Semantics of Simple Arrow Diagrams
Yohei Kurata and Max J. Egenhofer
National Center for Geographic Information and Analysis & Department of Spatial Information Science and Engineering
University of Maine{yohei, max}@spatial.maine.edu

Why Arrows?

Research Goal

Arrows are a major component of diagrams, which areused multi-purposely to facilitate the communication ofspatial and temporal knowledge.

To develop a computational method for interpretingthe meaning of arrow diagrams*.

Pen-based interactions withcomputers are expected to support
the use of diagrams with various
meanings of arrows.

Approach
The appearance of the arrow symbol alone does not determine any
meaning—the meaning is established when the arrow symbol
originates from, traverses, or points to other elements in the diagram.

Follow this way
and meet here.

We focus on the structure that the arrow-related
elements organizes around an arrow symbol.

Fish Catches
El Niño

Current pen-based systems restrict the use of arrows
to a small set of meanings or require their users tospecify the meaning of every arrow.

El Niño influences
the decrease of
Fish catches inSouth America.

As a first step, this paper points out
three structural properties of arrow diagrams
that contribute to their interpretation.

* Arrow diagram := Arrow symbol + Arrow-related components

1. Component Alignment

2. Component Types

meaningless patterns
3. Object’s Orientations

Different alignment of components leads to different
interpretations of arrow diagrams.

A component of an arrow diagram may be mentioned by an icon, a text, ora specific position in the background drawing. At a semantic level,
however, the following five types of components are distinguished:

An object expressed by an icon often has an intrinsic
orientation toward which the object usually moves. Thisorientation is often a key for successful interpretation.

Removing a wheel from a car.

Mounting a wheel to a car,Thus, to formalize the alignment of components,
we introduce three component slots where thecomponents are located.
Tail slot

Body slot

An object takes an action.
An event occurs in time, and is characterized by a set of changes.
A location is a position in space (point or region).
A moment is a position in time (instant or interval).
A note is a description that supplements another component.
objectobjectobjectobject

event

Å

Æ

A person gets out of a car.

location

AAAI
SpringSymposium

Head slot
A person leaves a bag.

A person participates in a symposium.

A person goes to Maine.

Æobject

location

objectlocation(car, –, wheel)ÆA car approaches a person ora person gets out of a car.

Different types of components lead to different types of interpretations,but arrow diagrams with identical alignments of component types often
lead to the same class of interpretation.

Then, an arrow diagram can be rewritten like:ÅÆA car approaches a person.

(object, – , location)
movable inany direction

immovable

Mounting a wheel to a car.

go_to (object, location)

ÅÅSomething undrawn moves
from a car to a person ?

An object is supposed to move
only when its intrinsic orientation
corresponds to the direction of
the arrow symbol.

Ongoing Work
With the three component slots and the five
types of components, we can distinguish 63 =216 types of simple arrow diagrams.

simple arrow diagrams := (c, c, c)
c := – | object | event | moment | location | noteWe investigated what semantics eachtype of arrow diagrams may illustrate, byclassifying the arrow-related semantics
into four classes (property, annotation,conjunction, and action) and considering
the structural requirements for illustratingeach class of semantics.

We found that:83 types of arrow diagrams
are meaningless.
15+4+12+50 = 81 types leadto a unique interpretation.
4+4+44 = 52 types are still
ambiguous

Propertyv1

Conjunction

15124 4 4Annotation
You arehere4450

Action83

Possible semantics of 216 types of simple arrow diagrams

For the 52 types of ambiguous
arrow diagrams, we are now
trying to determine the mostreliable interpretation, making
use of various clues in diagrams,
such as the intrinsic orientationsof objects.