Analytic Tableaux Calculi for KLM Logics of Nonmonotonic Reasoning

@article{Giordano2009AnalyticTC,
  title={Analytic Tableaux Calculi for KLM Logics of Nonmonotonic Reasoning},
  author={Laura Giordano and Valentina Gliozzi and Nicola Olivetti and Gian Luca Pozzato},
  journal={ACM Trans. Comput. Log.},
  year={2009},
  volume={10},
  pages={18:1-18:47}
}
We present tableau calculi for the logics of nonmonotonic reasoning defined by Kraus, Lehmann and Magidor (KLM). We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative, and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered and we study their complexity. 
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