Intuitionistic dependence logic was introduced by Abramsky and Väänänen [AV09] as a variant of dependence logic under a general construction of Hodges’ (trump) team semantics. It was proven that there is a translation from intuitionistic dependence logic sentences into second order logic sentences. In this paper, we prove that the other direction is also true, therefore intuitionistic dependenc...

We study the system IFP of intuitionistic fixed point logic, an extension first-order logic by strictly positive inductive and coinductive definitions. define a realizability interpretation use it to extract computational content from proofs about abstract structures specified arbitrary classically true disjunction free formulas. The is shown be sound with respect domain-theoretic denotational ...

In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of statements, and added formulas expressing questions and dependencies to this classical core. In this paper, we broaden the scope of these investigations by studying...

The intuitionistic sequent calculus (at most one formula on the right-hand side of sequents) comes with a natural dual system: the dual-intuitionistic sequent calculus (at most one formula on the left-hand side). We explain how the duality between these two systems exactly corresponds to the intensively studied duality between call-by-value systems and call-by-name systems for classical logic. ...

We define a propositionally quantified intuitionistic logic Her+ by a natural extension of Kripke's semantics for propositional intuitionistic logic. We then show that Har+ is recursively isomorphic to full second order classical logic. Her+ is the intuitionistic analogue of the modal systems S57r+, S47r+, S4.27r+, K47r+, Tir+, K7r+ and Bir+, studied by Fine. ?

There are many symmetries in intuitionistic fuzzifying topology. In the present paper, notion of topology as an extension and a preliminary research on bi-intuitionistic fuzzy is introduced. A theory with semantic method logic established.