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Centre for Logic, Epistemology and the History of Science (CLE) |
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Rules and Instructions | Sites Pointing to CLE e-Prints |
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ISSN 1519-9681 |
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ISSN 1519-9614 |
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Completeness Preservation |
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Publication Information |
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final version of this paper is published as:
C. Caleiro, W.A. Carnielli,
M.E. Coniglio, A. Sernadas, C. Sernadas, "Fibring Non-Truth-Functional
Logics: Completeness Preservation". Journal of Logic, Language
and Information 12, no. 2, pp. 183-211, 2003.
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Fibring
has been shown to be useful for combining logics endowed with truth-functional
semantics. One wonders if fibring can be extended in order to cope with logics
endowed with non-truth-functional semantics as, for example, paraconsistent
logics.
The first
main contribution of the paper is a positive answer to this question. Furthermore,
it is shown that this extended notion of fibring preserves completeness under
certain reasonable conditions. This completeness transfer result, the second
main contribution of the paper, generalizes the one established in previous
papers and is obtained using a new technique exploiting the properties of
the meta-logic where the (possibly non-truth-functional) valuations are defined.
The modal paraconsistent logic of da Costa and Carnielli is obtained by fibring
and its completeness is so established.
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