# zbMATH — the first resource for mathematics

Proving contradictions in formal theories. II. (English. Russian original) Zbl 0532.03008
Autom. Remote Control 44, No. 7, 908-914 (1983); translation from Avtom. Telemekh. 1983, No. 7, 97-104 (1983).
Summary: In this continuation of part I [see the review above], we consider logical calculi which allow proving contradictions. A first-order classical language LPCont is constructed, with PCont as the object language and the classical logic as the formalized metalanguage. Some extensions of the language LPCont are considered and its relationship with Bochvar’s logic $$B_ 3$$ [D. A. Bochvar, Mat. Sbornik 4, 287-308 (1938; Zbl 0020.19402)] is established. In conclusion we consider some broader aspects of the logic of inconsistent systems (in particular, the problem of logical paradoxes).

##### MSC:
 03B60 Other nonclassical logic