=Paper=
{{Paper
|id=Vol-2050/fomi-paper6
|storemode=property
|title=Encountering the Physical World
|pdfUrl=https://ceur-ws.org/Vol-2050/FOMI_paper_6.pdf
|volume=Vol-2050
|authors=Bahar Aameri,Michael Gruninger
|dblpUrl=https://dblp.org/rec/conf/jowo/AameriG17
}}
==Encountering the Physical World==
https://ceur-ws.org/Vol-2050/FOMI_paper_6.pdf
Encountering the Physical World
Bahar AAMERI a , Michael GRÜNINGER a
a Department of Mechanical and Industrial Engineering, University of Toronto, Ontario,
Canada M5S 3G8
Abstract. Manufacturing and product design are grounded in the physical world.
The entire product lifecycle involves a wide range of integrated tasks that focus on
the properties of physical objects, beginning with begins with the design of physical
objects and the specification of the materials from which the physical objects are
made. Thus, reasoning tasks within manufacturing and product design requires an
ontology of physical world. In this paper, we present the current status of a project
that is developing a suite of ontologies, which are modules of an overarching ontol-
ogy called the PhysicalWorld Ontology. Each module of the PhysicalWorld Ontol-
ogy captures a particular class of physical phenomena or property of physical ob-
jects, such as shape, location, connectedness, parthood, and kinetic and kinematic
behaviour.
Keywords. manufacturing ontologies, physical objects, mereotopology, shape
1. Introduction
Although it may be obvious, manufacturing and product design are essentially grounded
in the physical world. Manufacturing is concerned with processes that involve the cre-
ation of physical objects, such as assembly, joining, fastening, fabrication, machining,
coating, and more recently in additive processes such as 3D printing. From a wider per-
spective, manufacturing begins with the design of these physical objects (i.e. products)
and the specification of the materials from which the physical objects are made. The
entire product lifecycle (conceptual design, detailed design, manufacture, maintenance,
disposal) involves a wide range of integrated tasks that focus on the properties of phys-
ical objects. The supply chain of the manufacturing enterprises spans the sourcing of
raw materials and the delivery of products in logistics. All of this is supported by a vast
ecosystem of product data management software as well as international standards. It is
instructive to consider the scope of ISO 10303, also known as STEP (Standard for the
Exchange of Product Data): standard data definitions for geometry (wire frame, surfaces
and solid models), product identification, product structure, configuration and change
management, materials, finite element analysis data, drafting, visual presentation, toler-
ances, kinematics, electrical properties, and process plans [2].
Even with this cursory inspection, we can see that a rich set of ontologies about the
physical world is needed for manufacturing. Within this paper, we present the current
status of a project that is developing such a suite of ontologies, which are modules of
an overarching ontology that we refer to as the PhysicalWorld Ontology. Based on the
idea that solid physical objects are self-connected objects that are made of matter, have
Figure 1. Schematics of swing axle, trailing swing axle, semi-trailing arm, and Macpherson strut suspension
systems [1]
a shape with boundaries, and are located in space, the ontologies will support reason-
ing about physical objects, their behaviors and interaction. Each module of the Phys-
icalWorld Ontology captures a particular class of physical phenomena or property of
physical objects.
We begin in Section 2 by identifying semantic requirements for the representation of
physical objects and their behaviour. We then explore the primary modules of the Phys-
icalWorld Ontology in Section 3 – Shape, Multidimensional Mereotopology, and Loca-
tion. We finish with a look forward to the remaining ontology modules that will focus on
physics and axiomatize the fundamental concepts required for representing kinetic and
kinematic behaviour of physical systems.
2. Extracting Requirements for PhysicalWorld Ontology
We will begin by delineating the requirements for representing properties and behavior
of physical objects. Throughout this section, we consider suspension design systems
(see Figure 1) as our main use cases for extracting requirements. A suspension system
consists of wheels, beams, struts, springs and dampers, related to each other by different
types of joints.
2.1. Shape
Perhaps shape is the first feature that comes to mind when thinking about a physical ob-
jects; it is also a key concept in representing physical domains. As an example, consider
the different suspension systems shown in Figure 1. One of the features that distinguishes
these systems from each other is the shape of the beams between the two wheels. Later
in Section 3.4.1, we will raise the problem of distinguishing between different rivet fas-
tening methods, and we will show that a description of the shape of rivets is required in
order to make this distinction.
