ИСТИНА

I will start with an observation of the Pietz and Rivieccio exactly true logic (ETL) being a four-valued Balnap-style logic whose consequence relation preserves only one designated value T. In so doing, I will sequentially consider some interesting semantic properties of this logic and the peculiarities of its axiomatization proposed by Pietz and Rivieccio. An alternative axiomatization of the same logic as a two-level bi-consequence system was developed by Shramko, Zaitsev and Belikov. It appeared to be a calculus with two organized subordinately consequence relations: the first one, so to say, 'ground' relation serving as a basis for the second 'main' relation. Also, we have put into circulation a standard binary consequence system and proved the deductive equivalence of these two calculi. However, the problem of finding a direct completeness proof for the latter system remains open. In my talk, I will present two ideas of solving this problem and discuss corresponding machinery.