Non-classical logic

Non-classical logics are formal systems that differ significantly from the classical logic systems such as propositional logic and predicate logic. There are several ways in which this may be the case - for example by variation of certain fundamental laws of classical logic or by their amendments or extensions. The aim of all such differences is to show different ways of logical inference and logical truth and to vary principles that apply within the classical systems as self-evident and unshakable.

Examples

Para Consistent logics are formal systems,

" ... In which the logical principle contradictione ex quodlibet sequitur (Latin for" from a contradiction follows Any " ) does not apply where it is therefore not possible from two contradictory statements A, ¬ A, or a contradiction A ∧ ¬ A infer any statement. "

The intuitionistic logic is based on a different concept of truth than classical logic:

"While in classical logic, the statement truth-functional (see truth value ) is interpreted as " A is true or B is true, " the same statement in the intuitionistic logic is interpreted as" There is a proof of A or there is a proof for B ".

From this different interpretation of the connectives ( connectives ) shows that certain theorems of classical logic into intuitionistic are not valid. One example is the law of excluded middle. The classical interpretation is " A is true or A is not true " and is easily recognizable as valid. The intuitionistic interpretation is " A is proved, or A is refuted ." Under this interpretation of the law of excluded middle is obviously not valid, because on the one hand, there are statements that are neither proven nor disproved, partly because there are statements that are neither provable nor refutable at all. "

Extensions of classical logic

A special type of non-classical logics are extensions of classical logic. In a non-classical extension of additional logical operators are added, eg " " In the modal logic; this new logo stands for "It is necessary, dass .. ". - For extensions of classical logic:

• The amount of well-formulated formulas (expressions) is a proper superset of the set of terms generated by the classical logic.
• The set of provable theorems is a proper superset of the set of theorems which are valid in classical logic - but only in the sense that the " new" theorems of extended logic on the formation of the new expressions are based.

Important classes of non-classical logics

• Multi-valued logic
• Fuzzy logic
• Intuitionistic logic
• Quantum logic
• Modal logic
• Para Consistent logic
• Linear logic, a refinement of classical and intuitionistic logic.
• Relevance logic
• Nonmonotonic logic
• Temporal logic