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

paraconsistent logic has been dubbed paraconsistency, which encompasses the school of dialetheism. In classical logic (as well as intuitionistic logic and most...

Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the...

mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, is an explanation of the meaning of proof in intuitionistic logic, proposed...

In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent...

connectives "and" and "or" of intuitionistic logic do not satisfy de Morgan's laws as they do in classical logic. Intuitionistic logic substitutes constructability...

arguments. Modal logics explore concepts like possibility and necessity, examining the inferential structure of these concepts. Intuitionistic, paraconsistent...

classical logic, negation is normally identified with the truth function that takes truth to falsity (and vice versa). In intuitionistic logic, according...

notions of intuitionistic truth values, see the Brouwer–Heyting–Kolmogorov interpretation and Intuitionistic logic § Semantics. Multi-valued logics (such as...

In intuitionistic analysis and in computable analysis, indecomposability or indivisibility (German: Unzerlegbarkeit, from the adjective unzerlegbar) is...

although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting...

Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory (MLTT)) is a type theory and an alternative foundation of...

added to intuitionistic logic to create new intuitionistic connectives and to simulate the monadic elements of intuitionistic first order logic. In the...

in modal logic. The method of forcing is employed in set theory, model theory, and recursion theory, as well as in the study of intuitionistic mathematics...

mathematics. Founder(s): K F. Gödel (1933) showed that intuitionistic logic can be embedded into modal logic S4. (other systems) Interpretation (Gödel): ◻ P...

logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson. It is an intuitionistic and paraconsistent logic,...

theory, the Dialectica interpretation is a proof interpretation of intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive recursive...

(P\lor \neg P)} already in the more conservative minimal logic. In words, intuitionistic logic still posits: It is impossible to rule out a proposition...

Three out of the four implications of de Morgan's laws hold in intuitionistic logic. Specifically, we have ¬ ( P ∨ Q ) ↔ ( ( ¬ P ) ∧ ( ¬ Q ) ) , {\displaystyle...

inference in classical logic but it is invalid in intuitionistic logic. Another classical principle not part of intuitionistic logic is the law of excluded...

logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡...

principles of classical logic and are often seen as its rivals. Intuitionistic logic is based on the idea that truth depends on verification through a...

Heyting algebras were introduced in 1930 by Arend Heyting to formalize intuitionistic logic. Heyting algebras are distributive lattices. Every Boolean algebra...

probability theory. He also contributed to the mathematics of topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory...

opposed to classical logic, which is a formal theory of truth—that integrates and extends classical, linear and intuitionistic logics. Dynamic semantics...

(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...

truth of "if P then Q". Peirce's law does not hold in intuitionistic logic or intermediate logics and cannot be deduced from the deduction theorem alone...

non-classical logic (such as intuitionistic logic), and in the study of modal logic. Interpretations used to study non-classical logic include topological...

theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic. Born into a wealthy German-speaking family in Brno,...

to intuitionistic logic and other non-classical systems. The development of Kripke semantics was a breakthrough in the theory of non-classical logics, because...