Definition - 'Logic' can be defined as the philosophical study and analysis of arguments.
Definition - An 'argument' is a set of claims, one of which is meant to be supported by the others.
Definition - a 'premise' is any statement which acts as the reason or evidence to support a conclusion.
Definition - a 'conclusion' is any statement which is supported by a premise or premises.
Self defense is a basic human right. - premise
Therefore, everyone should carry a handgun. - conclusion
Definition - The logical connection that links a premise and conclusion is an 'inference'.
Definition - a 'statement' is a sentence which is either true or false (i.e., that has a truth-value).
Definition - a 'proposition' is the meaningful content of a statement.
If it's cloudy outside, then it will rain today.
Sufficient condition - If you let go of the hammer, it will fall to the ground.