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Literal‐paraconsistent and literal‐paracomplete matrices
Author(s) -
Lewin Renato A.,
Mikenberg Irene F.
Publication year - 2006
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.200510044
Subject(s) - literal (mathematical logic) , iterated function , mathematics , negation , paraconsistent logic , class (philosophy) , propositional calculus , algebra over a field , discrete mathematics , pure mathematics , computer science , algorithm , description logic , theoretical computer science , programming language , artificial intelligence , higher order logic , mathematical analysis
We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)