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 mappings has been 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.

In order to tackle the need of sharing knowledge within and across organisational boundaries, the last decade has seen researchers both in academia and industry advocating for the use of ontologies as a means for providing a shared understanding of common domains. But with the generalised use of large distributed environments such as the World Wide Web came the proliferation of many di#erent ontologies, even for the same or similar domain, hence setting forth a new need of sharing---that of sharing ontologies. In addition, if visions such as the Semantic Web are ever going to become a reality, it will be necessary to provide as much automated support as possible to the task of mapping di#erent ontologies. Although many e#orts in ontology mapping have already been carried out, we have noticed that few of them are based on strong theoretical grounds and on principled methodologies. Furthermore, many of them are based only on syntactical criteria. In this paper we present a theory and method for automated ontology mapping based on channel theory, a mathematical theory of semantic information flow.

As ontologies become ever more important for semanticallyrich information exchange and a crucial element for supporting knowledge sharing in a large distributed environment, like the Web, the demand for sharing them increases accordingly. One way of achieving this ambitious goal is to provide mechanised ways for mapping and merging ontologies. This has been the focus of recent research in knowledge engineering.

I propose a formalisation of knowledge sharing scenarios that aims at capturing the crucial role played by an existing duality between ontological theories one wants to merge and particular situations that need to be linked. I use diagrams in the Chu category and colimits over these diagrams to account for the reliability and optimality of knowledge sharing systems. Furthermore, I show how we may obtain a deeper understanding of a system that shares knowledge between a probabilistic logic program and Bayesian belief networks by re-analysing the scenario in terms of the present approach.