Logic is a feminine noun from the Greek term logo, related to the logos, reason, word or speech, which means the reasoning science.
In a figurative sense, the word logic is related to a specific way of reasoning, rightly. For example: This will never work! Your plan has no logic!
You problems or logic games are activities where an individual has to use a logical reasoning to solve the problem.
Aristotelian logic
According to Aristotle, logic has as its object of study the thought, as well as the laws and rules that control it, for that thought to be correct. For the Greek philosopher, the constituent elements of logic are the concept, judgment and reasoning. The laws of logic correspond to the connections and relationships that exist between these elements.
Some successors of Aristotle were responsible for the foundations of medieval logic, which lasted until the thirteenth century. Medieval thinkers such as Galen, Porphyry and Alexander of Aphrodisia classified logic as the science of judging correctly, which makes it possible to reach correct and formally valid reasoning.
Programming logic
Programming logic is the language used to create a computer program. Programming logic is essential for developing computer programs and systems, as it defines the logical chain for that development. The steps for this development are known as an algorithm, which consists of a logical sequence of instructions for the function to be executed.
Argumentation logic
Argumentation logic allows checking the validity or whether a statement is true or not. It is not made with relative or subjective concepts. They are tangible propositions whose validity can be verified. In this case, logic aims to evaluate the form of the propositions and not the content. Syllogisms (composed of two premises and a conclusion) are an example of argumentation logic. For example:
Cornmeal is a dog.
All dogs are mammals.
Therefore, cornmeal is a mammal.
Mathematical logic
Mathematical logic (or formal logic) studies logic according to its structure or form. Mathematical logic consists of a deductive system of statements that aim to create a group of laws and rules to determine the validity of reasonings. Thus, a reasoning is considered valid if it is possible to reach a true conclusion from true premises.
Mathematical logic is also used to build valid reasoning through other reasonings. The reasonings can be deductive (the conclusion is obligatorily obtained from the truth of the premises) and inductive (probabilistic).
Formal logic can be divided into two groups: propositional logic and predicate logic.
Leibniz is seen by many as the mind that initiated the concept of formal logic or mathematics, which addresses the core issues of mathematics. However, it was not until after 1890, with Peano, that the questioning of the consistency of axioms began. Some important principles of formal logic are found in The Mathematical Analysis of Logic by George Boole (author of Boole's logic or algebra).
propositional logic
Propositional logic is an area of logic that examines reasoning according to the relationships between clauses (propositions), the minimal units of discourse, which can be true or false.