Paraconsistência como preservação de evidências

[Walter Carnielli]

Colegas:


para aqueles que murmuram nos cantos que a ``escola paraconsistentista
brasileira precisa ser mais ativa na sua vertente filosófica e
interpretativa'', aqui um seminário que Melvin Fiting apresentou no
CUNY Graduate Center (Nova Iorque) sobre uma interpretação que ele
ouviu de mim em Praga, relativo a um trabalho em conjunto com Abilio
Rodrigues sobre interpretaçãod e paraconsistencia com base na noção de
preservação de evidências, e que sequer foi publicado ainda:

"Paraconsistent logic, evidence, and justification"

Melvin Fitting Lehman College - CUNY Graduate Center

http://nylogic.org/topic/paraconsistency

In a forthcoming paper, Walter Carnielli and Abilio Rodriguez propose
a Basic Logic of Evidence (BLE) whose natural deduction rules are
thought of as preserving evidence instead of truth. BLE turns out to
be equivalent to Nelson’s paraconsistent logic N4, resulting from
adding strong negation to Intuitionistic logic without Intuitionistic
negation. The Carnielli/Rodriguez understanding of evidence is
informal. We provide a formal alternative, using justification logic.
First we introduce a modal logic, KX4, in which box-X can be read as
asserting there is implicit evidence for X, where we understand
evidence to permit contradictions. We show BLE embeds into KX4 in the
same way that Intuitionistic logic embeds into S4. Then we formulate a
new justification logic, JX4, in which the implicit evidence
motivating KX4 is made explicit. KX4 embeds into JX4 via a realization
theorem. Thus BLE has both implicit and explicit evidence
interpretations in a formal sense.

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Walter Carnielli
Centre for Logic, Epistemology and the History of Science and
Department of Philosophy
State University of Campinas –UNICAMP
13083-859 Campinas -SP, Brazil
Phone: (+55) (19) 3521-6517
Institutional e-mail: walter.c...@cle.unicamp.br
Website: http://www.cle.unicamp.br/prof/carnielli