New Essays on Belnap-Dunn Logic

0505161 - ÚI 2020 RIV CH eng M - Část monografie knihy
Sedlár, Igor - Majer, Ondrej
Modelling sources of inconsistent information in paraconsistent modal logic.
New Essays on Belnap-Dunn Logic. Cham: Springer, 2019 - (Omori, H.; Wansing, H.), s. 293-310. Synthese Library. Studies in Epistemology, Logic, Methodology, and Philosophy of Science, 418. ISBN 978-3-030-31135-3
Grant CEP: GA ČR GBP202/12/G061; GA ČR(CZ) GC16-07954J
Institucionální podpora: RVO:67985807 ; RVO:67985955
Klíčová slova: Compatibility * Ex falso quodlibet * First degree entailment * Inconsistent information * Modal logic * Paraconsistent logic * Paraconsistent modal logic * Sources of information
Obor OECD: Pure mathematics; Philosophy, History and Philosophy of science and technology (FLU-F)

Epistemic logics based on normal modal logic are notoriously bad at handling inconsistent and yet non-trivial information. This fact motivates epistemic logics based on paraconsistent logic, examples of which can be traced back at least to the 1980s. These logics handle inconsistent and non-trivial information, but they usually do not articulate sources of the inconsistency. Yet, making the origin of an inconsistency present in a body of information explicit is important to assess the body - can we trace the mutually conflicting pieces of information to sources of information relevant to the body or is the inconsistency a result of an error unrelated to any outside sources? Is the inconsistency derived from various equally trustworthy sources or from a single inconsistent source? In this article we show that a paraconsistent modal logic, namely, the logic BK introduced by Odintsov and Wansing, is a first step toward a formalism capable of making these distinctions explicit. We interpret the accessibility relation between states in a model as a source relation - states accessible from a given state are seen as sources of potential justification of the information contained in the original state. This interpretation also motivates the study of a number of extensions of BK. We focus here on extensions of BK able to articulate the relation of compatibility between bodies of information and extensions working with labels explicitly differentiating between bodies of information. In the case of compatibility-based extensions a more detailed technical study including a completeness proof is provided, technical features of the simpler case of label-based extensions, on the other hand, are discussed without going into details.
Trvalý link: http://hdl.handle.net/11104/0296660