Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. Viewpoints-based approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this paper, we propose a category-theoretic framework for the analysis of fuzzy viewpoints. Informally, a fuzzy viewpoint is a graph in which the elements of a lattice are used to specify the amount of knowledge available about the details of nodes and edges. By defining an appropriate notion of morphism between fuzzy viewpoints, we construct categories of fuzzy viewpoints and prove that these categories are (finitely) cocomplete. We then show how colimits can be employed to merge the viewpoints and detect the inconsistencies that arise independent of any particular choice of viewpoint semantics. We illustrate an application of the framework through a case-study showing how fuzzy viewpoints can serve as a requirements elicitation tool in reactive systems. 1

This paper is concerned with establishing broadly-based system-theoretic foundations and practical techniques for the problem of system identification that are rigorous, intuitively clear and conceptually powerful. A general formulation is first given in which two order relations are postulated on a class of models: a constant one of complexity; and a variable one of approximation induced by an observed behaviour. An admissible model is such that any less complex model is a worse approximation. The general problem of identification is that of finding the admissible subspace of models induced by a given behaviour. It is proved under very general assumptions that, if deterministic models are required then nearly all behaviours require models of nearly maximum complexity. A general theory of approximation between models and behaviour is then developed based on subjective probability concepts and semantic information theory The role of structural constraints such as causality, locality, finite memory, etc., are then discussed as rules of the game. These concepts and results are applied to the specific problem or stochastic automaton, or grammar, inference. Computational results are given to demonstrate that the theory is complete and fully operational. Finally the formulation of identification proposed in this paper is analysed in terms of Klir’s epistemological hierarchy and both are discussed in terms of the rich philosophical literature on the acquisition of knowledge. 1

View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, or to perform various types of end-to-end analysis. View merging is complicated by incompleteness and inconsistency of views. Once views are merged, it is useful to be able to trace the elements of the merged view back to their sources. In this paper, we propose a framework for merging incomplete and inconsistent graph-based views. We introduce a formalism, called poset-annotated graphs, which incorporates a systematic annotation scheme capable of modeling incompleteness and inconsistency as well as providing a built-in mechanism for ownership traceability. We show how structure-preserving maps can capture the relationships between disparate views modeled as poset-annotated graphs, and provide a general algorithm for merging views with arbitrary interconnections. We use the i ∗ modeling language [26] as an example to demonstrate how our approach can be applied to existing graph-based modeling languages, especially in the domain of early Requirements Engineering. 1

Abstract. This paper describes a generic strategy for “intelligently ” querying hierarchical semantic networks whose objects are characterized by fuzzy attributes. The strategy is self-adaptable in the sense that the network will keep structuring itself (as long as the user queries the system) by adding more and more detail to an underlying semi-lattice built on top of a (fuzzy) object comparison partial order. Technical bounds are imposed on the fuzziness of the system by formally specifying the network and reasoning about it. In the one direction, fuzziness is welcome insofar as it increases the flexibility and discriminating power of the comparison mechanism. In the opposite direction, arbitrary fuzziness may be counterproductive because it will end up destroying the formal properties desirable for such a mechanism. An experimental illustration of the proposed strategy is presented which re-interprets Prieto-Diáz faceted (fuzzy) scheme for software-component classification and reuse. 1

Data Types and Algebraic Semantics The history of programming languages, and to a large extent of software engineering as a whole, can be seen as a succession of ever more powerful abstraction mechanisms. The first stored program computers were programmed in binary, which soon gave way to assembly languages that allowed symbolic codes for operations and addresses. fortran began the spread of "high level" programming languages, though at the time it was strongly opposed by many assembly programmers; important features that developed later include blocks, recursive procedures, flexible types, classes, inheritance, modules, and genericity. Without going into the philosophical problems raised by abstraction (which in view of the discussion of realism in Section 4 may be considerable), it seems clear that the mathematics used to describe programming concepts should in general get more abstract as the programming concepts get more abstract. Nevertheless, there has been great resistance to u...

The paper discusses some open problems in the field of mathematical fuzzy logic which may have a decisive influence for the future development of fuzzy logic within the next decade. 1

Abstract — A grammatical framework is presented that augments context-free production rules with semantic production rules that rely on fuzzy relations as representations of fuzzy natural language concepts. It is shown how the well-known technique of syntax-driven semantic analysis can be used to infer from an expression in a language defined in such a semantically augmented grammar a weak ordering on the possible worlds it describes. Considering the application of natural language query processing, we show how to order elements in the domain of a relational database scheme according to the degree to which they fulfill the intuition behind a given natural language statement like “Carol lives in a small city near San Francisco”. Key words — context-free grammar, fuzzy relations, linguistics, natural language processing, query interfaces.

Abstract not found

This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy interpretation. It is shown that all fundamental concepts of probability and statistics such as joint distribution, conditional distribution, etc., have meaningful analogs in new context. This approach makes it possible to utilize rich conceptual experience of statistics. Connection with underlying fuzzy logic reveals the logical semantics for fuzzy decision making. Decision-making problems within the framework of IT-categories and generalizes Bayesian approach to decision-making with a prior information are considered. It leads to fuzzy Bayesian approach in decision making and provides methods for construction of optimal strategies. 1 1