Intermediate logic (original) (raw)

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In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent superintuitionistic logic; thus, consistent superintuitionistic logics are called intermediate logics (the logics are intermediate between intuitionistic logic and classical logic).

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dbo:abstract In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent superintuitionistic logic; thus, consistent superintuitionistic logics are called intermediate logics (the logics are intermediate between intuitionistic logic and classical logic). (en) 논리학에서 초직관 논리(超直觀論理, 영어: superintuitionistic logic) 또는 중간 논리(中間論理, 영어: intermediate logic)는 직관 논리보다는 더 강하지만, 고전 논리보다 더 약한 논리 체계이다. (ko) 中間論理 (英: Intermediate logic) は、数理論理学の分野において古典論理と直観主義論理の中間に位置する論理。 この「中間」という意味は、直観主義論理での恒真な命題は中間論理でも恒真であり、古典論理で恒真でない命題は中間論理でも恒真でない、という意味である。 (ja) Na lógica matemática, a lógica superintuicionista é a lógica proposicional estendendo a lógica intuicionista. Lógica clássica é a lógica superintuicionista consistente mais forte; assim, a lógica superintuicionista consistente é chamada de lógica intermediária (a lógica é intermediária entre lógica intuicionista e a lógica clássica). (pt) 中介逻辑是在直觉主义逻辑和经典逻辑之间的中介，这是在它们包含在直觉主义逻辑中不可证明的定理，而又不等于的经典逻辑的意义上说的。这种逻辑也叫做超直觉主义或次经典逻辑。 有連續統的勢个不同的中介逻辑，通常是向直觉主义逻辑增加一个或多个公理而获得的。这种逻辑的例子有： * 直觉主义逻辑（IPC, Int, IL, H） * 经典逻辑（CPC, Cl, CL）：IPC + P ∨ ¬P * 弱排中律逻辑（KC, 逻辑，德·摩根定律逻辑）: IPC + ¬¬P ∨ ¬P * 哥德尔-逻辑（LC）：IPC + (P → Q) ∨ (Q → P) * -Putnam逻辑：IPC +(¬P →(Q ∨ R))→((¬P → Q) ∨ (¬P → R)) * 有限问题的逻辑 * 可实现性逻辑 * Scott逻辑：IPC + ((¬¬P → P) → (P ∨ ¬P)) →（¬¬P ∨ ¬P） * Smetanich逻辑：IPC + (¬Q → P) →（（(P → Q) → P）→ P） 研究中介逻辑的工具类似于直觉主义逻辑所使用的，比如Kripke语义。例如，Gödel-Dummett逻辑相对于线序的Kripke模型完全。 (zh)
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rdfs:comment In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent superintuitionistic logic; thus, consistent superintuitionistic logics are called intermediate logics (the logics are intermediate between intuitionistic logic and classical logic). (en) 논리학에서 초직관 논리(超直觀論理, 영어: superintuitionistic logic) 또는 중간 논리(中間論理, 영어: intermediate logic)는 직관 논리보다는 더 강하지만, 고전 논리보다 더 약한 논리 체계이다. (ko) 中間論理 (英: Intermediate logic) は、数理論理学の分野において古典論理と直観主義論理の中間に位置する論理。 この「中間」という意味は、直観主義論理での恒真な命題は中間論理でも恒真であり、古典論理で恒真でない命題は中間論理でも恒真でない、という意味である。 (ja) Na lógica matemática, a lógica superintuicionista é a lógica proposicional estendendo a lógica intuicionista. Lógica clássica é a lógica superintuicionista consistente mais forte; assim, a lógica superintuicionista consistente é chamada de lógica intermediária (a lógica é intermediária entre lógica intuicionista e a lógica clássica). (pt) 中介逻辑是在直觉主义逻辑和经典逻辑之间的中介，这是在它们包含在直觉主义逻辑中不可证明的定理，而又不等于的经典逻辑的意义上说的。这种逻辑也叫做超直觉主义或次经典逻辑。 有連續統的勢个不同的中介逻辑，通常是向直觉主义逻辑增加一个或多个公理而获得的。这种逻辑的例子有： * 直觉主义逻辑（IPC, Int, IL, H） * 经典逻辑（CPC, Cl, CL）：IPC + P ∨ ¬P * 弱排中律逻辑（KC, 逻辑，德·摩根定律逻辑）: IPC + ¬¬P ∨ ¬P * 哥德尔-逻辑（LC）：IPC + (P → Q) ∨ (Q → P) * -Putnam逻辑：IPC +(¬P →(Q ∨ R))→((¬P → Q) ∨ (¬P → R)) * 有限问题的逻辑 * 可实现性逻辑 * Scott逻辑：IPC + ((¬¬P → P) → (P ∨ ¬P)) →（¬¬P ∨ ¬P） * Smetanich逻辑：IPC + (¬Q → P) →（（(P → Q) → P）→ P） 研究中介逻辑的工具类似于直觉主义逻辑所使用的，比如Kripke语义。例如，Gödel-Dummett逻辑相对于线序的Kripke模型完全。 (zh)
rdfs:label Intermediate logic (en) 초직관 논리 (ko) 中間論理 (ja) Lógica intermediária (pt) 中间逻辑 (zh)
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