Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2009, Number 2, Pages 62–65 (Mi vmumm863)  

Short notes

Lambek calculus with one division and one primitive type permitting empty antecedents

S. L. Kuznetsov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The following assertion is proved: a deduction rule given by a scheme is admissible in the Lambek calculus with one division $\mathrm{L}^*(\backslash)$ permitting empty antecedents if and only if it is admissible in the fragment of $\mathrm{L}^*(\backslash)$ with one primitive type $\mathrm{L}^*(\backslash; p_1)$. To do that, a type substitution is used which reduces the derivability in $\mathrm{L}^*(\backslash)$ to the derivability in $\mathrm{L}^*(\backslash;p_1)$.

Key words: Lambek calculus, admissible rules, proof nets.

Full text: PDF file (237 kB)

Bibliographic databases:
UDC: 510.649
Received: 28.04.2008

Citation: S. L. Kuznetsov, “Lambek calculus with one division and one primitive type permitting empty antecedents”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2009, no. 2, 62–65

Citation in format AMSBIB
\Bibitem{Kuz09}
\by S.~L.~Kuznetsov
\paper Lambek calculus with one division and one primitive type permitting empty antecedents
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2009
\issue 2
\pages 62--65
\mathnet{http://mi.mathnet.ru/vmumm863}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2543175}
\zmath{https://zbmath.org/?q=an:1304.03054}


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