LUA World Logic Day 2025 - Logic in All its Dimensions

An alternative definition of paraconsistent logic is one that allows for inconsistent but non-trivial theories. In most cases, these two definitions are considered equivalent. The question then arises: are there theories that are inconsistent but still non-trivial? The answer is yes, and this is a major reason for studying paraconsistency. An example can be found in set theory, known as knife set theory. This simple and basic set theory, commonly taught in schools, includes the knife comprehension scheme which allows for the creation of sets based on specific properties. Additionally, the Extensionality Principle states that two sets are equal if they share all the same elements.