Model-theoretic Approaches to Semantic Integration (Extended Abstract)

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Heterogeneous Theories and the Heterogeneous Tool Set

Heterogeneous multi-logic theories arise in different contexts: they are needed for the specification of large software systems, as well as for mediating between different ontologies. This is because large theories typically involve different aspects that are best specified in different logics (like equational logics, description logics, first-order logics, higher-order logics, modal logics), but also because different formalisms are in practical use (like RDF, OWL, EML). Using heterogeneous theories, different formalims being developed at different sites can be related, i.e. there is a formal interoperability among languages and tools. In many cases, specialized languages and tools have their strengths in particular aspects. Using heterogeneous theories, these strengths can be combined with comparably small effort. By contrast, a true combination of all the involved logics into a single logic would be too complex (or even inconsistent) in many cases. We propose to use emph{institutions} as a formalization of the notion of logical system. Institutions can be related by so-called institution morphsims and comorphisms. Any graph of institutions and (co)morphisms can be flattened to a so-called emph{Grothendieck institution}, which is kind of disjoint union of all the logics, enriched with connections via the (co)morphisms. This semantic basis for heterogeneous theories is complemented by the heterogeneous tool set, which provides tool support. Based on an object-oriented interface for institutions (using type classes in Haskell), it implements the Grothendieck institution and provides a heterogeneous parser, static analysis and proof support for heterogeneous theories. This is based on parsers, static analysers and proof support for the individual institutions, and on a heterogeneous proof calculus for theories in the Grothendieck institution. See also the Hets web page: http://www.tzi.de/cofi/het

Basic Semantic Integration

The use of highly abstract mathematical frameworks is essential for building the sort of theoretical foundation for semantic integration needed to bring it to the level of a genuine engineering discipline. At the same time, much of the work that has been done by means of these frameworks assumes a certain amount of background knowledge in mathematics that a lot of people working in ontology, even at a fairly high theoretical level, lack. The major purpose of this short paper is provide a (comparatively) simple model of semantic integration that remains within the friendlier confines of first-order languages and their usual classical semantics and logic

Semantic Integration in the Information Flow Framework

The Information Flow Framework (IFF) is a descriptive category metatheory currently under development, which is being offered as the structural aspect of the Standard Upper Ontology (SUO). The architecture of the IFF is composed of metalevels, namespaces and meta-ontologies, whose core forms a metastack representing the set-theoretic notions of the "small", the "large", the "very large" and the "generic". The main application of the IFF is institutional: the notion of institutions and their morphisms are being axiomatized in the upper metalevels of the IFF, and the lower metalevel of the IFF has axiomatized various institutions (information flow, equational logic, many sorted first order logic, the common logic standard) in which semantic integration has a natural expression

Theoretical Foundations of Learning Communities

This chapter describes the historical and contemporary theoretical underpinnings of learning communities and argues that there is a need for more complex models in conceptualizing and assessing their effectiveness

Theoretical foundations of quantum hydrodynamics for plasmas

Beginning from the semiclassical Hamiltonian, the Fermi pressure and Bohm potential for the quantum hydrodynamics application (QHD) at finite temperature are consistently derived in the framework of the local density approximation with the first order density gradient correction. Previously known results are revised and improved with a clear description of the underlying approximations. A fully non-local Bohm potential, which goes beyond of all previous results and is linked to the electron polarization function in the random phase approximation, for the QHD model is presented. The dynamic QHD exchange correlation potential is introduced in the framework of local field corrections, and considered for the case of the relaxation time approximation. Finally, the range of applicability of the QHD is discussed

Theoretical foundations for information representation and constraint specification

Research accomplished at the Knowledge Based Systems Laboratory of the Department of Industrial Engineering at Texas A&M University is described. Outlined here are the theoretical foundations necessary to construct a Neutral Information Representation Scheme (NIRS), which will allow for automated data transfer and translation between model languages, procedural programming languages, database languages, transaction and process languages, and knowledge representation and reasoning control languages for information system specification