An effectively decidable theory is a formal system where an algorithm can definitively prove any statement as either true or…
The double turnstile (⊨) symbol signifies semantic entailment or logical consequence. It indicates that the truth of certain propositions guarantees…
Discharge is the act of eliminating an assumption within a logical derivation. It's a crucial step, often used to prove…
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…
A derivable rule is a logical rule that can be derived from the existing axioms and inference rules of a…
The deduction theorem states that if a statement can be derived from a set of premises plus an additional statement,…
A theory with a decision procedure, allowing algorithmic determination of truth or falsehood for any statement within its framework. This…
A conservative extension adds new axioms or rules to a theory without altering the truth of existing statements. This ensures…
Completeness in logic refers to a system's ability to derive every logically valid formula. It ensures that all truths provable…