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Zap. Nauchn. Sem. LOMI, 1972, Volume 32, Pages 90–97 (Mi znsl2569)  

Cut-elimination theorem for relevant logics

G. E. Mints


Abstract: Cut-elimination theorem is proved for $R^+$ that is the positive fragment of $R$ (cf. [4]) supplied with $S4$-modality and intensional conjunction. This gives a decision procedure for the $\{\rightarrow,&,0\}$ fragment of $R$. An extension of cut-elimination theorem to the positive part of Aekermann's calculus $E$ is only sketched. The formula $[(a\to u\vee v)&(a\to(u\to v))]\to(a\to v)$ proposed as a counterexample to the conjencture that the replacement of $A\to B$ by $N(A\to B)$ is an embedding of $E$ into $R^+$. Formula (4) is a counterexample to Anderson's conjencture: if $\rceil((A\to B)\to(C\to D))$ is provable in $E$ then $A\to B$ is too.

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Citation: G. E. Mints, “Cut-elimination theorem for relevant logics”, Studies in constructive mathematics and mathematical logic. Part V, Zap. Nauchn. Sem. LOMI, 32, "Nauka", Leningrad. Otdel., Leningrad, 1972, 90–97

Citation in format AMSBIB
\Bibitem{Min72}
\by G.~E.~Mints
\paper Cut-elimination theorem for relevant logics
\inbook Studies in constructive mathematics and mathematical logic. Part~V
\serial Zap. Nauchn. Sem. LOMI
\yr 1972
\vol 32
\pages 90--97
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2569}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=344083}


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