The dynamic multi-attribute decision making problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two new aggregation operators: dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator and uncertain dynamic intuitionistic fuzzy weighted averaging (UDIFWA) operator are pr...

The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results re...

Bi-intuitionistic logic is a conservative extension of intuitionistic logic with a connective dual to implication, called exclusion. We present a sound and complete cut-free labelled sequent calculus for bi-intuitionistic propositional logic, BiInt, following S. Negri’s general method for devising sequent calculi for normal modal logics. Although it arises as a natural formalization of the Krip...

This paper provides a call-by-name and a call-by-value term calculus, both of which have a Curry-Howard correspondence to the box fragment of the intuitionistic modal logic IK. The strong normalizability and the confluency of the calculi are shown. Moreover, we define a CPS transformation from the call-by-value calculus to the call-by-name calculus, and show its soundness and completeness.

Let T be a first-order theory. A T -normal Kripke structure is one in which every world is a classical model of T . This paper gives a characterization of the intuitionistic theory HT of sentences intuitionistically valid (forced) in all T -normal Kripke structures and proves the corresponding soundness and completeness theorems. For Peano arithmetic (PA), the theory HPA is a proper subtheory o...

‎In this paper we prove that a finite group $G$ having at most three‎ ‎conjugacy classes of non-normal non-abelian proper subgroups is‎ ‎always solvable except for $Gcong{rm{A_5}}$‎, ‎which extends Theorem 3.3‎ ‎in [Some sufficient conditions on the number of‎ ‎non-abelian subgroups of a finite group to be solvable‎, ‎Acta Math‎. ‎Sinica (English Series) 27 (2011) 891--896.]‎. ‎Moreover‎, ‎we s...

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

We consider a general format for sequent rules for not necessarily normal modal logics based on classical or intuitionistic propositional logic and provide relatively simple local conditions ensuring cut elimination for such rule sets. The rule format encompasses e.g. rules for the boolean connectives and transitive modal logics such as S4 or its constructive version. We also adapt the method o...

A natural deduction system NDIL described here admits normalization and has subformula property. It has standard axioms A ` A, ` 1, standard introduction and elimination rules for &,−◦ (linear implication), ⊕ and quantifiers. The rules for ⊗ are now standard too. Structural rules are (implicit) permutation plus contraction and weakening for m-formulas. The rules for ! use an idea of D. Prawitz....