Dear All,

I am trying to teach myself some modal logic by reading A Short Introduction to Modal Logic by Grigori Mints. (If anyone recommends another introduction, I will look into that.)

Already on p.4 I encounter a problem. I cite. “We can also state the truth-table definitions of the logical connectives in abbreviated linear form. First of all we have

value of not-a = 1 - value of a."

Okay, I can see why, since if v(a) = 1, then v(not-a)=1-1=0, whereas it is 1 if v(a)=0. This makes perfect sense. Then Mintis proceeds to defining the truth table of the disjunctive connective V in "abbreviated linear form" as well.

"The table for V has only one zero value for the case when both arguments are zero. This gives

1) v(aVb)=max(v(a),v(b))
2) v(aV0)=v(a)
3) v(aV1)=1"

It is (1) above that I don't understand. I don't know what max(v(a),v(b)) stands for. Mintis has not previously defined the "max(v(x))". 2) and 3) are obvious to me, but not 1)...

I would appreciate any help in explaining this. I googled for "abbreviated linear form" but could not find any explanation as to what the max stands for.