The focus of the majority of the existing shape formalisms is on representing con-
vexity and curvature (see [7,13]). In cases where information about convexity and cur-
vature are not required, a shape can be described based on the adjacency and order of
its points, edges, and surfaces. This approach has been taken in [10] for developing first-
order ontologies for two-dimensional and three-dimensional shapes. We will discuss this
approach further in Section 3.1.
2.2. Connection and Parthood between Physical Objects
Formalizing the part-whole relationship between a physical system (e.g., a suspension
system) and its parts, as well as the physical relationships among the different parts of
the system, requires a mereotopology for physical objects. A mereotopology is a formal
theory which combines topology with mereology. The topological subtheory expresses
connection relations between a set of individuals, while the mereological subtheory ex-
presses parthood relations.
Mereotopological systems differ in their basic assumptions about supplementation,
atomicity, extensibility, and closure under sum and product of spatial entities. Ground
Mereotopology (MT) [6] is the weakest theory among the existing mereotopological the-
ories, and does not take any of these assumptions. The signature of the MT theory con-
sists of two primitive binary relations, parthood and connection. The axioms of the the-
ory state that connection is a reflexive and symmetric relation, while parthood is a reflex-
ive, transitive, and anti-symmetric relation. In addition, if one individual is connected to
another, then the first one is also connected to any individual which the second is part of.
[9] shows that the MT theory is logically synonymous with a non-conservative ex-
tension of the RCC8 theory, called RCC8*, meaning MT and RCC8* are semantically
equivalent, and only differ in signature (i.e., the non-logical symbols). In other words,
MT is the mereotopology that underlies RCC8. 1
The RCC8 relations have widely been used for describing spatial relationships
within physical settings. This means that the underlying mereotopology (i.e., MT) used
in such settings does not include any of the basic mereotopological principles (i.e., sup-
plementation, atomicity, extensibility, and closure under sum and product). In the fol-
lowing, we provide examples of physical objects that do not satisfy atomicity, extensi-
bility, and closure under sum. It remains, however, an open question whether physical
mereotopologies should be supplemental and/or closed under product.
Many mereotopological theories, such as the Region Connection Calculus (RCC)
[14], entail that domain entities are atomless. Within a domain, individuals are atomless
1 RCC8 is a set of eight jointly exhaustive and pairwise disjoint binary relations representing mereotopolog-
ical relationships between ordered pairs of individuals.
if every element has a proper part. However, physical objects are not necessarily atom-
less. For assembling a bookshelf, we do not care about proper parts of shelves and di-
vider. In many applications we want to have a finite domain, meaning that the elements
of the domain are not atomless. Thus, using atomless mereotopologies for representing
physical objects is inappropriate as the additional unnecessary constraints result in the
elimination of valid models. On the other hand, there might be domains which require
an atomless representation of some classes of physical objects. Thus, a general physical
mereotopology should not make any commitment about the atomicity of objects, and the
atomicity assumption should be taken with respect to domain-specific requirements.
A relation R is said to be extensional if it satisfies the following sentence
(∀z) (R(z, x) ≡ R(z, y)) ⊃ x = y.
Mereotopologies like RCC assume that the connection relation is extensional. However,
extensionality does not always apply to physical objects. Consider a model with two
elements. The two elements are obviously connected to the same set of elements, but
they are not identical. In fact, any model with finite number of elements (which is the
case in many physical domains) may not be extensional.
The following axiom entails that if two (self-connected) entities are connected, they
add up to a self-connected whole (C(x, y) denotes ‘x is connected to y’ and P(x, y) denotes
‘x is part of y’):
(∀x, y)C(x, y) ⊃ (∃z) P(x, z) ∧ P(y, z).
However, there are physical domains that do not satisfy this axiom. For example,
within the geospatial applications, two neighboring countries are connected, but their
summation is not an entity in the domain. If a glass is placed on a desk, their sum does
not make a new entity. With a similar example, we can also argue that physical domains
are not necessarily closed under the summation of two underlapping objects.
