Abstract
In this work, we investigate the relationship between paraconsistent semantics and some well-known topological spaces such as connected and continuous spaces. We also discuss homotopies as truth preserving operations in paraconsistent topological models.
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Notes
Thanks to the anonymous referee for bringing this point to my attention.
For instance, classical oriented readers of paraconsistency may find it quite puzzling when paraconsistent logicians employ proof by contradiction as a proof method. Paraconsistent logic or dialetheism, note again, does not claim that all contradictions are acceptable.
Thanks to Chris Mortensen for pointing this work out. Even if the paper appeared in 1981, the work had been carried out around 1978. In his paper, Goodman indicated that the results were based on an early work that appeared in 1978 only as an abstract.
Remember that our meta-theory is classical, thus the subset relation we resort to is also classical.
See Ferguson (2012) for a more detailed treatment of non-classical logics that do not satisfy DeMorgan’s laws.
Also, note that connectedness as a property is not definable in the (classical) modal language (Cate et al. 2009).
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Acknowledgments
I thank to Chris Mortensen for pointing this out. I am grateful to Chris Mortensen and Graham Priest for their encouragement and feedback. I acknowledge the help and the detailed comments of anonymous referees.
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Başkent, C. Some topological properties of paraconsistent models. Synthese 190, 4023–4040 (2013). https://doi.org/10.1007/s11229-013-0246-8
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DOI: https://doi.org/10.1007/s11229-013-0246-8