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.

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.

Abstract. Semantic interoperability has become a key issue for realizing the Semantic Web in its full potential. However, there is a lot of controversy regarding the meaning and scope of the term and scarce formal approaches to the problem of semantic heterogeneity. In this paper, we discuss these approaches and propose a formalisation of semantic interoperability based on the Barwise-Seligman theory of information flow. We argue for a theoretical framework that favours the analysis and implementation of semantic interoperability scenarios. We present an example case of such a scenario where our framework has been applied as well as variations of it in the domain of ontology mapping. 1

. Starting from symmetric monoidal closed (= autonomous) categories, Po-Hsiang Chu showed how to construct new - autonomous categories, i.e., autonomous categories that are self-dual by virtue of having a dualizing object. Recently, Michael Barr extended this to the non-symmetric, but closed, case, utilizing monads and modules between them. Since these notions are well-understood for bicategories, we introduce a notion of cyclic - autonomy for these that implies closedness and, moreover, is inherited when forming bicategories of monads and of interpolads. Since the initial step of Barr's construction also carries over to the bicategorical setting, we recover his main result as an easy corollary. Furthermore, the Chu-construction at this level may be viewed as a procedure for turning the endo1 -cells of a closed bicategory into the objects of a new closed bicategory, and hence conceptually is similar to constructing bicategories of monads and of interpolads. Keywords: closed bicate...

This note investigates two generic constructions used to produce categorical models of linear logic, the Chu construction and the Dialectica construction, in parallel. The constructions have the same objects, but are rather di#erent in other ways. We discuss similarities and di#erences and prove that the dialectica construction can be done over a symmetric monoidal closed basis. We also point out several interesting open problems concerning the Dialectica construction.