Simulation for lattice-valued doubly labeled transition systems

  • Authors:

  • Haiyu Pan;Yongzhi Cao;Min Zhang;Yixiang Chen

  • Affiliations:

  • College of Computer and Information, Anhui Polytechnic University, Wuhu 241000, China;Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China and Key Laboratory of High Confidence Software Technologies, Peking Universi ...;Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2014

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Abstract

During the last decades, a large amount of multi-valued transition systems, whose transitions or states are labeled with specific weights, have been proposed to analyze quantitative behaviors of reactive systems. To set up a unified framework to model and analyze systems with quantitative information, in this paper, we present an extension of doubly labeled transition systems in the framework of residuated lattices, which we will refer to as lattice-valued doubly labeled transition systems (LDLTSs). Our model can be specialized to fuzzy automata over complete residuated lattices, fuzzy transition systems, and multi-valued Kripke structures. In contrast to the traditional yes/no approach to similarity, we then introduce lattice-valued similarity between LDLTSs to measure the degree of closeness of two systems, which is a value from a residuated lattice. Further, we explore the properties of robustness and compositionality of the lattice-valued similarity. Finally, we extend the Hennessy-Milner logic to the residuate lattice-valued setting and show that the obtained logic is adequate and expressive with lattice-valued similarity.