Conclusion: the final step of the argument; the statement it was meant to establish.

Fallacious: An inference in an argument is fallacious if it does not logically follow from the previous steps.

Inference: A statement in an argument that is claimed to logically follow from one or more previous steps in the argument.

Premise: A statement in an argument that is accepted without any further argument—without it following from anything else.

Sound: A valid argument in which the premises are true. Since its premises are true and its premises logically imply the conclusion, the conclusion of a sound argument must be true as well.

Valid: an argument in which the premises logically imply the conclusion, irrespective of the truth of the premises. So an argument can be valid even if its conclusion is false.  For example:

(1)       If aliens have landed, then Donald Trump has purple hands. [Premise]

(2)       Aliens have landed. [Premise]

(3)       Donald Trump has purple hands.  [1,2]