Proof-theoretic validity defines a valid proof within proof-theoretic semantics. It focuses on the constructive nature of proofs and their role…
An alternative to truth-condition semantics, proof-theoretic semantics emphasizes the role of proof in understanding meaning. It focuses on how propositions…
Proof-theoretic consequence, also known as syntactic consequence, explores logical entailment based on the structure of proofs within formal systems. It…
Proof theory is a branch of mathematical logic focused on the structure and properties of mathematical proofs. It formalizes reasoning,…
Permutation is a structural rule in logic that enables the exchange of two formulas on the same side of an…
Peirce's law, ((P → Q) → P) → P, is a fundamental principle in logic. It is valid in classical…
Negation introduction is a natural deduction rule enabling the derivation of negation. It typically involves assuming the opposite and deriving…
Metatheory involves the theoretical analysis of mathematical and logical systems. It examines properties, structure, and foundational aspects, providing a meta-level…
A maximal consistent set is a collection of logical formulas that is both consistent and cannot be extended further without…
Mathematical logic is the study of logic within mathematical reasoning. It explores the formal properties of logical systems, proving theorems,…