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.

1

INTRO LOGICINTRO LOGICDAY 13DAY 13

Derivations in SLDerivations in SL55

2

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)

3

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

––––

I

––––––

––––––

O

()––––––––

O––––––

––––––

I ––––––

––––––

O

–––––– &

–––––– &

&I & ––––––

& ––––––

&O

–––––

–––––

DN

()––––––––&

O

(&)––––––––

&O

4

Rules (so far)Rules (so far)

D: D As :

CD: CD As:

DD: DD

ID: ID As :

5

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

6

Show-Conditional StrategyShow-Conditional Strategy

: As

: °

°

°

CD

??

7

Show-Negation StrategyShow-Negation Strategy

: As

: °

°

D

DD

8

Show-Atomic StrategyShow-Atomic Strategy

: As

: °

°

ID

DD

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

9

Show-Disjunction StrategyShow-Disjunction Strategy

: [] As

: °

°

ID

DD

10

Show-Conjunction StrategyShow-Conjunction Strategy

: &&

: ° ° °

: ° ° °

&D

??

??

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)

&O

O

&O

O

12

(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

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

IOO

14

THETHE END END