Many-Valued Logic

SYMBOLIC LOGIC

MANY-VALUED LOGIC

ANSWERS TO REVIEW QUESTIONS

#1

p | ~p

T | F

I | I

F | T

#2

p | q | p à q

T | T | T

T | I | I

T | F | F

I | T | T

I | I | I

I | F | I

F | T | T

F | I | T

F | F | T

#3

p | q | p & q

T | T | T

T | I | I

T | F | F

I | T | I

I | I | I

I | F | F

F | T | F

F | I | F

F | F | F

#4

p | q | p V q

T | T | T

T | I | T

T | F | T

I | T | T

I | I | I

I | F | I

F | T | T

F | I | I

F | F | F

#5

p | q | q & p | p à (q & p)

T | T | T | T

T | I | I | I

T | F | F | F

I | T | I | T

I | I | I | I

I | F | F | I

F | T | F | T

F | I | F | T

F | F | F | T

#6

Classical logic evaluates any given sentence as either true or false. How does Kleene’s system evaluate any given sentence?

True, false, or indeterminate

#7

Classical logic classifies sentences as either: tautological, contingent, or contradictory. How does Kleene’s many-valued system classify sentences?

Unexceptional, contradictory, contingent

#8

Classify each of the following sentences:

(1) Larry is the best midshipmen in the bunch. contingent

(2) Either you will graduate or you will not. unexceptional

(3) She was and was not born in Greenville, North Carolina. contradictory

#9

Classical logic holds as a logical truth the law of the excluded middle, that is, the rule p V ~p. Does many-valued logic also hold this principle to be true? Why or why not?

No, it does not. Because what makes the rule true is the fact that any given sentence is either true or false. And in many-valued logic sentences can have 3 possible truth values.