Stone-Type Dualities for Separation Logics

Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a framework through which both algebraic and topological methods can be brought to bear on a logic. We give a systematic treatment of Stone-type duality for the structures that interpret bunched logics, starting with the weakest systems, recovering the familiar BI and Boolean BI (BBI), and extending to both classical and intuitionistic Separation Logic. We demonstrate the uniformity and modularity of this analysis by additionally capturing the bunched logics obtained by extending BI and BBI with modalities and multiplicative connectives corresponding to disjunction, negation and falsum. This includes the logic of separating modalities (LSM), De Morgan BI (DMBI), Classical BI (CBI), and the sub-classical family of logics extending Bi-intuitionistic (B)BI (Bi(B)BI). We additionally obtain as corollaries soundness and completeness theorems for the specific Kripke-style models of these logics as presented in the literature: for DMBI, the sub-classical logics extending BiBI and a new bunched logic, Concurrent Kleene BI (connecting our work to Concurrent Separation Logic), this is the first time soundness and completeness theorems have been proved. We thus obtain a comprehensive semantic account of the multiplicative variants of all standard propositional connectives in the bunched logic setting. This approach synthesises a variety of techniques from modal, substructural and categorical logic and contextualizes the "resource semantics" interpretation underpinning Separation Logic amongst them

Multiple hierarchies : new aspects of an old solution

In this paper, we present the Multiple Annotation approach, which solves two problems: the problem of annotating overlapping structures, and the problem that occurs when documents should be annotated according to different, possibly heterogeneous tag sets. This approach has many advantages: it is based on XML, the modeling of alternative annotations is possible, each level can be viewed separately, and new levels can be added at any time. The files can be regarded as an interrelated unit, with the text serving as the implicit link. Two representations of the information contained in the multiple files (one in Prolog and one in XML) are described. These representations serve as a base for several applications

A distributed file service based on optimistic concurrency control

The design of a layered file service for the Amoeba Distributed System is discussed, on top of which various applications can easily be intplemented. The bottom layer is formed by the Amoeba Block Services, responsible for implementing stable storage and repficated, highly available disk blocks. The next layer is formed by the Amoeba File Service which provides version management and concurrency control for tree-structured files. On top of this layer, the appficafions, ranging from databases to source code control systems, determine the structure of the file trees and provide an interface to the users