Some definitions for BF questions.

Premise: An assumption; A presupposition.
Fact: A piece of information presented as having objective reality.
Consideration: Information that should be kept in mind (while making a decision).
Evidence: The basis for belief or disbelief.
Inference: Logical judgement on the basis of circumstantial evidence and prior conclusions rather than on the basis of direct observation.

Argument : Central to every CR question is the argument. An argument is an ordered line of reasoning composed of premises, assumptions, and a conclusion. Understanding the elements of an argument is essential to performing well in this section.

Premise
Each CR argument contains at least one premise. Premises are pieces of information that provide evidence used to support the conclusion of the argument. For the purposes of Critical Reasoning arguments, premises are facts not subject to dispute.

Conclusion
The conclusion is the endpoint of the line of reasoning of an argument. Think of it as the result of the argument. The line of reasoning leading to a conclusion is often where errors in logic are made.

Assumption
Assumptions are unstated facts and logical connections in an argument. In order for the conclusion of an argument to be true, the assumptions upon which that argument is based must also be true.

Principle: something fundamental that we do not question. This would be somewhat stronger than a fact because it is not specific to a limited number of cases but instead, apply to a broader range of scenarios(and often deeper in meaning). For instance, you will not talk about the principle that crime is increasing in large cities. Instead, it is a fact which applies to large cities. However, you will talk about the principles of Physics or the fundamental principles of Human Rights. I believe principles convey a stronger connotation than mere facts.

Fact: something taken as true at face value (stats, historical events)

Evidence: what is used to support a conclusion (examples, stats, historical events). Although these may include facts, it is usually stronger than facts because they are direct elements needed for the conclusion to stand whereas facts are not necessary for the latter to stand

Pre-evidence: This is a bit of a stretch. It will not often be on the test but it seems very similar to "background" information as described below.

Background: Elements needed to put the evidence into context but which, as stand alone pieces of information, might not constitute what is called an evidence necessary to arrive at a conclusion. For instance, blood tests performed on one thousand persons may reveal that 35% of those persons were HIV infected. However, the background information could be that the test was performed in more underinformed regions of the world where AIDS knowledge is at a minimum. As you can see, the fact that the test was performed in more underinformed regions is not in and of itself an evidence because it does not allow us to come to a conclusion. Instead, the 35% stats, as a stand-alone piece of info, is what will lead us to the conclusion we want. However, the background info is also crucial and cannot be omitted; it is required background info.

Consideration: Something which was taken into account or given some thought before arriving to the conclusion.

Premise: This is usually a required statement to arrive at a conclusion. Evidence and facts want to prove something to you whereas premises are there to logically lead you to a conclusion. The best example of premises is the ones included in syllogisms. For instance, you can say that(premise1) when it rains, you go outside. Then, it rains(premise2). You have to be outside(conclusion).

Assumption: Unstated information which will link the argument to a logical conclusion. Without this, the argument falls apart.

Conclusion: Self-explanatory

Inference: Something that might not be explicitly stated or proved. For instance, you may say that 95% of GMAT test-takers have over 340. We can reasonably infer that Anthony will get more than 340 on his GMAT based on the fact given. I think the main difference b/w an inference and a conclusion is that the former might not be the final line of an argument. For instance, there could be facts/evidence given, an inference in b/w, and then the conclusion. An inference can be an intermediate step before the conclusion which will sum up the whole passage. Also, a conclusion seems to be stronger because it is based on stronger facts/evidence.

I find these from foreign websites. Hope this helps.

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