Relevant first-order logic LP~# and Curry's paradox resolution

摘要

In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry's Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C_n~#,1≤n<ω, in fact, provide an effective way of circumventing triviality of da Costa's paraconsistent Set Theories NF_n~C