A substitution instance is the result of replacing variables in a well-formed formula with other formulas. Each variable must be…
A subformula is a constituent part of a larger logical formula, sharing its own well-formed structure. Understanding subformulas is crucial…
A structural rule in logic, particularly proof theory, governs the manipulation of sequent components. It operates without regard to the…
A strong counterexample in intuitionistic logic disproves an instance of the law of excluded middle. It's a proof of negation,…
Soundness ensures that a logical system's derived theorems are always true under any interpretation. It's a fundamental property for reliable…
The single turnstile (⊢) symbol in logic signifies syntactic entailment. It indicates that a formula or set of formulas can…
Sequent calculus is a formal system for logical entailments, representing deductions as sequences of formulas. It emphasizes structural rules, providing…
Sequent calculus is a formal system representing logical deductions. It uses sequences of formulas before and after a turnstile, signifying…
A fundamental principle in formal logic that permits substituting logically equivalent expressions within proofs. This ensures the argument's validity is…
Reverse mathematics investigates the logical strength of mathematical theorems. It aims to identify the minimal axiomatic systems required to prove…