A granularity-based framework of deduction, induction, and abduction

  • Authors:

  • Yasuo Kudo;Tetsuya Murai;Seiki Akama

  • Affiliations:

  • Department of Computer Science and Systems Engineering, Muroran Institute of Technology, 27-1 Mizumoto, Muroran 050-8585, Japan;Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo 060-0814, Japan;1-20-1 Higashi-Yurigaoka, Asao-ku, Kawasaki 215-0012, Japan

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this paper, we propose a granularity-based framework of deduction, induction, and abduction using variable precision rough set models proposed by Ziarko and measure-based semantics for modal logic proposed by Murai et al. The proposed framework is based on @a-level fuzzy measure models on the basis of background knowledge, as described in the paper. In the proposed framework, deduction, induction, and abduction are characterized as reasoning processes based on typical situations about the facts and rules used in these processes. Using variable precision rough set models, we consider @b-lower approximation of truth sets of nonmodal sentences as typical situations of the given facts and rules, instead of the truth sets of the sentences as correct representations of the facts and rules. Moreover, we represent deduction, induction, and abduction as relationships between typical situations.