How can working memory relate to the role of visual imagery in deductive reasoning?

Current views on working memory:

"flexibly deployable, limited cognitive resources, namely activation, that support both the execution of various symbolic computations and the maintenance of intermediate products generated by these computations" (Shah & Miyake, 1996, p. 4).

"the brain system for holding and manipulating a small amount of information temporarily" (Cowan & Morey, 2006, p. 139)

"a system responsible for the active maintenance, manipulation, and retrieval of task relevant information" (Unsworth & Engle, 2008, p. 616)

"is needed when control is needed to override automatic response tendencies" (Unsworth & Engle, 2007, p. 105)

"fulfills two basic functions, maintenance and retrieval: (a) Maintenance is needed to keep new and novel information in a heightened state of activity, particularly in the presence of internal and external distraction. (b) Because the system is limited by how much information can be maintained at any given time, sometimes retrieval of that information in the presence of irrelevant information is required. To retrieve task relevant information, a discrimination process is needed to differentiate between relevant and irrelevant information on the basis of a combination of cues, particularly context cues" (Unsworth & Engle, 2007, p. 105)

A system for temporarily storing and maintaining information in the performance of complex cognitive processing (Baddeley, 2001)

Thus, after Unsworth & Engle (2007), I take the view that individual differences in working memory have a lot to do with the degree to which the system is able to effectively focus on what's relevant, and keep what's irrelevant (at least at the present moment) out of focus while working on the task at hand.

This has implications for understanding the relationship between visual imagery and deductive reasoning. Regardless of the theoretical controversy surrounding computational explanations of deductive reasoning, we can probably agree that the nature of the task requires that the system focus on the logical relations between the entities described in the premises in order to make a deductive inference. For this reason, if Knauff & Johnson-Laird (2002) argue that the deductive reasoning process can be impeded by the phenomenal experience of a visual image, than it follows that working memory should be implicated, and that individual differences in working memory might constrain the direction or degree of this relationship. For instance, individuals with "high working memory capacity" or "high-spans" are, by our understanding of working memory, more effective at maintaining task-relevant processing; therefore, the impeding effect of a visual image should be smaller for high-spans. Conversely, the impeding effect might be larger for "low-spans" due to their diminished capacity to maintain task-relevant processing.