First order theory for literal‐paraconsistent and literal‐paracomplete matrices

Mathematical Logic Quarterly 56 (4):425-433 (2010)
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In this paper a first order theory for the logics defined through literal paraconsistent-paracomplete matrices is developed. These logics are intended to model situations in which the ground level information may be contradictory or incomplete, but it is treated within a classical framework. This means that literal formulas, i.e. atomic formulas and their iterated negations, may behave poorly specially regarding their negations, but more complex formulas, i.e. formulas that include a binary connective are well behaved. This situation may and does appear for instance in data bases



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Natural 3-valued logics—characterization and proof theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.
Paraconsistent extensional propositional logics.Diderik Batens - 1980 - Logique and Analyse 90 (90):195-234.
On The Imaginary Logic of N. A. VASILIEV.Leila Z. Puga & Newton C. A. Da Costa - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3):205-211.

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