2.3. Location
Mereotopologies alone are not sufficient for describing different configurations of physi-
cal objects. In standard mereotopologies, overlap relation between two individuals is de-
fined with respect to their common parts; that is, two individuals a, b overlap if and only
if there exists an individual which is part of both a and b. When two physical objects
overlap, they do not necessarily have a common part. A book on a shelf, for example,
overlaps with the shelf, however they do not have a part in common. In this case, the
overlap relationship between physical objects should not be defined based on common
parts; it should be defined based on a common abstract region that two physical objects
occupy.
There are also mechanical objects with components which coincide but do not share
parts. For example, while cartridges inside the cylinder of a revolver coincide with the
cylinder, they are not part of the cylinder. Similarly, the ball of a ball joint coincides with
the space that the hole of the joint surrounds. Definition of relations such as coincide
requires a logical theory that axiomatizes relationships between physical objects and the
spatial region they occupy. This is what is called a location ontology.
A location ontology is also required to distinguish between different types of spatial
change. A moving object, for example, occupies a region that overlaps with the region
the object originally occupies, while a shrinking object occupies a region that is a proper
part of its original region. So, for distinguishing between movement and shrinkage of an
object we need to know the relationships between the spatial region they occupy at each
state.
2.4. Joints and Attachment
With topological connection it is only possible to express contact between objects. How-
ever, in many application domains we require to distinguish between being “in contact”
and being “attached”. A book on a shelf of a bookshelf, for example, is only in contact
with the shelf, while the shelf is attached to the side panels of the bookshelf. In addi-
tion, in some domains, such as manufacturing and assembly, representations for different
ways that physical objects can be join together are required.
There has been previous work on the ontologies for attachment. [12] suggests a set
of first-order definitions describing mechanical joints. They use Smith’s mereotopology
[15] for describing the relationships between mechanical parts. The descriptions they
have provided are, however, incomplete in the sense that it does not capture the intended
specifications of different types of joints. Consider the joining methods depicted in Fig-
ure 2. [12] proposes the following definition for threaded fasteners:
J j f (x, y) ≡ (∃u, v) (X(u, x) ∧ X(u, y))∧
(T (v, x) ∨ T (v, y)) ∧ (P(u, fs ) ∧ P(v, fs )) ∧ X( fs , j) (1)
and the following definition for fastening by rivets:
Jr f (x, y) ≡ (∃u, v) (X(u, x) ∧ X(u, y))∧
T (v, x) ∧ T (v, y) ∧ P(u, fs ) ∧ P(v, fs ) ∧ X( fs , j) (2)
Here, P(x, y) denotes ‘x is part of y’, X(x, y) denotes ‘x crosses y’, and ‘T (x, y) denotes x
tangents y’.
The description for rivet fastening relays on the shape of the rivet (denoted by v): a
part like the one shown in Figure 2 would satisfy both Definition 1 and Definition 2. In
fact, to have a sound and complete description for rivets fastening, and so be able to dis-
tinguish it from threaded fasteners, we need to be able to describe the shape of the rivet.
That is, in addition to mereotopological relations, a complete ontology of mechanical
joints requires an ontology for specifying shapes of parts involved in joining methods.
2.5. Boundary
Specifying properties of mechanical joints and physical attachments requires a formal
representation of the notion of boundary.
Consider, for example, a ball joint. Each of the ball and the hole of a ball joint have
their own boundary surfaces, and one of the boundary surfaces of the ball is connected
(in the topological sense) to one of the boundary surfaces of hole. However, if we weld
Figure 2. Examples of mechanical fastening methods [12].
two three-dimensional objects, the welded surfaces of the objects will be transformed
into a single surface, and more importantly, the surface will not be a boundary surface
anymore.
[15] defines boundary based on the interior of entities, using the closure operators.
In Smith’s theory a boundary is a region which has empty interior. That is, unlike other
existing approaches, boundaries are not considered as lower-dimensional entities. More-
over, each boundary is a part of the region it bounds, and is a boundary of itself.
