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Intuitionistic logic is related by duality to a paraconsistent logic known as Brazilian, anti-intuitionistic or dual-intuitionistic logic. [13] The subsystem of intuitionistic logic with the FALSE (resp. NOT-2) axiom removed is known as minimal logic and some differences have been elaborated on above.
In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, of intuitionistic logic was proposed by L. E. J. Brouwer and Arend Heyting, and independently by Andrey Kolmogorov. It is also sometimes called the realizability interpretation, because of the connection with the realizability theory of Stephen ...
In intuitionistic analysis and in computable analysis, indecomposability or indivisibility (German: Unzerlegbarkeit, from the adjective unzerlegbar) is the principle that the continuum cannot be partitioned into two nonempty pieces.
Jankov logic (KC) is an extension of intuitionistic logic, which can be axiomatized by the intuitionistic axiom system plus the axiom [13] ¬ A ∨ ¬ ¬ A . {\displaystyle \neg A\lor \neg \neg A.} Gödel–Dummett logic (LC) can be axiomatized over intuitionistic logic by adding the axiom [ 13 ]
The logic of here and there (HT, also referred as Smetanov logic SmT or as Gödel G3 logic), introduced by Heyting in 1930 [21] as a model for studying intuitionistic logic, is a three-valued intermediate logic where the third truth value NF (not false) has the semantics of a proposition that can be intuitionistically proven to not be false ...
The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician can assert the truth of a statement only by verifying the validity of that ...
In intuitionistic logic, the Harrop formulae, named after Ronald Harrop, are the class of formulae inductively defined as follows: [1] [2] [3] Atomic formulae are Harrop, including falsity (⊥); A ∧ B {\displaystyle A\wedge B} is Harrop provided A {\displaystyle A} and B {\displaystyle B} are;
A second-order propositional logic is a propositional logic extended with quantification over propositions. A special case are the logics that allow second-order Boolean propositions , where quantifiers may range either just over the Boolean truth values , or over the Boolean-valued truth functions .