If the logic was primary abstracted from its initial conversational context, there is not necessary to leave apart the movement that inspires any debate.
On the contrary, to abstract and retain movement from a conversational context could prove to be a deeper way of making abstractions. A representational view of conversations is the imagistic counterpart of reducing speeches to some logical chains of unmoved propositions. And if we describe a conversation picturing its interlocutors and its surrounding place, we did not say much about it.
However, we are always in need of a profound abstraction in order to place ourselves on a position as high as possible for an intelligible apprehension of the things observed. By representation, imagistic or logical, we are just far from things and not in an apprehensive way. Also, if we are too close to things, they cannot say anything to us.
The abstraction of movement from a conversation means that we have to consider reasoning starting from our common way of understanding movement. For instance, an argument which stays firmly related to some initial admissions or postulates would be viewed as a useless and confusing turning around.