Before I gave up on finding out what this was and closed the website, I saw that the copyright author on the bottom of the page was German or affiliated with a German university. I'm fine with giving the person a pass on some of this language, and drawing on the German I know (and having lived there, somewhat familiar with how Germans would say things in English), I think:

- argumentation should be arguments or in more words: "these are the arguments I'm presenting to support my claims."

- pro/contra is pros/cons

- I have never heard the word 'dialectical'

- premise-conclusion structure I think is something like hypothesis-conclusion, maybe?