Conditional Logic Cb and Its Tableau System

  • Yuri Ozaki
  • Daisuke Bekki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6736)


Conditional logic is a kind of modal logic for analyzing the truth conditions and inferences of conditional sentences in natural language. However, it has been pointed out in the literature that empirical problems plague all of the previously proposed conditional logics. Moreover, C 1 and C 2 are defined by imposing certain restrictions on their Kripke frames, and there exist no corresponding proof systems.

In order to solve these problems, we propose a new system of conditional logic, which we call C b . C b is an extension of C  +  through the addition of new rules on accessibility, and it has a corresponding tableau system. We show that C b has empirical advantages over C 1 and C 2 as a model of inference in natural language, and compare it with other proof systems of conditional logic.


Natural Language Modal Logic Classical Logic Logic System Proof System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yuri Ozaki
    • 1
  • Daisuke Bekki
    • 1
  1. 1.Graduate School of Humanities and SciencesOchanomizu UniversityJapan

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