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First order theory for literal‐paraconsistent and literal‐paracomplete matrices
Author(s) -
Lewin Renato A.,
Mikenberg Irene F.
Publication year - 2010
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200810062
Subject(s) - literal (mathematical logic) , iterated function , negation , mathematics , order (exchange) , binary number , algebra over a field , pure mathematics , arithmetic , computer science , algorithm , programming language , mathematical analysis , finance , economics
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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)