When you ask a question in Blawx, you are asking Blawx to find one or more minimal combination of statements in which a statement matching your question is true.
It is as though you are saying to Blawx "how might this statement be true?", where "this statement" can be either specific (a yes/no question with no variables) or generic (a search question with variables).
For example, if you ask "[Who] is in the category mortal", where [Who] is a variable, you are asking Blawx to search for any combination of truth statements that are minimally sufficient to support one another, and include a version of the question where "Who" has been replaced with a value from the database and is true.
One answer set might be "socrates is in the category mortal", and "socrates is in the category human". Those two statements together are the minimal valid set that includes a true version of the target statement.
Blawx then displays those answer sets (or models) to you as a set of answers and explanations.
First, Blawx looks at the values that were replaced for the variables in your question (called the bindings), if any, and it groups the answer sets by those bindings. These groups are called "answers", are numbered, and if there are bindings, the bindings are displayed.
Note that if your question is a yes/no question, there are no bindings, and so there can only ever by one answer, which represents "yes".
For each answer, Blawx takes each answer set that had those bindings, and displays it as an explanation for that answer. The explanations are reformatted into a tree, so that statements that were used to derive other statements are nested inside one another, and the statements are translated into natural language, to make them readable.
In the above example, the explanation might read "socrates is mortal, because socrates is human".
If there is more than one answer provided, that means there is more than one set of values that can be used to make the question statement true. For example, if you ask for children of morticia, you will get two answers, one in which the value of "child" is "wednesday", and another in which the value of "child" is "pugsley".
If Blawx is unable to find a set of statements that are consistent with your rules and include the target question statement, Blawx will answer "no models". In a yes/no question, this can be understand to mean that the answer is "no". In a search question, "no models" can be understood to mean "none".
It is possible for your rules to have more than one way of deriving the same bindings. If that is true, each of the different ways of reaching the same conclusion will appear as different explanations for the same answer.
This, in combination with hypothetical reasoning, is very helpful when you are encoding your legislation. You can have Blawx generate all the hypothetical scenarios in which a legal conclusion might hold, according to your code. If any of those explanations do not make sense, that may indicate that you have made a mistake in your code.
We mentioned that the sets returned by Blawx are "minimal". To be more precise, that means that Blawx does not return any information inside an explanation that is not necessary for that explanation to hold. Anything else that can be said that might also be true without contradicting any of the statements in the explanation could also be true, and that explanation would still hold for that reason.
If you ask Blawx "how might it be true that someone is mortal", it may give you an answer. If you then ask Blawx "how might it not be true that someone is mortal", it may give you a different answer, and perhaps about the same person. Why is that? How can both "yes" and "no" be valid answers at the same time?
They aren't, because each explanation that Blawx generates is a different possible world.
Blawx's reasoning deals with uncertainty. It is possible to ask Blawx to simply assume that something is either true, or not, either in your code, or in your tests. If those sorts of assumptions are available, Blawx might very easily find you valid answers and explanations for two opposite questions.
This means that you have to be careful to consider whether the answer to your question is really available by asking Blawx one question, or whether you need to ask that question and its opposite.
Consider a situation in which you want to know if age is ever relevant to eligibility for a benefit. You might ask "under what circumstances is a person eligible for this benefit", and discover that nowhere in any of the explanations is age mentioned. But that doesn't actually answer your question. You would also need to ask "under what circumstances is a person not eligible for this benefit", and see whether age is mentioned in any of those.
It is possible that age is a factor that can exclude you, but cannot include you. So you would not really be getting the answer to your question unless you ran both queries.