## Fibring Non-Truth-Functional Logics: Completeness Preservation (2000)

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Venue: | Journal of Logic, Language and Information |

Citations: | 26 - 20 self |

### BibTeX

@ARTICLE{Caleiro00fibringnon-truth-functional,

author = {Carlos Caleiro and Walter Carnielli and Marcelo E. Coniglio and Amilcar Sernadas and Cristina Sernadas},

title = {Fibring Non-Truth-Functional Logics: Completeness Preservation},

journal = {Journal of Logic, Language and Information},

year = {2000},

volume = {12},

pages = {2003}

}

### Years of Citing Articles

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### Abstract

Fibring has been shown to be useful for combining logics endowed with truth-functional semantics. One wonders if bring can be extended in order to cope with logics endowed with non-truth-functional semantics as, for example, paraconsistent logics. The rst main contribution of the paper is a positive answer to this question. Furthermore, it is shown that this extended notion of bring preserves completeness under certain reasonable conditions. This completeness transfer result, the second main contribution of the paper, generalizes the one established by Zanardo et al. and is obtained using a new technique exploiting the properties of the metalogic where the (possibly non-truth-functional) valuations are de ned. The modal paraconsistent logic of da Costa and Carnielli is obtained by bring and its completeness is so established.

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Citation Context ... preservation results and/orsnding preservation counterexamples within the community of logicians working in the problem of combining logics. Among the dierent techniques for combining logics,sbring [=-=11, 12, 21, 22, 23]-=- deserves close attention. But what issbring? The answer can be given in a few paragraphs for the special case of logics with a propositional base, that is, with propositional variables and connective... |

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Citation Context ...nding preservation counterexamples within the community of logicians working in the problem of combining logics. Among the dierent techniques for combining logics,sbring (Gabbay, 1996; Gabbay, 1998; S=-=ernadas et al., 1999-=-; Sernadas et al., 2000; Zanardo et al., 2000) deserves close attention. But what issbring? The answer can be given in a few paragraphs for the special case of logics with a propositional base, that i... |

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Citation Context ... preservation results and/orsnding preservation counterexamples within the community of logicians working in the problem of combining logics. Among the dierent techniques for combining logics,sbring [=-=11, 12, 21, 22, 23]-=- deserves close attention. But what issbring? The answer can be given in a few paragraphs for the special case of logics with a propositional base, that is, with propositional variables and connective... |

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Citation Context ...with several formalisms at the same time is the rule rather than the exception. We refer the reader, for instance, to (Finger and Gabbay, 1992; Goguen and Burstall, 1992; Sannella and Tarlecki, 1993; =-=Astesiano and Cerioli, 1994-=-) for a discussion of this and related problems, including some early attempts at their solution. Obviously, an approach to the combination of logics will be of significance only if general preservati... |

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Citation Context ...atory". In order to recover C D 1 at the semantic level in our setting we have to add one additional meta-axiom for valuations: (v(y 1 ) = > ! v((L y 1 ) ) = >): Using the terminology introduced=-= in [4]-=-, this procedure can be seen as a splitting of C D 1 in the components KD and C 1 . 5 Logic systems This section is devoted to extending thesbring techniques to the syntactical counterpart of isp's. A... |

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Citation Context ...semantic entailment (as dened below). Note that it is easy to extend this example in order to set up the isp's for the whole hierarchy C n by specifying the paraconsistent n-valuations introduced in [=-=17]-=-. 7 With respect to the second example (modal system KD), it is also straightforward to verify that every Kripke model has a counterpart in Int(S): consider the algebra of truth-values given by the po... |

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Citation Context ...assical logic in which the principle of Pseudo Scotuss; :s`sdoes not hold. Some systems of paraconsistent modal logic were investigated in (Deutsch, 1979; Deutsch, 1984; da Costa and Carnielli, 1988; =-=Puga et al., 1988-=-). One might wonder if we should try to obtain such a mixed logic as thesbring of the underlying modal and paraconsistent logics. Thesrst main contribution of this paper is a positive answer to this q... |

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Citation Context ...sistent systems C n of [6] are subsystems of propositional classical logic in which the principle of Pseudo Scotuss; :s`sdoes not hold. Some systems of paraconsistent modal logic were investigated in =-=[9, 10, 8, 20]-=-. One might wonder if we should try to obtain such a mixed logic as thesbring of the underlying modal and paraconsistent logics. Thesrst main contribution of this paper is a positive answer to this qu... |

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Citation Context ...sistent systems C n of [6] are subsystems of propositional classical logic in which the principle of Pseudo Scotuss; :s`sdoes not hold. Some systems of paraconsistent modal logic were investigated in =-=[9, 10, 8, 20]-=-. One might wonder if we should try to obtain such a mixed logic as thesbring of the underlying modal and paraconsistent logics. Thesrst main contribution of this paper is a positive answer to this qu... |

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