The whole topic has both its more philosophical aspects and its more mathematical aspects. If you want to explore the more mathematical aspects, you probably want to start here https://en.wikipedia.org/wiki/Paraconsistent_mathematics and then end up reading something like https://www.amazon.com/Inconsistent-Mathematics-Its-Applicat...

EDIT: see also https://ir.canterbury.ac.nz/bitstream/handle/10092/5626/1263...