A formal system of arithmetic using axioms by Giuseppe Peano, it provides a foundational basis for the theory of natural…
A standardized method for structuring logical formulas like CNF or DNF. Normal forms simplify logical expressions, aiding in analysis, comparison,…
Negation introduction is a natural deduction rule enabling the derivation of negation. It typically involves assuming the opposite and deriving…
Logic is the systematic study of valid inference. It explores the structures that ensure conclusions necessarily follow from given premises,…
A formal framework for modal logic using possible worlds. Developed by Saul Kripke, it enables rigorous analysis of necessity, possibility,…
Gödel numbering assigns unique natural numbers to symbols, formulas, and proofs in formal systems. This allows mathematical statements to be…
A frame in modal logic defines a set of possible worlds and the accessibility relation between them. It serves as…
A first-order theory formalizes mathematical reasoning using first-order logic. It defines relationships between individuals, properties, and relations, forming the foundation…
The field of a function encompasses both its domain (inputs) and its range (outputs). It represents the complete set of…
An explicit definition replaces every instance of a term with its precise meaning. This contrasts with implicit definitions, offering clarity…