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A capacity-based framework encompassing Belnap-Dunn logic for reasoning about multisource information

Ciucci, Davide and Dubois, Didier A capacity-based framework encompassing Belnap-Dunn logic for reasoning about multisource information. (2019) International Journal of Approximate Reasoning, 106. 107-127. ISSN 0888-613X

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Official URL: https://doi.org/10.1016/j.ijar.2018.12.014

Abstract

Belnap–Dunn four-valued logic is one of the best known logics for handling elementary information items coming from several sources. More recently, a conceptually simple framework, namely a two-tiered propositional logic augmented with classical modal axioms (here called BC logic), was suggested by the second author and colleagues, for the handling of multisource information. It is a fragment of the non-normal modal logic EMN, whose semantics is expressed in terms of two-valued monotonic set functions called Boolean capacities. We show BC logic is more expressive than Belnap–Dunn logic by proposing a consequence-preserving translation of Belnap–Dunn logic in this setting. As special cases, we can recover already studied translations of three-valued logics such as Kleene and Priest logics. Moreover, BC logic is compared with the source-processor logic of Avron, Ben Naim and Konikowska. Our translation bridges the gap between Belnap–Dunn logic, epistemic logic, and theories of uncertainty like possibility theory or belief functions, and paves the way to a unified approach to various methods for handling inconsistency due to several conflicting sources of information.

Item Type:Article
Additional Information:Selected papers from 14th European Conference on Symbolic and Quantitative Appro
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 > Università degli Studi di Milano-Bicocca - BICOCCA (ITALY)
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Deposited On:28 Feb 2020 15:03

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