# Intuitionistic

### Some articles on intuitionistic:

Realizability
... be seen as a formalization of the BHK interpretation of intuitionistic logic in realizability the notion of "proof" (which is left undefined in the BHK interpretation) is ... Beyond giving insight into intuitionistic provability, realizability can be applied to prove the disjunction and existence properties for intuitionistic theories and to ...
General Frame - Intuitionistic Frames
... The frame semantics for intuitionistic and intermediate logics can be developed in parallel to the semantics for modal logics ... An intuitionistic general frame is a triple, where is a partial order on F, and V is a set of upper subsets (cones) of F which contains the empty set, and is ... In particular, an intuitionistic frame is called tight, if implies , compact, if every subset of with the finite intersection property has a non-empty intersection ...
Variants of Linear Logic
... Different intuitionistic variants of linear logic have been considered ... When based on a single-conclusion sequent calculus presentation, like in ILL (Intuitionistic Linear Logic), the connectives ⅋, ⊥, and ? are absent, and linear implication is treated as a ... In FILL (Full Intuitionistic Linear Logic) the connectives ⅋, ⊥, and ? are present, linear implication is a primitive connective and, similarly to ...
Arend Heyting
... of Luitzen Egbertus Jan Brouwer at the University of Amsterdam, and did much to put intuitionistic logic on a footing where it could become part of mathematical logic ... Heyting gave the first formal development of intuitionistic logic in order to codify Brouwer's way of doing mathematics ... opposed in principle to the formalisation of certain intuitionistic principles (and went as far as calling Heyting's work a "sterile exercise") ...
Encoding Classical/intuitionistic Logic in Linear Logic
... Both intuitionistic and classical implication can be recovered from linear implication by inserting exponentials intuitionistic implication is encoded as !A ⊸ B, and classical implication as !A ⊸ ?B ... many times as we need, which is always possible in classical and intuitionistic logic ... Formally, there exists a translation of formulae of intuitionistic logic to formulae of linear logic in a way which guarantees that the original formula ...