Philosophy Formal Logic Questions Medium
Classical and non-classical substructural logic are two different approaches within formal logic that differ in their treatment of structural rules and assumptions.
Classical logic, also known as standard logic, is based on the principle of bivalence, which states that every proposition is either true or false. It follows the law of excluded middle, which asserts that for any proposition P, either P or its negation (not P) must be true. Classical logic also employs the principle of non-contradiction, which states that a proposition and its negation cannot both be true at the same time.
On the other hand, non-classical substructural logic challenges some of the assumptions made in classical logic. It relaxes or modifies certain structural rules, such as weakening, contraction, and exchange, which are fundamental to classical logic. These rules allow for the introduction or elimination of assumptions in logical reasoning.
Non-classical substructural logics, such as relevance logic, linear logic, and paraconsistent logic, reject or restrict some of these structural rules. For example, relevance logic places a stronger emphasis on the relevance of assumptions to the conclusion, while linear logic restricts the use of contraction and weakening rules to ensure a more resource-conscious reasoning.
The main difference between classical and non-classical substructural logic lies in their treatment of assumptions and structural rules. Classical logic assumes the unrestricted use of structural rules, while non-classical substructural logic challenges or modifies these rules to explore alternative approaches to logical reasoning.