Spatial Cognition and Computation 1: 329–348, 1999.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Geometric structures of frames of reference and
natural language semantics
Fachbereich Informatik-WSV, University of Hamburg, Hamburg, Germany
Abstract. This article aims at formal speciﬁcations of reference systems in spatial cognition.
It concentrates on two roles of reference systems connected to spatial language: reference
systems resolving ambiguities and reference systems forming a basis for the classiﬁcation of
linguistic terms. Although coordinate systems are often seen as candidates for the geometric
structure of reference systems, it is shown here that they do not appear in the explanations
that go into the details. An analysis of the German terms vor, hinter, rechts and links (in front
of, in back of, right, left) presents an alternative model for the geometric structure of spatial
Key words: axiomatic characterization, frame of reference, geometry, spatial language, spatial
Spatial reference systems in spatial cognition
Spatial reference systems are structures that support spatial cognition. They
are essential for the analysis of natural language terms, such as German
vor, hinter, rechts and links (in front of, in back of, right, left). This article
proposes a coordinate-free speciﬁcation of the geometric structure of refer-
ence systems that are essential for describing the meaning of these terms.
To prepare this analysis, the roles of spatial reference systems for natural
language analysis are distinguished from other roles. Concrete reference
systems are set apart from frames of reference as their geometric repres-
entatives. It is shown that existing analyses of similar terms do not clearly
separate the contribution of the frame of reference from the meaning of the
lexical item and that essential contributions of the frame of reference have to
be distinguished from conceivable geometric constructions based on them.
The technical terms ‘spatial reference system’ and ‘spatial frame of refer-
ence’ fulﬁll at least four roles in the analysis of spatial language, spatial
knowledge and perception. These roles shall ﬁrst be distinguished to restrict
the following discussion.