Proof theory is a branch of mathematical logic focused on the structure and properties of mathematical proofs. It formalizes reasoning,…
A logical or mathematical argument that demonstrates the truth of a statement or theorem. Proofs rely on axioms, definitions, and…
Permutation is a structural rule in logic that enables the exchange of two formulas on the same side of an…
Monotonic logic ensures that adding new information never invalidates existing conclusions. This property guarantees that derived truths remain valid as…
Logic is the systematic study of valid inference. It explores the structures that ensure conclusions necessarily follow from given premises,…
A lemma is a proven proposition used as a stepping stone to prove larger theorems. It's a foundational tool in…
An inference rule is a logical structure that permits deriving conclusions from premises. It specifies the valid steps in reasoning,…
Logical implication connects two statements: if the first (antecedent) is true, the second (consequent) must also be true. It's a…
Immediate inference is a direct reasoning process where a conclusion is drawn from a single premise. It bypasses intermediate steps,…
An elimination rule in logic simplifies formulas by removing connectives or quantifiers. It's crucial for deriving conclusions from premises, forming…