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

Ciucci, Davide and Dubois, Didier and Lawry, Jonathan Borderline vs. unknown: comparing three-valued representations of imperfect information. (2014) International Journal of Approximate Reasoning, 55 (9). 1866-1889. ISSN 0888-613X

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Official URL: http://dx.doi.org/10.1016/j.ijar.2014.07.004


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.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at International Journal of Approximate Reasoning website : http://www.sciencedirect.com/science/article/pii/S0888613X14001157#
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > University of Bristol (UNITED KINGDOM)
Other partners > Università degli Studi di Milano-Bicocca - BICOCCA (ITALY)
Laboratory name:
Deposited On:11 Feb 2015 08:49

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