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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 ...
This principle was established by Brouwer in 1928 [1] using intuitionistic principles, and can also be proven using Church's thesis. The analogous property in classical analysis is the fact that every continuous function from the continuum to {0,1} is constant.
Intermediate logics are in between intuitionistic logic and classical logic. Here are a few intermediate logics: Jankov logic (KC) is an extension of intuitionistic logic, which can be axiomatized by the intuitionistic axiom system plus the axiom [13].
The cut-elimination theorem (or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus.It was originally proved by Gerhard Gentzen in part I of his landmark 1935 paper "Investigations in Logical Deduction" [1] for the systems LJ and LK formalising intuitionistic and classical logic respectively.
A more complex definition of hereditary Harrop formulae is used in logic programming as a generalisation of Horn clauses, and forms the basis for the language λProlog. Hereditary Harrop formulae are defined in terms of two (sometimes three) recursive sets of formulae. In one formulation: [4]
A process theory is a system of ideas that explains how an entity changes and develops. [1] Process theories are often contrasted with variance theories, that is, systems of ideas that explain the variance in a dependent variable based on one or more independent variables. While process theories focus on how something happens, variance theories ...
Kripke semantics for intuitionistic logic follows the same principles as the semantics of modal logic, but it uses a different definition of satisfaction. An intuitionistic Kripke model is a triple W , ≤ , ⊩ {\displaystyle \langle W,\leq ,\Vdash \rangle } , where W , ≤ {\displaystyle \langle W,\leq \rangle } is a preordered Kripke frame ...