When you want to reject an invitation, do you say no automatically? Even if you think you do, the chances are that you don't. It is very difficult for somebody to reject an invitation outright without giving an excuse or trying to worm their way around the question. This is because certain utterances expect certain responses and if these responses aren't given, then it can be impolite. However, there are several ways to avoid accepting an invitation without being impolite and most people will do this automatically without having to think about it.
Take, for example, a situation whereby your friend invites you to a party that evening and he tells you how fun it will be: they have plenty of drinks and games to play and they are going to order several kinds of pizzas in. He has used every trick in the book to entice you to this party, but you have prior engagements with a maths assignment. First of all, he will ask you if you want to go and, if you really want to go, you would reply almost immediately with a "yes, that sounds great!" However, you have paused for a few moments and delaying a reponse is the first sign of rejection. It is usually followed shortly after by a "well" or some sort of mumbling. Your friend begins to expect that a rejection is coming. To make him feel better, an appreciation of the offer - "well, that's really nice of you to ask, but..." - is added, followed by some sort of mitigated rejection, such as "I don't think I can make it". Interesting to note that this is rarely "I can't make it", but is usually mitigated with modals of uncertainty. The final part of the rejection comes in the form of an obligatory account as to why you cannot go. Modal verbs are also used here, but this time the deontic type, to secure your need to do something else, like your maths assignment.
Such as great deal of work goes into rejecting an invitation that it is suprising that an acceptance is quite the opposite. We can simply say "yes" and end the conversation, but with rejection it is so much more difficult and a lot more is going on.