Exclusion negation in three-valued logic strictly denies the truth of a proposition. Unlike constructive negation, it doesn't assert an opposite…
An effectively decidable theory is a formal system where an algorithm can definitively prove any statement as either true or…
The domain of discourse is the set of all objects under consideration in a logical system. It defines the scope…
A crucial lemma in Gödel's incompleteness theorems. It states that for any formula with one free variable, there exists a…
Deviant logic refers to logical systems that differ from classical logic. These systems explore alternative rules and structures, offering new…
Two theories are deductively equivalent if they can prove the exact same set of theorems. This means they offer the…
A fundamental procedure in proof theory that systematically removes 'cuts' from a proof. This process simplifies proofs and demonstrates that…
A cut rule in proof theory introduces an intermediate conclusion within a deductive proof. This intermediate step is then utilized…
Contradictory statements cannot both be true or both be false. They represent opposing propositions where one negates the other, forming…
Completeness in logic refers to a system's ability to derive every logically valid formula. It ensures that all truths provable…