Semantics of logic

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In logic, the semantics of logic or formal semantics is the study of the meaning and interpretation of formal languages, formal systems, and (idealizations of) natural languages. This field seeks to provide precise mathematical models that capture the pre-theoretic notions of truth, validity, and logical consequence. While 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-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 (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.