : Q6,9, 3,8, P1,6, QDD : As PD : P&D: P & QPrQ PPrQ PPrP Q

(16) 14,15,

IOO

OOI

Page 13: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

13(17)(16)

(12)(13)(14)(15)

(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) Example 3Example 3

13,16, 4,15, P

ID : PAs PDD : 2,13, Q

7,10, 4,9, Q1,7, PDD : As QID : Q&D : Q & PAs P QCD: (P Q) (Q & P)PrP QPrP Q

IOO

Page 14: 1. 2 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct

THETHE END END

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