Computing Theory Prime Implicates in Modal Logic

  • Manoj K. Raut
  • Tushar V. Kokane
  • Rishabh Agarwal
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 736)


The algorithm to compute theory prime implicates, a generalization of prime implicates, in propositional logic has been suggested in [9]. As a preliminary result, in this paper we have extended that algorithm to compute theory prime implicates of a modal knowledge base X with respect to another modal knowledge base \(\Box Y\) using [1], where Y is a propositional knowledge base and \(X\models Y\) in modal system \(\mathcal {T}\) and we have also proved its correctness. We have also proved that it is an equivalence preserving knowledge compilation and the size of theory prime implicates of X with respect to \(\Box Y\) is less than the size of the prime implicates of \(X\wedge \Box Y\). We have also extended the query answering algorithm in modal logic.


Modal logic Theory prime implicates Knowledge compilation 



Authors thank the National Board for Higher Mathematics, Department of Atomic Energy, Mumbai, India for financial support under grant reference number 2/48(16)/2014/NBHM(R.P.)/R&D II/1392.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Manoj K. Raut
    • 1
  • Tushar V. Kokane
    • 1
  • Rishabh Agarwal
    • 1
  1. 1.Dhirubhai Ambani Institute of Information and Communication TechnologyGandhinagarIndia

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