Towards MKM in the Large: Modular Representation and Scalable Software Architecture

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

Ontology mapping: the state of the art

Ontology mapping is seen as a solution provider in today's landscape of ontology research. As the number of ontologies that are made publicly available and accessible on the Web increases steadily, so does the need for applications to use them. A single ontology is no longer enough to support the tasks envisaged by a distributed environment like the Semantic Web. Multiple ontologies need to be accessed from several applications. Mapping could provide a common layer from which several ontologies could be accessed and hence could exchange information in semantically sound manners. Developing such mapping has beeb the focus of a variety of works originating from diverse communities over a number of years. In this article we comprehensively review and present these works. We also provide insights on the pragmatics of ontology mapping and elaborate on a theoretical approach for defining ontology mapping

A model for information retrieval driven by conceptual spaces

A retrieval model describes the transformation of a query into a set of documents. The question is: what drives this transformation? For semantic information retrieval type of models this transformation is driven by the content and structure of the semantic models. In this case, Knowledge Organization Systems (KOSs) are the semantic models that encode the meaning employed for monolingual and cross-language retrieval. The focus of this research is the relationship between these meanings’ representations and their role and potential in augmenting existing retrieval models effectiveness. The proposed approach is unique in explicitly interpreting a semantic reference as a pointer to a concept in the semantic model that activates all its linked neighboring concepts. It is in fact the formalization of the information retrieval model and the integration of knowledge resources from the Linguistic Linked Open Data cloud that is distinctive from other approaches. The preprocessing of the semantic model using Formal Concept Analysis enables the extraction of conceptual spaces (formal contexts)that are based on sub-graphs from the original structure of the semantic model. The types of conceptual spaces built in this case are limited by the KOSs structural relations relevant to retrieval: exact match, broader, narrower, and related. They capture the definitional and relational aspects of the concepts in the semantic model. Also, each formal context is assigned an operational role in the flow of processes of the retrieval system enabling a clear path towards the implementations of monolingual and cross-lingual systems. By following this model’s theoretical description in constructing a retrieval system, evaluation results have shown statistically significant results in both monolingual and bilingual settings when no methods for query expansion were used. The test suite was run on the Cross-Language Evaluation Forum Domain Specific 2004-2006 collection with additional extensions to match the specifics of this model