@phdthesis{Srinivasa2001, author = {Srinivasa, Srinath}, title = {An algebra of fixpoints for characterizing interactive behavior of information systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-000000143}, school = {BTU Cottbus - Senftenberg}, year = {2001}, abstract = {The dynamics of an information system (IS) is characterized not only by its computational behavior, but also by its interactive behavior. Interactive dynamics forms an integral part of most information systems. Despite this, an understanding of the interactive nature of an IS is still low. Interaction impacts expressiveness of an IS at such fundamental levels that Wegner [Weg97, Weg99a] came with a contention saying interactive behavior cannot be modeled by Turing Machines (TMs). A TM is considered the foundational model of computation. It models computable functions that map between problem and solution domains. However, a TM models only non-interactive mappings. A mapping between a problem and a solution domain that is interactive in nature can change its direction of computation resulting from intermediate interactions. Based on this contention, Wegner proposes interaction (rather than computation) as the fundamental framework for IS modeling [Weg99]. In this thesis, we address Wegner's contention and the nature of interactive dynamics. An information system is modeled as a collection of semantic processes or Problem Solving Processes (PSPs). If these PSPs are interactive in nature, they are called open systems; and if they are non-interactive, such an IS is called a closed system. Intuitively, open system dynamics are known to be richer than closed system dynamics. We make this distinction precise in this thesis. Interaction is shown to be made up of three properties: computation, persistence of state across computations, and channel sensitivity. Persistence of state and channel sensitivity each contribute to richer behavioral semantics than just computation. This is shown by introducing a concept called the solution space of a semantic process. A solution space is the abstract domain characterized by the process dynamics. Interactive solution spaces are found to be richer than algorithmic solution spaces and also interactive solution spaces require at least a three-valued system of logic for their characterization. The earlier question of interactive behavior as applied to IS design is then revisited. Interactive dynamics of an IS characterize the IS functionality. We call the solution space of interactive IS behavior as its interaction space. The interaction space of an IS is contrasted with the object space of the IS which is concerned with the IS structure and state maintenance dynamics. The interaction space has a degree of autonomy with respect to the object space. This aspect is often not acknowledged in IS design, resulting in the intermixing of structural and functionality concerns. Separating these concerns can avoid certain conflicting problems in IS design, as well as provide better maintainability. We call this the "dual" nature of open systems. Based on this insight we propose an IS design paradigm called dualism, where an IS model is made up of an object schema, characterizing the IS structure and an interaction schema, characterizing the IS functionality. The interaction schema is characterized by a three-valued system of logic, representing a set of obligated (or liveness) behavior, permitted (or possible) behavior and forbidden behavior. The system should perform the obligated behavior to be termed functional; it may perform any of the permitted behavior and it may not perform forbidden behavior. An analysis of the dynamics of any real world system can make these three-valued characteristics apparent. Domain theory is used to propose solution space concept, and deontic logic is used to represent the three modalities of interactive IS behavior.}, subject = {Dialogsystem; Informationssystem; Semantischer Bereich; Fixpunkt ; Bereichstheorie; Deontische Logik; Interactive behavior of information systems; Tuning machine; Persistence of state; Object schema; Interaction schema}, language = {en} }