On Improving the Scalability of Checking Satisfiability in Probabilistic Description Logics

  • Authors:

  • Pavel Klinov;Bijan Parsia

  • Affiliations:

  • The University of Manchester, Manchester, UK M13 9PL;The University of Manchester, Manchester, UK M13 9PL

  • Venue:
  • SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
  • Year:
  • 2009

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Abstract

This paper presents an approach aimed at improving scalability reasoning in the probabilistic description logic P-$\mathcal{SHIQ}$(D). The satisfiability problem is currently intractable as the existing algorithm generates exponentially large linear optimization systems. To cope with this, we employ advanced optimization techniques that do not require the systems to be fully generated before starting to solve them. One such technique, namely, column generation, can be applied by exploiting the structure of the reasoning problems in P-$\mathcal{SHIQ}$(D) analogously to how it has been used for solving such large optimization problems as constrained shortest path, cutting stock and many others. We present the formulation of the linear systems for the satisfiability problems in the column generation form, describe methods for solving them, discuss their difference from the known column generation approaches to propositional probabilistic logic, and finally show preliminary experimental results that demonstrate a useful improvement of scalability.