50,820 research outputs found
Compositional bisimulation metric reasoning with Probabilistic Process Calculi
We study which standard operators of probabilistic process calculi allow for
compositional reasoning with respect to bisimulation metric semantics. We argue
that uniform continuity (generalizing the earlier proposed property of
non-expansiveness) captures the essential nature of compositional reasoning and
allows now also to reason compositionally about recursive processes. We
characterize the distance between probabilistic processes composed by standard
process algebra operators. Combining these results, we demonstrate how
compositional reasoning about systems specified by continuous process algebra
operators allows for metric assume-guarantee like performance validation
Generalised Compositional Theories and Diagrammatic Reasoning
This chapter provides an introduction to the use of diagrammatic language, or
perhaps more accurately, diagrammatic calculus, in quantum information and
quantum foundations. We illustrate the use of diagrammatic calculus in one
particular case, namely the study of complementarity and non-locality, two
fundamental concepts of quantum theory whose relationship we explore in later
part of this chapter.
The diagrammatic calculus that we are concerned with here is not merely an
illustrative tool, but it has both (i) a conceptual physical backbone, which
allows it to act as a foundation for diverse physical theories, and (ii) a
genuine mathematical underpinning, permitting one to relate it to standard
mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G.
Chirabella, R. Spekken
Approximate Reasoning with Fuzzy Booleans
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp antecedents; in case of fuzzy booleans this set contains only two rules. It is shown that Zadeh's extension principle is equivalent to the compositional rule of inference using a complete set of fuzzy rules with singleton crisp antecedents. The results are applied to describe the use of approximate reasoning with fuzzy booleans to object-oriented design methods
The compositional rule of inference with several relations
The compositional rule of inference with several relations, which is the mainly used inference rule in approximate reasoning, is considered in this paper. Stability results are given and exact computational formulae are provided
- …