The alternative approach, adopted in GFO-Space theory [3] and CODIB [11], is to
consider boundary as a lower-dimensional entity which is part of the bounded entity. A
model of the GFO-Space theory is partitioned into four categories: space regions, sur-
face regions, line regions and point regions, corresponding to three-, two-, one-, and
zero-dimensional space entities, respectively. A boundary is a lower-dimensional entity
which does not exist independently of the entity it bounds. Moreover, a boundary always
bounds an entity with a higher dimension. A boundary does not necessarily fully cover
the entity it bounds, and in that case, is part of another boundary which covers more of
the entity. Within the GFO-Space theory it is assumed that boundaries are not connected
(in topological sense) to other entities (including other boundaries). Rather, two bound-
aries may be coincide, meaning that they are congruent and there is no distance between
them. [11] takes a similar approach, but provides a stronger specification of properties of
boundaries, and their relationships to the corresponding bounding entity
Note that the multi-dimensional approach for axiomatizing boundary requires a mul-
tidimensional mereotopology. Since physical objects are multidimensional themselves,
it seems (even without considering which approach for representing boundary is taken)
that using multidimensional mereotopologies is more adequate than equidimensional
mereotopologies.
2.6. Kinematic and Kinetic Behaviour
In addition to the static properties of a physical system, one might be interested in the
kinematic and kinetic behaviour of a system. Consider again a suspension system. Ax-
iomatizing the behaviour of springs and dampers requires an axiomatic representation of
force, which in turn requires axiomatic theories of mass, acceleration, velocity, time, and
displacement.
3. Design of the PhysicalWorld Ontology
The PhysicalWorld Ontology is being developed in an ongoing project that aims to ax-
iomatize concepts and properties required for representation and reasoning about phys-
ical domains. The PhysicalWorld Ontology consists of five main modules, namely the
Multi-Dimensional Mereotopology, the Occupation Ontology, the Shape Ontology, the
Attachment Ontology, and the Physics Ontology. Each of these ontologies have their
own modules, and captures one or more of the required concepts described in Section 2.
Figure 3 shows the relationship between modules of the PhysicalWorld Ontology.
3.1. The Shape Ontology
The Shape Ontology is a qualitative representation of shape of physical objects. The
Shape Ontology is an extension of the BoxWorld Ontology presented in [10], which is
based on Hilbert’s axiomatic theory of geometry. Hilbert’s theory consists of three sub-
theories: the first subtheory axiomatizes properties of the incidence relation; the second
one is a theory of betweenness; and the third one describes congruence relationships. The
focus of the Shape Ontology is on the incidence and betweennes relations, and ignores
geometrical notions such as length and relative alignment of lines, or curvature and areas
of surfaces.
The Shape Ontology consists of three main modules: CardWorld, BoxWorld, Poly-
World. Within the domain of a model of the Shape Ontology there are four disjoint cat-
egories of entities – points, edges, surfaces, and boxes, where they respectively corre-
spond to zero-, one-, two-, and three-dimensional objects. CardWorld captures the rela-
tionship between points, edges, and surfaces. Describing properties of a single box and
its parts (i.e., its edges and surfaces) are the focus of the BoxWorld Ontology, whereas
the PolyWorld Ontology axiomatizes the relationships between multiple boxes.
The signature of the Shape Ontology includes a binary relation, part, that captures
the incidence relations between different categories of objects. A lower-dimensional en-
tity cannot exist independently and is always part of a higher dimensional object. For
each box, there exists at least one surface which is part of the box. Similarly, for each
surface exists at least an edge, and for each edge exists at least one point.
The set of edges in a surface, and the set of surfaces in a box, form cyclic orderings.
The edges in a surface are partitioned into disjoint cyclic orderings so that one of these
orderings is formed by the outer edges of the surface, and the remaining cycles represent
holes within the surface. For each surface, there exists a unique set of outer edges that
are all elements of the same cycle.
PhysicalWorld
Attachment
Physics
Multi-Dimensional Mereotopology
Boundary
Displacement Units of Measure
Shape Occupation
Velocity Acceleration Time Force
Ground Mereotopology (MT)
RCC
Figure 3.: Modules of the PhysicalWorld Ontology
Round objects (like circles) are the simplest two-dimensional object that can be
described by the Shape Ontology. A Round object is a surface which has exactly one
edge.
