Punctuation in "or in other words"

In a Math.SE question, I used the sentence:

“some two of these propositions are true and the third one is false”, or in other words, “exactly 2 of 3 propositions are true”

Here I used “or in other words” to rephrase a statement for better comprehension, but I didn’t use a comma after “or”. On the Net, I see people both using and omitting the comma in that phrase. What is the correct punctuation in the phrase “or in other words” and why?

The comma after words needs to be complemented by one before in because in other words is an integral phrase interrupting the rest of the sentence.

Use a semicolon to join two independent clauses when the second clause begins with a conjunctive adverb (however, therefore, moreover, furthermore, thus, meanwhile, nonetheless, otherwise) or a transition (in fact, for example, that is, for instance, in addition, in other words, on the other hand, even so).

Terrorism in the United States has become a recent concern; in fact, the concern for America's safety has led to an awareness of global terrorism.

http://owl.english.purdue.edu/owl/resource/566/01/ Retrieved on Mar 11, 2013. 11:02 am