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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Paraconsistent set theory by predicating on consistency

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Autor(es):
Carnielli, Walter [1] ; Coniglio, Marcelo E. [1]
Número total de Autores: 2
Afiliação do(s) autor(es):
[1] Univ Estadual Campinas, UNICAMP, Ctr Log Epistemol & Hist Sci CLE, Rua Sergio Buarque de Holanda 251, BR-13083859 Campinas, SP - Brazil
Número total de Afiliações: 1
Tipo de documento: Artigo Científico
Fonte: JOURNAL OF LOGIC AND COMPUTATION; v. 26, n. 1, SI, p. 97-116, FEB 2016.
Citações Web of Science: 5
Resumo

This article intends to contribute to the debate about the uses of paraconsistent reasoning in the foundations of set theory, by means of using the logics of formal inconsistency and by considering consistent and inconsistent sentences, as well as consistent and inconsistent sets. We establish the basis for new paraconsistent set-theories (such as ZFmbC and ZFCil) under this perspective and establish their non-triviality, provided that ZF is consistent. By recalling how George Cantor himself, in his efforts towards founding set theory more than a century ago, not only used a form of `inconsistent sets' in his mathematical reasoning, but regarded contradictions as beneficial, we argue that Cantor's handling of inconsistent collections can be related to ours. (AU)

Processo FAPESP: 10/51038-0 - Logical consequence, reasoning and computation - LOGCONS
Beneficiário:Walter Alexandre Carnielli
Linha de fomento: Auxílio à Pesquisa - Temático