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Logical argumentation is the framework within which reasoning and proof are undertaken. It involves presenting a series of statements that, when taken together, lead the listener or reader to a logical conclusion. The foundation of this systematic process rests upon well-defined premises and the logical connections that link them to a conclusion.

In the context of the given exercise, our starting point is the formulation of an 'If A, then B' statement, known as a conditional statement. The contrapositive, an integral part of logical argumentation, then takes the form 'If not B, then not A'. This could be seen as flipping the original statement on its head. But why is this useful? Formulating an argument through contrapositive allows us to deduce information from what is not present or what did not occur, which can be just as informative as understanding what did happen. Thinking contrapositively is a powerful logical technique that can strengthen a deductive argument and provide clarity in situations where direct evidence may not be available.

Within the realm of logical reasoning, 'if-then statements', technically known as conditionals, form the backbone of deductive reasoning. They establish a relationship between two propositions, where the occurrence of the first (the antecedent) is a sufficient condition for the occurrence of the second (the consequent).

The typical structure is 'If A (antecedent), then B (consequent)'. For example, 'If an animal is a dog, then it is a mammal'. In practice, such statements are widely used to form hypotheses or predictions that can be tested. They are the basic unit from which more complex logical arguments are made.

However, crucially, the truth of a conditional statement doesn't guarantee the existence of a causal relationship between A and B, but rather a conditional or dependent connection. The contrapositive of such a statement carries the same truth value as the original statement. Understanding how to utilize 'if-then statements' in logical arguments is critical for analyzing premises and reaching valid conclusions.

Logical reasoning is the process of using a rational, systematic series of steps based on premises, rules, and axioms to arrive at a conclusion. It's a cornerstone of mathematics, philosophy, and logic, and is divided into two main types: inductive reasoning and deductive reasoning.

Deductive reasoning involves starting with a general premise and moving towards a specific conclusion. With the contrapositive — essential for deductive reasoning — we establish a definitive link between the original statement and its contrapositive. If one is true, the other must be true, and if one is false, the other must be false as well. In the given exercise, the argument, 'If the ground is not wet, then it has not rained', is a product of deductive reasoning based on the observable condition of the ground.

This form of reasoning allows us to make conclusions based on the rules and premises set forth in our starting statement. In everyday life as in academics, being adept at logical reasoning is invaluable for problem-solving, decision-making, and analyzing complex situations.