Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991 Association of Mizar Users

## Preliminaries to the Lambek Calculus

Wojciech Zielonka
Adam Mickiewicz University, Poznan
This paper was written during author's visit at the Warsaw University (Bia{\l}ystok) in Winter 1991.

### Summary.

Some preliminary facts concerning completeness and decidability problems for the Lambek Calculus [14] are proved as well as some theses and derived rules of the calculus itself.

#### MML Identifier: PRELAMB

The terminology and notation used in this paper have been introduced in the following articles [16] [9] [19] [18] [13] [1] [6] [21] [5] [10] [12] [17] [20] [7] [8] [15] [11] [2] [3] [4]

Contents (PDF format)

#### Bibliography

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[3] Grzegorz Bancerek. Introduction to trees. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek. K\"onig's Lemma. Journal of Formalized Mathematics, 3, 1991.
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[6] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
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[8] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
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[13] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[14] Joachim Lambek. The mathematics of sentence structure. \em American Mathematical Monthly, (65):154--170, 1958.
[15] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[17] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[18] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[20] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[21] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received February 13, 1991