Fuzzy Logic

Question 1

What is the only designated value?

Answer 1

{1}

Question 2

What are the two new connectives in fuzzy?

Answer 2

1. t-norm conjunction (⊗)

2. An added conditional –> (as in L3 and RM3)

Question 3

What are the semantics for infinite valued logic?

Answer 3

(1) ν(A) ∈ [0,1] for all atomic A
(2) ν(A∨B) = max{ν(A),ν(B)}.
(3) ν(A∧B) = min{ν(A),ν(B)}.
(4) ν(¬A) = 1 − ν(A)

(5) ν(A→B) = 1 if ν(A) ≤ ν(B),
1 − ν(A) + ν(B) otherwise

(6) ν(A⊗B) = max{0,ν(A) + ν(B) − 1}

Question 4

When does t-norm get 0?

Answer 4

When both conjuncts are less than zero

Only definitely true when both conjuncts are definitely true

Question 5

When is it valid?

Answer 5

Iff every model of P’s is a model of the Conc

Designation preserving

Question 6

What is the difference in semantics between L and G?

Answer 6

1. ν(¬A) = 1 if ν(A) = 0
   - 0 if ν(A) > 0
2. ν(A→B) = 1 if ν(A) ≤ ν(B)
   - ν(B) otherwise

Question 7

For t-norm, what is useful to remember?

How does this work in G?

Answer 7

Residuation

v(A⊗B) ≤ v(C) iff v(A) ≤ v(B–>C)

Holds in Classical logic

Question 8

Look at lecture notes for the rest

Answer 8

Fuck Aye