formalizations
Formalization is the process of converting informal statements, theories, or reasoning into a formal system consisting of a formal language with precise syntax, semantics, and inference rules. The aim is to remove ambiguity, enable rigorous deduction, and, where possible, support automated verification of correctness.
A formal language defines symbols and formation rules; semantics assign meaning through models or interpretations; a
The typical workflow is to select a suitable formalism (for example, first‑order logic, higher‑order logic, or
Well known applications include the formalization of arithmetic in Peano axioms, set theory in ZFC, and the
Benefits include increased precision and reproducibility, the possibility of machine‑checkable proofs, and the ability to reason
Limitations involve abstraction away from intuition, potential encoding complexity, and undecidability in many systems; formalization can
In philosophy and foundations, formalization is debated as a means to secure certainty versus a risk of