Logic system

There are numerous systems of logic today. The splits came about due to differences in the focus of study, but also as a result of disagreements. Initial forks of the "original", pretty much unified, logic system, such as it was beginning with Aristotle, up to the XIX century, occurred due to the disagreements over the fundamental principles.

For instance, the Aristotelian, or the classic logic as it is now referred to, is based on the principle of excluded middle. In a traditional logic system something is either true or false, the system does not recognize any other (middle) option. A logic system that does is, for example, a 3-valued logic system that's widely used today in relation to databases - SQL. The SQL logic system has 3 truth values: true, false and null, and a set of rules describing the possible inferences related to these truth values.

As mentioned, a traditional logic system is bi-valued logic system, it has two truth values, namely, true and false. In such a system something is either true or false, not both and not neither. Another of its fundamental rules says that negating a true value yields a false value, and vice-versa, negated false gives (is) true. And yet another rule states that a double negation of a tem is equal to the term, e.g. not not true is true.

These fundamental rules that every logic system has act like axioms in mathematical theorems. A system gets founded on a set of carefully chosen rules, and these rules, i.e. axioms do not require proof, they are taken for granted.

Logic vs logics: The study of logic is not covered by a single uniform system, but there are numerous types of logics (logic systems), divided with respect to the numerous sets of criteria they support.