THE COUNT

What makes postfix notation somewhat difficult at first is the need to see how a particular string is made up. We can do this easily by keeping a count for each letter we have. Any variable will increase the count by 1 and the binary signals A,B,C,D,E,M,O (so-called because each has two elements) decrease the count by 1. The signals N,V,W do not change the count at all, and the presence of a small letter does not change the count. Look at the following examples:

.....1..2..1..2..1.........1..1..2..1..2..1
(1) P Q A R C... (2) P N R C Q O

.....1..1..2..3..2..1..........1..1..2.....1..1
(3) F V G H D C... (4) G W H a O N

The elements for C in (1) are A and R.
...We read this as "If P and Q then R."
The elements for C in (2) are N and R, but the elements for O are C and Q.
...We read this as "Either not-P only if R is true, or Q is true."
The elements for D in (3) are G and H, but the elements for C are V and D.
...We read this as "If everyone is F then everyone who is G is H."
The elements for O in (4) are W and Ha.
...We read this as "It's false that either someone is G or a is H."

One thing to be noted is that every legal string (or well-formed formula) will have a count that begins and ends with 1, and there will never be a 0. What this means in practice is that you have at least a negative check on your symbolization: if the count on your proposed string is incorrect, then you need to see what you have done wrong (usually neglecting to insert a signal where one belongs).

Return to PLN Notation or to Variables and Signals.