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What is this central dot? I thought a central dot in boolean logic means logical and but then the axiom is clearly false..... I don't get what this is about.
by cjfd 2y ago
What is this central dot? I thought a central dot in boolean logic means logical and but then the axiom is clearly false..... I don't get what this is about.
- ur-whale 2y ago> 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
- hulium 2y agoTechnically, 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.
- NooneAtAll3 2y agoit'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
- larschdk 2y agoThe source uses ○, not •, for the NAND operation.
- BetterWhisper 2y agoIn "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"
- Tainnor 2y agoAs others have already said, think of it as NAND, although in traditional logic this is typically called the "Sheffer stroke".
- etwas 2y agoThe dot is not simply NAND or NOR. Search for "What Actually Is the “·”?" for the answer, it's quite complex and fascinating.
- NooneAtAll3 2y agothe 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