The weak excluded middle asserts that for any proposition P, either P or not-P is provable. This differs from classical…
The turnstile symbol (⊢) signifies syntactic entailment or provability in formal logic. It indicates that a statement on the right…
The single turnstile (⊢) symbol in logic signifies syntactic entailment. It indicates that a formula or set of formulas can…
A theory is Post consistent if it contains at least one unprovable statement. If all statements are provable, the theory…
Negation completeness signifies a logical system's ability to prove either any given statement or its negation. This ensures that no…
The necessitation rule in modal logic states that if a proposition is provable (a theorem), then its necessity is also…
Metamathematics examines mathematical systems and theories from an elevated viewpoint, employing principles of mathematical logic. It explores the foundations and…
Löb's paradox, a puzzle in modal logic, questions the formalization of provability within a system. It leads to counterintuitive results…
A paradox in epistemic logic concerning self-reference, where a statement claims its own unprovability or unknowability, leading to logical contradictions.
A theorem stating that if A implies B is provable, a formula C exists using only common symbols. Both A…