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Z is a formal specification language for describing sequential software systems. As the use of Z increases, the quality of Z specifications as effective means of communication arises. The aim of this paper is to contribute to a systematic assessment of the quality of Z specifications as perceived by their stakeholders. A pragmatic quality framework for Z specifications using notions from semiotics, cognitive psychology, and information system quality is proposed. The goals for pragmatic quality, and manageable criteria and mechanisms to address them in a feasible manner are identified. The utility and trade-offs of the mechanisms in achieving the quality goals of the framework are analyzed. Examples that lead to compromise of pragmatic quality in a Z specification, and techniques for improvement, are given.

Theoretical and computational frameworks of complexity science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal binary operations in mathematical models, limits our capacity to faithfully capture irreducible polyadic interactions in higher-order systems. A paradigmatic example of a higher-order interaction is the Borromean link of three interlocking rings. In this paper, we propose a mathematical framework via hypergraphs and hypermatrix algebras that allows to formalize such forms of higher-order bonding and connectivity in a parsimonious way. Our framework builds on and extends current techniques in higher-order networks — still mostly rooted in binary structures such as adjacency matrices — and incorporates recent developments in higher-arity structures to articulate the compositional behavior of adjacency hypermatrices. Irreducible higher-order interactions turn out to be a widespread occurrence across natural sciences and socio-cultural knowledge representation. We demonstrate this by reviewing recent results in computer science, physics, chemistry, biology, ecology, social science, and cultural analysis through the conceptual lens of irreducible higher-order interactions. We further speculate that the general phenomenon of emergence in complex systems may be characterized by spatio-temporal discrepancies of interaction arity.

As software agents get more sophisticated, it becomes difficult to understand and model such systems. This paper contends that all developers bring to the task of development some implicit or explicit assumptions of the agent communication pattern. This issue is not readily addressed in current literature and represents a gap in knowledge. For this purpose, a generic pattern of inter-agent communication is introduced and discussed in this paper. For better understanding and modelling of agent-based e-commerce systems, the semiotic approach and the DEMO transaction concept are briefly introduced. It is shown that the semiotic approach offers a unifying framework for identifying the roles of agents, the responsible human agents and the right/constraints associated with each role. The DEMO transaction concept is applied to model the communicative interaction between agents.

This paper reports some novel approach on linguistic logic with our intention to realize CWW, Computing With Words, via a simple example which consists of only five words. As a by product, this simple example of the linguistic logical system may serve as a mathematical model, modeling the degree of truthfulness in daily usage. The five words set of a linguistic variable modeling the degree of truthfulness are; true, nearly true, undecided, nearly false and false. We subjectively choose trapezoidal fuzzy numbers as our linguistic truth values in order to model our linguistic logic system. Firstly, some natural operations and linguistic logic operators are defined to suit our objective of developing a closed linguistic variable set. Then the computation of linguistic truth values for this linguistic logical system is developed in order to facilitate us to perform the linguistic inferences. Properties of these natural operations can be derived accordingly. It is perhaps quite rewarding to see numerous linguistic truth relations defined on a single linguistic truth set and linguistic implications ended up with numerous linguistic truth tables. In addition, the linguistic inferences of generalized modus ponens and generalized tollens determined by linguistic compositional rules based on the linguistic truth relation and some natural operations are introduced. The simple examples of the linguistic inferences of the various generalized tautologies are illustrated. Finally, we have proved via a simple dictionary that a closed and self consistent linguistic logical system indeed can be constructed and it is possible to move a chunk of information as modeled by a fuzzy set to a higher level according to the theory of semiotics. These results have shown some promise in realizing the appealing theory of CWW.