Skeptical Inference Based on C-Representations and Its Characterization as a Constraint Satisfaction Problem

  • Christoph Beierle
  • Christian Eichhorn
  • Gabriele Kern-Isberner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9616)

Abstract

The axiomatic system P is an important standard for plausible, nonmonotonic inferences that is, however, known to be too weak to solve benchmark problems like irrelevance, or subclass inheritance (so-called Drowning Problem). Spohn’s ranking functions which provide a semantic base for system P have often been used to design stronger inference relations, like Pearl’s system Z, or c-representations. While each c-representation shows excellent inference properties and handles particularly irrelevance and subclass inheritance properly, it is still an open problem which c-representation is the best. In this paper, we focus on the generic properties of c-representations and consider the skeptical inference relation (c-inference) that is obtained by taking all c-representations of a given knowledge base into account. In particular, we show that c-inference preserves the properties of solving irrelevance and subclass inheritance which are met by every single c-representation. Moreover, we characterize skeptical c-inference as a constraint satisfaction problem so that constraint solvers can be used for its implementation.

Notes

Acknowledgment

This work was supported by DFG-Grant KI1413/5-1 of Prof. Dr. Gabriele Kern-Isberner as part of the priority program “New Frameworks of Rationality” (SPP 1516). Christian Eichhorn is supported by this Grant. This work benefitted very much from discussions led during Dagstuhl Seminar 15221 “Multi-disciplinary approaches to reasoning with imperfect information and knowledge - a synthesis and a roadmap of challenges”.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Christoph Beierle
    • 1
  • Christian Eichhorn
    • 2
  • Gabriele Kern-Isberner
    • 2
  1. 1.Department of Computer ScienceUniversity of HagenHagenGermany
  2. 2.Department of Computer ScienceTU DortmundDortmundGermany

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