Journal of Logic, Language and Information

, Volume 17, Issue 3, pp 285–306

Notions of Sameness by Default and their Application to Anaphora, Vagueness, and Uncertain Reasoning

  • Ariel Cohen
  • Michael Kaminski
  • Johann A. Makowsky
Article

DOI: 10.1007/s10849-008-9057-6

Cite this article as:
Cohen, A., Kaminski, M. & Makowsky, J.A. J of Log Lang and Inf (2008) 17: 285. doi:10.1007/s10849-008-9057-6

Abstract

We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter’s Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We prove that the corresponding default theory has a unique extension, in which every two objects are indistinguishable if and only if their non-equality cannot be proved from the known facts. We show that the indistinguishability relation has some desirable properties: it is reflexive, symmetric, and, while not transitive, it has a transitive “flavor.” The second formalization is an extension (modification) of the ordinary language equality by a similar default: two objects are equal if and only if their non-equality cannot be proved from the known facts. It appears to be less elegant from a formal point of view. In particular, it gives rise to multiple extensions. However, this extended equality is better suited for most of the applications discussed in this paper.

Keywords

Anaphora Default Logic Equality Herbrand models Indistinguishability Rough Set Theory Sorites Vagueness 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Ariel Cohen
    • 1
  • Michael Kaminski
    • 2
  • Johann A. Makowsky
    • 2
  1. 1.Department of Foreign Literatures and LinguisticsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.Department of Computer ScienceTechnion—Israel Institute of TechnologyHaifaIsrael

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