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

Ariel Cohen, Michael Kaminski, Johann A. Makowsky

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
Pages (from-to)285-306
Number of pages22
JournalJournal of Logic, Language and Information
Volume17
Issue number3
DOIs
StatePublished - 1 Jul 2008

Keywords

  • Anaphora
  • Default logic
  • Equality
  • Herbrand models
  • Indistinguishability
  • Rough set theory
  • Sorites
  • Vagueness

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Philosophy
  • Linguistics and Language

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