substructural logic

Substructural logics are a class of logics where the standard properties of the deduction symbol are weakened. These logics are studied in different fields: relevance logic by philosophers, linear logic by computer scientists, and a noncommutative version of linear logic by linguists.1

While classical logic operates with principles like the excluded third, other logics exist, such as many-valued logics, fuzzy logic, and quantum logic. However, substructural logics represent a significant area of research by modifying the fundamental rules of logical deduction.1

Mathematics can be formulated within axiomatic set theory, and much mathematical reasoning uses logical terms, particularly first-order logic. Symbolic logic, developed in the late 19th century, has profoundly changed the understanding of logic, allowing for the representation of complex statements and inferences.23