As others have already said, think of it as NAND, although in traditional logic this is typically called the "Sheffer stroke".

the whole point of this discipline is that this dot is simply a "generic Operator"

you can use whatever symbol you want

all you really know - is the axiom you're given, which transforms one tree structure of operator application into a different one

NAND suggested in replies isn't THE operator, it's AN operator that follows given rules

In "The proof as we know" section he states that the dot is a NAND operation

Quote: "the · dot here can be thought of as representing the Nand operation"

The dot is not simply NAND or NOR.

Search for "What Actually Is the “·”?" for the answer, it's quite complex and fascinating.

I was not able to find anything, can you help with locating what you're talking about?

They meant search for that string in the article, it is a section heading.

It is whatever operation behaves in a manner that makes the statement true.

The source uses ○, not •, for the NAND operation.

> What is this central dot?

Yeah, I wish he had started by defining that. The is hard to understand without it.

Search for "Is There a Better Notation?" in the article, it seems "." is NAND

Technically, his axiom is the definition for what the operator is. Any set together with an operator "•" that satisfies this law is a boolean algebra. Binary logic where •=NAND is one such example because it satisfies the axiom.

it's simply "Generic Operator". The only requirements is to follow axioms for all its input values.

NAND isn't THE operator, it is AN operator that can be in that place.

If there's only 1 value that variables can be - "I", then "I \dot I = I" would be a valid operator that follows given axioms