Learn English – What’s the difference between “rise” and “arise”

"Raise" when used as a verb is transitive: it requires that you have a direct object, a noun of some kind that you are applying the verb to. For example, "I must raise an objection"—"an objection" is the object that the subject (I) is using the verb to act upon.

"Rise" on the other hand, is an intransitive verb: it does not require a direct object; your sentence can be complete without one. "Please rise" is entirely correct and complete.

"Hence" means "from here". "Get thee hence!" is old English for "get out of here". "Henceforwards" is "from this time on".

"Thus" means "in this way". In older English, you might say "he opened the door thus", while demonstrating the action.

In logical senses, you can use them in similar contexts. "If x is true, then y is true. X is true. Hence, y is also true." "If x is true, then y is true. I have proved x is true. Thus, I have proved y to be true also."

Think of them as "based on this fact" and "in this way" and you can't go far wrong.