Editing Semantics of logic (section)

{{Short description|Study of the semantics, or interpretations, of formal and natural languages}}
{{hatnote|For the linguistics branch, see [[Semantics]]. For other uses, see [[Semantics (disambiguation)]] and [[Formal semantics (disambiguation)]].}}
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{{Formal languages}}

In [[logic]], the '''semantics of logic''' or '''formal semantics''' is the study of the [[Semantics|meaning]] and [[Interpretation (logic)|interpretation]] of [[Formal language|formal languages]], [[Formal system|formal systems]], and (idealizations of) [[Natural language|natural languages]]. This field seeks to provide precise mathematical models that capture the pre-theoretic notions of [[truth]], [[Validity (logic)|validity]], and [[logical consequence]]. While [[Syntax (logic)|logical syntax]] concerns the formal rules for constructing well-formed expressions, logical semantics establishes frameworks for determining when these expressions are true and what follows from them.

The development of formal semantics has led to several influential approaches, including [[Model theory|model-theoretic semantics]] (pioneered by [[Alfred Tarski]]), [[proof-theoretic semantics]] (associated with [[Gerhard Gentzen]] and [[Michael Dummett]]), [[possible worlds semantics]] (developed by [[Saul Kripke]] and others for [[modal logic]] and related systems), [[Algebraic semantics (mathematical logic)|algebraic semantics]] (connecting logic to [[abstract algebra]]), and [[game semantics]] (interpreting logical validity through [[game-theoretic]] concepts). These diverse approaches reflect different philosophical perspectives on the nature of meaning and truth in logical systems.