Borderline vs. unknown: comparing three-valued representations of imperfect information |
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Institution: | 1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università di Milano-Bicocca, Viale Sarca 336/14, 20126 Milano, Italy;2. IRIT, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 4, France;3. Department of Engineering Mathematics, University of Bristol, Queen''s Building, University Walk, Bristol BS8 1TR, United Kingdom |
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Abstract: | 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. |
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Keywords: | Kleene logic Partial models Orthopairs Vagueness Incomplete information Belnap logic Supervaluations |
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