Geodesic
Lambek calculus with a unit and one division
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 55-57

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In this paper we present a substitution that reduces the derivability in the Lambek calculus with the unit and one division to the derivability in the Lambek calculus with one division permitting empty antecedents. Using this substitution, we establish the existence of an algorithm that checks the derivability in the Lambek calculus with the unit and one division in polynomial time. 
@article{VMUMM_2011_4_a10,
     author = {S. L. Kuznetsov},
     title = {Lambek calculus with a unit and one division},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {55--57},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a10/}
}
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S. L. Kuznetsov. Lambek calculus with a unit and one division. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 55-57. http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a10/