The assumption block is found in the Primary drawer of the Blawx toolbox.
The assumption block is used to tell Blawx to assume that the included statement may or may not be true, and enables Blawx to answer questions on the basis of those assumptions.
An assumption block is valid if it has exactly one statement block connected to it.
In the background, the assumption block is implemented as a set of two rules which say, essentially, "statement is true if it is not known false; statement is false if not true." This creates two possible sets of scenarios for Blawx to consider, and Blawx will provide answers from either scenario if the assumption is required in order to answer the question.
Note that because Blawx generates both scenarios, when you are using an assumption block it is typical for a question and it's opposite to both be answerable at the same time.
For instance, if you ask Blawx to assume eligibility, it will be able to find a scenario in which the person is entitled to payment (because they are assumed to be eligible), and a scenario in which they are not (because they are not to be eligible).
Note that if you use a large number of assumptions at the same time, you create exponentially more fact scenarios for Blawx to consider. That may slow down processing of your consider.