Foundations of Modal Deductive Databases

  • Authors:
  • Linh Anh Nguyen

  • Affiliations:
  • Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland. E-mail: nguyen@mimuw.edu.pl

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2007

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Abstract

We give formulations for modal deductive databases and present a modal query language called MDatalog. We define modal relational algebras and give the seminaive evaluation algorithm, the top-down evaluation algorithm, and the magic-set transformation for MDatalog queries. The results of this paper like soundness and completeness of the top-down evaluation algorithm or correctness of the magic-set transformation are proved for the multimodal logics of belief KDI4$_s$5, KDI45, KD4$_s$5$_s$, KD45$_{(m)}$, KD4I$_g$5$_a$, and the class of serial context-free grammar logics. We also show that MDatalog has PTIME data complexity in the logics KDI4$_s$5, KDI45, KD4$_s$5$_s$, and KD45$_{(m)}$.