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.

This paper begins the discussion of how the Information Flow Framework can be used to provide a principled foundation for the metalevel (or structural level) of the Standard Upper Ontology (SUO). This SUO structural level can be used as a logical framework for manipulating collections of ontologies in the object level of the SUO or other middle level or domain ontologies. From the Information Flow perspective, the SUO structural level resolves into several metalevel ontologies. This paper discusses a KIF formalization for one of those metalevel categories, the Category Theory Ontology. In particular, it discusses its category and colimit sub-namespaces. The Information Flow Framework The mission of the Information Flow Framework (IFF) is to further the development of the theory of Information Flow, and to apply Information Flow to distributed logic, ontologies, and knowledge representation. IFF provides mechanisms for a principled foundation for an ontological framework -- a framework for sharing ontologies, manipulating ontologies as objects, partitioning ontologies, composing ontologies, discussing ontological structure, noting dependencies between ontologies, declaring the use of other ontologies, etc. IFF is primarily based upon the theory of Information Flow initiated by Barwise (Barwise and Seligman 1997), which is centered on the notion of a classification. Information Flow itself based upon the theory of the Chu construction of -autonomous categories (Barr 1996), thus giving it a connection to concurrency and Linear Logic. IFF is secondarily based upon the theory of Formal Concept Analysis initiated by Wille (Ganter & Wille 1999) , which is centered on the notion of a concept lattice. IFF represents metalogic, and as such operates at the structural level of ...

This paper describes a natural deduction formulation for Full Intuitionistic Linear Logic (FILL), an intriguing variation of multiplicative linear logic, due to Hyland and de Paiva. The system FILL resembles intuitionistic logic, in that all its connectives are independent, but resembles classical logic in that its sequent-calculus formulation has intrinsic multiple conclusions. From the intrinsic multiple conclusions comes the inspiration to modify Parigot's natural deduction systems for classical logic, to produce a natural deduction formulation and a term assignment system for FILL.

This paper describes a natural deduction formulation for Full Intuitionistic Linear Logic (FILL), an intriguing variation of multiplicative linear logic, due to Hyland and de Paiva. The system FILL resembles intuitionistic logic, in that all its connectives are independent, but resembles classical logic in that its sequent-calculus formulation has intrinsic multiple conclusions. From the intrinsic multiple conclusions comes the inspiration to modify Parigot’s natural deduction systems for classical logic, to produce a natural deduction formulation and a term assignment system for FILL. keywords: linear logic, λµ-calculus, Curry-Howard isomorphism 1

We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc. 1 What Are Chu Spaces? 1.1 World According to Classical Physics It is well known that measurements can change the measured object: e.g., most methods of chemical analysis destroy a part of the analyzed substance; testing a car often means damaging it, etc. However, in classical (pre-quantum) physics it was assumed that in principle, we can make this adverse influence as small as possible. Therefore, ideally, each measurement can be described as a function r(x) from the set of all objects X to the set K of all measurement results. These measurements lead to a complete knowledge in the sense that an object x can be uniquely reconstructed from the results r(x) of all such measurements. 1.2 Non-Determinism in Modern Physics: En...

The work presented here proposes a framework, the Information Flow Framework (IFF) to accomplish the Standard Upper Ontology (SUO) goal of interoperability, as well as the SUO goals related to automated reasoning and application areas. The IFF is manifested in the formalism of the IFF Foundation Ontology, which is designed to allow not only the interoperability among software and database applications, but also the semantic interoperability among various object-level ontologies themselves. The IFF is designed to support the semantic interoperability among various object-level ontologies. The IFF supports this interoperability by its architecture and its use of a particular branch of mathematics known as category theory. A major reason that the IFF uses the architecture and formalisms that it does is to support modular ontology development.

This paper is an attempt to summarize most things that are related to multiset theory. We begin by describing multisets and the operations between them. Then we present hybrid sets and their operations. We continue with a categorical approach to multisets. Next, we present fuzzy multisets and their operations. Finally, we present partially ordered multisets. 1