Loading article…
In logic, the semantics 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.
The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested; the logician traditionally is not interested in the sentence as uttered but in the proposition, an idealised sentence suitable for logical manipulation.
近代論理学以前の論理学の解釈は、アリストテレスの『オルガノン』、特に『解釈論』に基づいていた。多重一般性の問題に対処するには量化子の導入が必要であり、そのためアリストテレスの論理学における主語と述語の分析は不可能であった。項論理学は、アリストテレスの論理学を現代化しようとする試みである。すなわち、アリストテレスの三段論法の精神に則った演繹体系を、量化子に基づく近代論理学の一般性をもって構築しようとするものである。
形式言語の意味論に関する主な現代的アプローチは以下のとおりです。