Logic and Logical Philosophy 8 (2):115-152 (2000)

Joao Marcos
Universidade Federal do Rio Grande do Norte
Walter Carnielli
University of Campinas
This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning.
Keywords logic  paraconsistency  databases
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DOI 10.12775/LLP.2000.008
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References found in this work BETA

On Inferences From Inconsistent Premises.Nicholas Rescher & Ruth Manor - 1970 - Theory and Decision 1 (2):179-217, 1970-1971.
Paraconsistent extensional propositional logics.Diderik Batens - 1980 - Logique and Analyse 90 (90):195-234.
Doklady Akademii Nauk SSSR.[author unknown] - 1964 - Journal of Symbolic Logic 29 (2):98-100.

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What If? The Exploration of an Idea.Graham Priest - 2017 - Australasian Journal of Logic 14 (1).

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