Derivation is the process of establishing a result from a set of premises or axioms using logical rules. It's fundamental…
A theorem is a statement proven true through logical deduction from accepted axioms and previously proven theorems. It forms a…
Syntactic consequence defines the relationship between premises and conclusions derived through logical rules and axioms within a formal system. It…
A subtheory is a specialized theory nested within a broader one. It shares some axioms and theorems but focuses on…
Soundness ensures that a logical system's derived theorems are always true under any interpretation. It's a fundamental property for reliable…
A schema is a template or pattern used in logic to represent a class of similar statements or propositions. It's…
A model in logic and mathematics interprets the symbols of a formal language, satisfying the axioms and theorems of a…
Modal operators like necessity (◻) and possibility (◊) alter a statement's truth value, indicating whether it must be true or…
A logical theorem is a statement proven true within a formal system. It relies on axioms and inference rules, representing…
A formal proof is a rigorous demonstration of truth within a formal system. Each step is precisely justified by a…