Non-deterministic Logic of Generalized Classical Truth Values

In this paper, we are going to combine two trends: non-deterministic logic and bi-facial logic of generalized truth values. Non-deterministic matrices allowed Avron, Ben-Naim, and Konikowska introduce a modification to Belnap and Dunn’s logic which may deal with the situation when the sources of information may give it about not only atomic formulas, but complex ones as well. Zaitsev and Shramko’s bi-facial truth logic distinguishes ontological and epistemic understanding of truth. The combination of these two approaches may allow to work with the sources providing epistemic truth values to complex formulas and evaluate their activity from the ontological point of view.