We define in precise terms the basic properties that an 'ideal propositional paraconsistent logic' is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n < 2 there exists an extensive family of ideal n-valued logics, each one of which is not equivalent to any k-valued logic with k < n.
Bibliographical noteFunding Information:
Acknowledgements. This research was supported by The Israel Science Foundation (grant No 280-10).
- Paraconsistent logics
- ideal paraconsistency
- many-valued logics
ASJC Scopus subject areas
- History and Philosophy of Science