An NP-complete fragment of fibring logic

  • Yin Wu
  • Min Jiang
  • Zhongqiang Huang
  • Fei Chao
  • Changle Zhou


The fibring method provides a semantic way to take various modal logics as arguments to produce an integrated one, and the benefit of this method is clear: a stronger expressive power. In this article, we prove the computational complexity of a class of fibring logics. Especially for a fibring logic composed of two S 5 systems, we present a novel reduction method, Fibring Structure Mapping, to settle its complexity. Then, we found a special N P -complete fragment for the fibred S 5 system. The significance of these results is that, on the one hand, the reduction method presented in this article can be generalized to settle the computational complexity problem of other fibring logics, and on the other hand, they help us to achieve a balance between the expressive power and the difficulty of computation.


Computability logic Combining logics Fibring semantics Computational complexity 

Mathematics Subject Classification (2010)

03B45 03B62 03D15 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Yin Wu
    • 1
  • Min Jiang
    • 1
  • Zhongqiang Huang
    • 1
  • Fei Chao
    • 1
  • Changle Zhou
    • 1
  1. 1.Department of Cognitive Science and TechnologyXiamen University and Fujian Key Laboratory of Brain-like Intelligent SystemsXiamenChina

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