David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Logic, Language and Information 12 (2):183-211 (2003)
Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established.
|Keywords||completeness fibring non-truth-functional logics|
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Citations of this work BETA
Carlos Caleiro, Ricardo Gonçalves & Manuel Martins (2009). Behavioral Algebraization of Logics. Studia Logica 91 (1):63 - 111.
Carlos Caleiro & Ricardo Gonçalves (2009). Behavioral Algebraization of da Costa's C-Systems. Journal of Applied Non-Classical Logics 19 (2):127-148.
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