Many valued paraconsistent logic

In contrast to most logics, in paraconsistent logic it is not true that everything followed from a contradiction. The semantics for one of the best known paraconsistent logics, LP, permits sentences to be both true and false; but at the same time, the semantic characterization of the logical particl...

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Bibliographic Details
Main Author: Morgan, C.G.
Format: Conference Proceeding
Language:English
Subjects:
Explosives
Formal languages
Humans
Multivalued logic
Online Access:Request full text
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Summary:In contrast to most logics, in paraconsistent logic it is not true that everything followed from a contradiction. The semantics for one of the best known paraconsistent logics, LP, permits sentences to be both true and false; but at the same time, the semantic characterization of the logical particles is classical. We define the notion of "molecular logic", of which all finite valued variants of LP are a type. Generally paraconsistent logics do not contain extensional conditionals. Molecular logics of n values may be conservatively extended to standard many valued logics of 2/sup n/-1 values, in which it is easy to define extensional conditionals with the usual detachment rules. The extension, while paraconsistent relative to a negation satisfying standard conditions on the original n values, is not paraconsistent relative to a negation satisfying standard conditions on the 2/sup n/-1 values of the extension. We conclude that the logic LP and its many valued generalizations are paraconsistent because of expressive incompleteness.
ISSN:0195-623X
2378-2226
DOI:10.1109/ISMVL.2001.924583