Rendering It Strictly Directed

Utrecht Institute of Linguistics OTS

Utrecht University

Trans 10

3512 JK Utrecht

The Netherlands

&

ILLC/Department of Philosophy

University of Amsterdam

Nieuwe Doelenstraat 15

1012 CP Amsterdam

The Netherlands

Herman.Hendriks@let.uu.nl

This paper solves the directed counterpart of a problem addressed in
van Benthem's *Language in Action*
There it is observed that **LP** derivability in an atomic goal
category can be mimicked by **LP** derivability using one atomic
category only.
The abbreviation **LP** refers to the non-directed Lambek calculus
with Permutation, a system which has also become known as the Lambek-Van
Benthem calculus, and the result is due to Ponse (1988).
In the present paper we will show that---a generalization of---this result
can be extended to the directed system **L**, i.e., the associative
calculus that was introduced in Lambek (1958): **L** derivability in
*any* category can be mimicked by **L** derivability using one
atomic category only.

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AXE, April 1st, 1999

© Peter van Emde Boas