Noncontradictory

Noncontradictory is an adjective used to describe statements, theories, or systems that do not contain contradictions. In logic, a theory or knowledge base is said to be noncontradictory if it is consistent: there is no proof of both a proposition and its negation within the system. In classical logic, consistency implies the non-derivation of any contradiction, and from a contradiction the principle of explosion would allow any statement to be inferred, rendering the system trivial. Therefore, maintaining noncontradictory premises is central to reliable reasoning.

The term also relates to the law of non-contradiction, a foundational principle of classical logic stating that a proposition cannot be both true and false at the same time. Some philosophical positions challenge this principle, but in everyday logical practice, noncontradictory arguments are expected to avoid internal conflicts.

In practical contexts, noncontradictory reasoning is important for mathematics, computer science, and knowledge representation. Ensuring that a database, a formal specification, or a software verifier does not entail contradictory claims helps preserve soundness and predictability. In some non-classical logics, such as paraconsistent logics, a controlled form of inconsistency is permitted without collapsing the system, allowing for reasoning in the presence of conflicting information.

See also: Law of non-contradiction, consistency, paraconsistent logic, model theory, knowledge representation.