论文信息 - Consequence–Inconsistency Interrelation: In the Framework of Paraconsistent Logics

Consequence–Inconsistency Interrelation: In the Framework of Paraconsistent Logics

This paper deals with a relativized notion of inconsistency, which turns out to be equivalent to a non-explosive consequence under certain sets of axiomatization in a propositional language. The paper also shows that several existing paraconsistent systems fall under this characterization.

Mihir Kumar Chakraborty | Soma Dutta

[1] J. Dunn,et al. Star and Perp: Two Treatments of Negation1 , 1993 .

[2] W. Carnielli,et al. Logics of Formal Inconsistency , 2007 .

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

[4] Diderik Batens,et al. A completeness-proof method for extensions of the implicational fragment of the propositional calculus , 1980, Notre Dame J. Formal Log..

[5] Florencio G. Asenjo,et al. A calculus of antinomies , 1966, Notre Dame J. Formal Log..

[6] V. Vasyukov. A NEW AXIOMATIZATION OF JAŚKOWSKI'S DISCUSSIVE LOGIC , 2004 .

[7] Greg Restall. Laws of Non-Contradiction, Laws of the Excluded Middle, and Logics * , 2004 .

[8] Stanisław J. Surma. THE GROWTH OF LOGIC OUT OF THE FOUNDATIONAL RESEARCH IN MATHEMATICS , 1981 .

[9] Newton C. A. da Costa,et al. On the theory of inconsistent formal systems , 1974, Notre Dame J. Formal Log..

[10] Arnon Avron,et al. Simple Consequence Relations , 1988, Inf. Comput..

[11] J. Dunn. A Comparative Study of Various Model-Theoretic Treatments of Negation: A History of Formal Negation , 1999 .

[12] Ayda I. Arruda. Aspects of the historical development of paraconsistent logic , 1989 .

[13] Graham Priest,et al. The logic of paradox , 1979, J. Philos. Log..