Abstract :
Summary form only given. Process of information system development consists of several phases including, in particular, system analysis, specification, design, and implementation. Each of these phases is based on some abstractions that can be roughly divided into two groups of general and specific abstractions respectively. In this talk we address to such general abstractions as intensionality, compositionality, and nominativity. Intensionality is understood in the traditional sense as a counterpart to extensionality that together complete each other and define the main aspects of notions in their integrity. Compositionality means that a system is constructed of smaller subsystems with the help of special construction operations called compositions. Nominativity emphasizes the importance of naming relations for system aspects description. We analyze and illustrate the use of the above mentioned abstractions in different phases of system development. Considering conventional mathematical formalisms we admit that they are based on the extensionality principle that restricts and complicates usage of such formalisms in system development. Therefore we construct formal mathematical structures based on the principles of intensionality, compositionality, and nominativity. These structures can be considered generalizations of traditional notions of algebras and logics for classes of "dynamic" data and functions. Introduction of such formalisms permits us to define also a special kind of intensionalized computability that better reflects specifics of executable components of information systems. We compare the constructed formalisms with the existing ones and demonstrate that they a rather expressive and more adequate for information system development.
