Why was $1 \text{ OR } 1$ undefined in Boole's logic?

Question

I read that Boole's original OR function in which 1 or 1 was undefined then it has been modified so that while the formerly undefined case is now defined it is defined to 0(XOR) .
1- why Boole's original OR function in which 1 or 1 was undefined ?
2- why they redefine it ?

Answer 1

What you have read is misrepresenting Boole. See page 57 of Boole's Investigation of the Laws of Thought. Boole used $x + y(1-x)\,$ for inclusive disjunction and $x(1-y) + y(1-x)\,$ for exclusive disjunction. So Boole's definitions give $1 \lor 1 = 1 + 1 \cdot (1 - 1) = 1\,$ and $1 \oplus 1 = 1\cdot 0 + 1\cdot 0 = 0\,$ just as we would expect today.