Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach

OpenDreamKit --- "Open Digital Research Environment Toolkit for the Advancement of Mathematics" --- is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015--2019, the ecosystem of open-source mathematical software systems. From that, OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Research Environments, customised to meet the varied needs of research projects in pure mathematics and applications. An important step in the OpenDreamKit endeavor is to foster the interoperability between a variety of systems, ranging from computer algebra systems over mathematical databases to front-ends. This is the mission of the integration work package (WP6). We report on experiments and future plans with the \emph{Math-in-the-Middle} approach. This information architecture consists in a central mathematical ontology that documents the domain and fixes a joint vocabulary, combined with specifications of the functionalities of the various systems. Interaction between systems can then be enriched by pivoting off this information architecture.Comment: 15 pages, 7 figure

A characteristics framework for Semantic Information Systems Standards

Semantic Information Systems (IS) Standards play a critical role in the development of the networked economy. While their importance is undoubted by all stakeholders—such as businesses, policy makers, researchers, developers—the current state of research leaves a number of questions unaddressed. Terminological confusion exists around the notions of “business semantics”, “business-to-business interoperability”, and “interoperability standards” amongst others. And, moreover, a comprehensive understanding about the characteristics of Semantic IS Standards is missing. The paper addresses this gap in literature by developing a characteristics framework for Semantic IS Standards. Two case studies are used to check the applicability of the framework in a “real-life” context. The framework lays the foundation for future research in an important field of the IS discipline and supports practitioners in their efforts to analyze, compare, and evaluate Semantic IS Standard

Mixing HOL and Coq in Dedukti (Extended Abstract)

We use Dedukti as a logical framework for interoperability. We use automated tools to translate different developments made in HOL and in Coq to Dedukti, and we combine them to prove new results. We illustrate our approach with a concrete example where we instantiate a sorting algorithm written in Coq with the natural numbers of HOL.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

Exploiting conceptual spaces for ontology integration

The widespread use of ontologies raises the need to integrate distinct conceptualisations. Whereas the symbolic approach of established representation standards – based on first-order logic (FOL) and syllogistic reasoning – does not implicitly represent semantic similarities, ontology mapping addresses this problem by aiming at establishing formal relations between a set of knowledge entities which represent the same or a similar meaning in distinct ontologies. However, manually or semi-automatically identifying similarity relationships is costly. Hence, we argue, that representational facilities are required which enable to implicitly represent similarities. Whereas Conceptual Spaces (CS) address similarity computation through the representation of concepts as vector spaces, CS rovide neither an implicit representational mechanism nor a means to represent arbitrary relations between concepts or instances. In order to overcome these issues, we propose a hybrid knowledge representation approach which extends FOL-based ontologies with a conceptual grounding through a set of CS-based representations. Consequently, semantic similarity between instances – represented as members in CS – is indicated by means of distance metrics. Hence, automatic similarity detection across distinct ontologies is supported in order to facilitate ontology integration

Spatial groundings for meaningful symbols

The increasing availability of ontologies raises the need to establish relationships and make inferences across heterogeneous knowledge models. The approach proposed and supported by knowledge representation standards consists in establishing formal symbolic descriptions of a conceptualisation, which, it has been argued, lack grounding and are not expressive enough to allow to identify relations across separate ontologies. Ontology mapping approaches address this issue by exploiting structural or linguistic similarities between symbolic entities, which is costly, error-prone, and in most cases lack cognitive soundness. We argue that knowledge representation paradigms should have a better support for similarity and propose two distinct approaches to achieve it. We first present a representational approach which allows to ground symbolic ontologies by using Conceptual Spaces (CS), allowing for automated computation of similarities between instances across ontologies. An alternative approach is presented, which considers symbolic entities as contextual interpretations of processes in spacetime or Differences. By becoming a process of interpretation, symbols acquire the same status as other processes in the world and can be described (tagged) as well, which allows the bottom-up production of meaning