A Rich Paraconsistent Extension Of Full Positive Logic

In the present paper we devise and study the most natural predicative extension of Schutte’s maximally paraconsistent logic. With some of its large fragments, this logic, CLuNs, forms the most popular family of paraconsistent logics. Devising the system involves some entanglements, and the system itself raises several interesting questions. As the system and fragments were studied by other authors, we restrict our attention to results that we have not seen in press.

[1]  H. A. Lewis,et al.  ENTAILMENT: The Logic of Relevance and Necessity (Volume I) , 1978 .

[2]  Itala M. Loffredo D'Ottaviano,et al.  Definability and Quantifier Elimination for J3-theories , 1987, Stud Logica.

[3]  Arnon Avron,et al.  Natural 3-valued logics—characterization and proof theory , 1991, Journal of Symbolic Logic.

[4]  Olivier Esser.  A Strong Model of Paraconsistent Logic , 2003, Notre Dame J. Formal Log..

[5]  Diderik Batens,et al.  In Defence of a Programme for Handling Inconsistencies , 2002 .

[6]  Diderik Batens.  Linguistic and Ontological Measures for Comparing the Inconsistent Parts of Models. , 1999 .

[7]  D. Batens.  Paraconsistent extensional propositional logics , 1980 .

[8]  G. Priest.  What not? A defence of dialetheic theory of negation , 1999 .

[9]  Diderik Batens.  Frontiers of Paraconsistent Logic , 2000 .

[10]  N. Costa,et al.  Non-Classical Logics, Model Theory, and Computability: Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976 , 1977 .

[11]  Nuel D. Belnap,et al.  Entailment : the logic of relevance and necessity , 1975 .

[12]  Diderik Batens,et al.  Embedding and Interpolation for some Paralogics. The Propositional Case , 1999, Reports Math. Log..

[13]  J. Martin Marcos,et al.  Formal inconsistency and evolutionary databases , 2004 .

[14]  Florencio G. Asenjo,et al.  Logic of antinomies , 1975, Notre Dame J. Formal Log..

[15]  D. Batens.  A General Characterization of Adaptive Logics , 2001 .

[16]  I. L. D'Ottaviano.  The completeness and compactness of a three-valued first-order logic , 1985 .

[17]  Ayda I. Arruda.  On the Imaginary Logic of N. A. Vasil'év , 1977 .

[18]  Graham Priest,et al.  Is arithmetic consistent , 1994 .

[19]  I. L. D'Ottaviano.  The model extension theorems for Л3-theories , 1985 .

[20]  Diderik Batens.  Inconsistency-Adaptive Logics , 1999 .

[21]  Diderik Batens,et al.  A Tableau Method for Inconsistency-Adaptive Logics , 2000, TABLEAUX.

[22]  H. Rasiowa,et al.  Logic at work : essays dedicated to the memory of Helena Rasiowa , 1999 .

[23]  Diderik Batens.  Against global paraconsistency , 1990 .

[24]  Arnon Avron,et al.  On an implication connective of RM , 1986, Notre Dame J. Formal Log..