On formal aspects of the epistemic approach to paraconsistency

In Max Freund, Max Fernandez de Castro & Marco Ruffino (eds.), Logic and Philosophy of Logic: Recent Trends in Latin America and Spain. London: College Publications. pp. 48-74 (2018)
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Abstract

This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for both BLE and LET J . The meanings of the connectives of BLE and LET J , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed.

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Author Profiles

Walter Carnielli
University of Campinas
Marcelo E. Coniglio
University of Campinas
Abilio Rodrigues
Federal University of Minas Gerais

References found in this work

The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Investigations into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.

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