We see cut-free sequent systems for the basic normal modal logics formed by any combination the axioms d, t,b, 4, 5. These systems are modular in the sense that each axiom has a corresponding rule and each combination of these rules is complete for the corresponding frame conditions. The systems are based on nested sequents, a natural generalisation of hypersequents. Nested sequents stay inside...

We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in Frege proof systems compared to lengths in these new systems. As applications we give near-linear simulations of the propositio...

Digital watermarking has attracted lots of researches to healthcare information management systems for access control, patients' data protection, and information retrieval. The well-known quantization index modulation-(QIM-) based watermarking has its limitations as the host image will be destroyed; however, the recovery of medical images is essential to avoid misdiagnosis. In this paper, we pr...

This paper presents a solution to check integrity constraints in database systems supporting nested transactions. Using nested transactions allows to introduce parallelism inside a transaction and to partially recover failing transactions by deening a hierarchy of sub-transactions. If a constraint is violated by some sub-transactions, it is possible to reach the validation of the nested transac...

This paper introduces a programming language that makes it convenient to extend large software systems and even to compose them in a modular way. JX/MI supports multiple nested inheritance, building on earlier work on nested inheritance in the language JX. Nested inheritance permits modular, type-safe extension of a package (including nested packages and classes), while preserving existing type...

Nested words introduced by Alur and Madhusudan are used to capture structures with both linear and hierarchical order, e.g. XML documents, without losing valuable closure properties. Furthermore, Alur and Madhusudan introduced automata and equivalent logics for both finite and infinite nested words, thus extending Büchi’s theorem to nested words. Recently, average and discounted computations of...

We study interior operators and interior structures in a fuzzy setting.We investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...