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Formal languages

Languages with precise, specified semantics. Mathematical logic, set theory, type theory, the predicate calculus, formal grammars. Language where meaning isn’t left to use and context but pinned down by rules.

Specification

Formal languages are defined: what expressions are well-formed, how they combine, what they mean. Every expression has a precise interpretation — no context-dependence, no ambiguity in principle. This is what “formal” buys: reasoning can be checked mechanically.

Compositionality

Meaning composes from parts. A formula’s meaning is determined by the meanings of its components and how they’re combined. This property is what lets formal languages scale — large expressions are understood through their structure.

Axiomatic base

Formal languages rest on axioms — primitive terms and rules accepted as starting points. The axioms are chosen, not derived. What follows from them is developed within the language.

Relation to natural languages

Formal languages are not replacements for natural languages. They are distillations — specific aspects of natural language made precise at the cost of expressive range. A formal language captures some structure cleanly by setting aside everything else natural language carries.