Dual-Belnap Logic and Anything but Falsehood.

This paper presents an inquiry into a proof system for a logic based on four Belnapian truth values, in which any truth value but the pure falsehood is designated. To this effect, I first implement a certain dualization of what Font terms ‘Belnap’s logic’, and then show how it can be suitably extended. The resulting systems are of the Fmla-Set type dually to the standard formulation of Belnap’s logic and the Exactly True Logic by Pietz and Rivieccio. I restate some philosophical motivation for the entailment relation of the Fmla-Set type by briefly comparing it with the usual Set-Fmla logical systems.

Authors

• Yaroslav Shramko

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