Strong completeness in logic means that if a formula is true in all interpretations (semantically valid), it can be proven…
Sequent calculus is a formal system for logical entailments, representing deductions as sequences of formulas. It emphasizes structural rules, providing…
Provability logic, a subset of modal logic, explores the formal properties of provability. It uses modal operators to express concepts…
Proof-theoretic consequence, also known as syntactic consequence, explores logical entailment based on the structure of proofs within formal systems. It…
A standardized structure for first-order logic where all quantifiers (universal and existential) are moved to the beginning of the formula,…
Negation elimination is a fundamental rule in natural deduction. It permits inferring a conclusion by negating a premise, provided it…
Negation consistency ensures a logical system is free from contradictions, meaning no statement and its negation can both be proven…
Negation completeness signifies a logical system's ability to prove either any given statement or its negation. This ensures that no…
Natural deduction is a system of logical inference that aims to emulate human reasoning. It uses introduction and elimination rules…
Instantiation is the core process of replacing bound variables with specific constants. This action effectively removes quantifiers, leading to concrete…