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Intermediate logic information


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).[1]

  1. ^ "Intermediate logic", Encyclopedia of Mathematics, EMS Press, 2001 [1994].

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Intermediate logic

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superintuitionistic logic; thus, consistent superintuitionistic logics are called intermediate logics (the logics are intermediate between intuitionistic logic and classical...

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Intuitionistic logic

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logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by...

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Outline of logic

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Formal logic Free logic Fuzzy logic Higher-order logic Infinitary logic Informal logic Intensional logic Intermediate logic Interpretability logic Intuitionistic...

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Contradiction

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considering theorems of classical logic that are not theorems of minimal logic. Each of these extensions leads to an intermediate logic: Double-negation elimination...

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Propositional calculus

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branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals...

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Hypersequent

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different components, such as the communication rule for the intermediate logic LC (Gödel–Dummett logic) Γ 1 ⇒ Δ 1 ∣ ⋯ ∣ Γ n ⇒ Δ n ∣ Σ ⇒ A Ω 1 ⇒ Θ 1 ∣ ⋯ ∣ Ω m...

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Classical logic

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Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had...

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Glossary of logic

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Look up Appendix:Glossary of logic in Wiktionary, the free dictionary. This is a glossary of logic. Logic is the study of the principles of valid reasoning...

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Structural proof theory

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\Box A} . Another example is given by the communication rule for the intermediate logic LC Γ 1 ⊢ Δ 1 ∣ ⋯ ∣ Γ n ⊢ Δ n ∣ Ω ⊢ A Σ 1 ⊢ Π 1 ∣ ⋯ ∣ Σ m ⊢ Π m ∣ Θ...

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Michael Dummett

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mathematical logic, he developed an intermediate logic, a logical system intermediate between classical logic and intuitionistic logic that had already...

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Logic level

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circumstances that produce intermediate levels, so that the circuit behaves predictably. Nearly all digital circuits use a consistent logic level for all internal...

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Natural deduction

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Michael (2022). Logic primer (3rd ed.). Cambridge, Massachusetts: The MIT Press. ISBN 978-0-262-54364-4. Bostock, David (1997). Intermediate logic. Oxford :...

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Law of excluded middle

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well-studied intermediate logic is given by De Morgan logic, which adds the axiom ¬ P ∨ ¬ ¬ P {\displaystyle \neg P\lor \neg \neg P} to intuitionistic logic, which...

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Fuzzy logic

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Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept...

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List of Hilbert systems

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A\to (A\to B)} Intermediate logics are in between intuitionistic logic and classical logic. Here are a few intermediate logics: Jankov logic (KC) is an extension...

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Logic model

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Logic models are hypothesized descriptions of the chain of causes and effects leading to an outcome of interest (e.g. prevalence of cardiovascular diseases...

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Outline of philosophy

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Face-to-face Classical logic Intermediate logic Intuitionistic logic Minimal logic Relevant logic Affine logic Linear logic Ordered logic Dialetheism Absurdism...

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Modal companion

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In logic, a modal companion of a superintuitionistic (intermediate) logic L is a normal modal logic that interprets L by a certain canonical translation...

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Boolean algebra

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In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the...

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Principle of bivalence

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value, either true or false. A logic satisfying this principle is called a two-valued logic or bivalent logic. In formal logic, the principle of bivalence...

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Truth value

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assigned a truth value. Unproven statements in intuitionistic logic are not given an intermediate truth value (as is sometimes mistakenly asserted). Indeed...

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Method of analytic tableaux

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(1997). Intermediate Logic. Oxford University Press. ISBN 978-0-19-156707-0. Carnielli, Walter A. (1987). "Systematization of Finite Many-Valued Logics Through...

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