Borderline vs. unknown: comparing three-valued representations of imperfect information

Davide Ciucci, Didier Dubois, Jonathan Lawry

Research output: Contribution to journalArticle (Academic Journal)peer-review

37 Citations (Scopus)
256 Downloads (Pure)


In this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and González-Rodríguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and with Belnap logic of conflicting information. The formal similarities between 3-valued approaches to vagueness and formalisms that handle incomplete information often lead to a confusion between degrees of truth and degrees of uncertainty. Yet there are important differences that appear at the interpretive level: while truth-functional logics of vagueness are accepted by a part of the scientific community (even if questioned by supervaluationists), the truth-functionality assumption of three-valued calculi for handling incomplete information looks questionable, compared to the non-truth-functional approaches based on Boolean possibility–necessity pairs. This paper aims to clarify the similarities and differences between the two situations. We also study to what extent operations for comparing and merging information items in the form of orthopairs can be expressed by means of operations on valuation pairs, three-valued valuations and underlying possibility distributions.
Original languageEnglish
Pages (from-to)1866–1889
Number of pages24
JournalInternational Journal of Approximate Reasoning
Issue number9
Publication statusPublished - 11 Jul 2014

Bibliographical note

Date of Acceptance: 03/07/2014


  • Kleene logic
  • Partial models
  • Orthopairs
  • Vagueness
  • Incomplete information
  • Belnap logic
  • Supervaluations


Dive into the research topics of 'Borderline vs. unknown: comparing three-valued representations of imperfect information'. Together they form a unique fingerprint.

Cite this