"if not" vs "unless"

Maybe a question more than an issue: I've gravitated toward using if not in certain circumstances, and I've figured out why:

In situations where I expect the condition to be false, and the code will normally run, I use unless:

unless name.empty?
  puts "Hello #{name}"
end

However, whenever I expect the condition to be true, and the code will not normally run, I use if not:

if not name == 'Paul'
  STDERR.puts "Unauthorized!"
end

Most people would probably use unless across the board, but in the latter example I'd find that difficult to understand at a glance, simply because the words "if" and "unless" have this semantic meaning associated with them. I'm interested in thoughts on this. This isn't something I particularly planned, so it's really not an attempt to over-complicate: I fell into this pattern of use because of my brain finding it easier to grok the keywords this way, and I eventually realised what I was doing. Thoughts?

Start with issue #329 and read its 29-comment discussion to understand the competing interpretations of if not and unless. Since the issue is framed as a question rather than a requested edit, completion would require an agreed style-guide position and a clearly identified documentation change.