(∀s) round(s) ≡ sur f ace(s) ∧ (∃e) edge(e) ∧ part(e, s)∧
(∀e1 )edge(e1 ) ∧ part(e1 , s) ⊃ (e1 = e).
The Shape ontology, however, cannot represent the difference between a circle and an
oval (i.e. curvature is not definable).
A box is a three-dimensional entity that contains at least one surface. For a box with
multiple distinct surfaces, each surface will contain edges, called ridges, that are part of
exactly two surfaces. In a polyhedron, every edge is a ridge. There are also models that
are not polyhedra; in such models, there exist edges that are parts of unique surfaces. An
edge that is part of a unique surface is a border.
Using the Shape Ontology, a sphere can be described as a box which has exactly one
surface:
(∀x) sphere(x) ≡ box(x) ∧ (∃s) sur f ace(s) ∧ part(s, x)∧
(∀s1 )sur f ace(s1 ) ∧ part(s1 , x) ⊃ (s1 = s).
And a cylinder can be described as a box that has three surfaces such that two of these
surfaces are round objects, and the round objects do not have a common edge:
(∀x) cylinder(x) ≡ box(x) ∧ (∃s1 , s2 , s3 , l1 , l2 ) sur f ace(s1 ) ∧ round(s2 )∧
round(s3 ) ∧ edge(l1 ) ∧ edge(l2 ) ∧ part(l1 , s1 ) ∧ part(l1 , s2 )
∧part(l2 , s1 ) ∧ part(l2 , s3 ) ∧ part(s1 , x) ∧ part(s2 , x) ∧ part(s3 , x).
3.2. Multidimensional Mereotopology
We use MT as the mereotopological theory for expressing connection and parthood be-
tween physical objects since MT is the weakest theory among the existng mereotopolo-
gies (recall from Section 2.2 that stronger mereotopologies impose constraints that may
not be applicable to all classes of physical objects). However, as we explained in Section
3.1, there are four classes of physical entities in the PhysicalWorld Ontology, namely
points, lines, surfaces, and boxes. Therefore, a multidimensional mereotopology is re-
quired.
Relationships between equidimensional individuals are captured by MT, while each
class of object is mereotopologically independent of other classes. Individuals with dif-
ferent dimensions are only related by part, which is an incidence relation (see Section
3.1).
3.3. The Occupation Ontology
All of the existing axiomatic theories of location (including [6,8,4,5]) use a mereotopol-
ogy stronger than MT over non-region entities. Thus, as we discussed in Section 2.2,
they are not desirable for representing locative properties of some classes of physical
objects. Moreover, some of these theories ([6]) allow mereotopological relationship be-
tween abstract regions and non-abstract objects, which leads to the existence of models
that physically do not make sense. To overcome these shortcomings, we developed a new
location theory called the Occupation Ontology.
The Occupation Ontology specifies physical location. Within the Occupation Ontol-
ogy space is consider as an abstract entity in which other elements are located. For exam-
ple, Canada is an object which is located on the abstract region between Atlantic Ocean
and Pacific Ocean. The following is the list of ontological commitments the Occupation
Ontology satisfies:
• Spatial regions and physical objects are distinct entities.
• There is no mereotopological relationship between spatial regions and physical
objects. That is, a physical object is not part of (or connected to) an spatial region,
or vice versa. Instead, physical objects occupy spatial regions.
• Occupation is a relation between a physical object and an spatial region. In other
words, we assume that a spatial region does not occupy itself, or other spatial
regions.
• There is no mereotopological relationships between spatial regions and physical
objects; that is, a physical object is neither part of nor connected to a spatial
region.
• The mereotopological relations between physical objects must be mirrored in the
mereotopological relations between the corresponding spatial regions. That is, if
a physical object a is part of (connected to) another physical object b, then the
region occupied by a is part of (connected to) the region occupied by b.
Considering these commitments, the Occupation Ontology consists of three mod-
ules: a mereotopology over abstract regions, namely the Region Connection Calculus
(RCC) [14], the MT theory relativised to physical objects, and the following axioms that
specify the occupation relationship between abstract regions and physical objects:
ob j(x) ⊃ ¬region(x).
occupy(x, y) ⊃ ob j(x) ∧ region(y).
occupy(x, y) ∧ occupy(x, z) ⊃ (y = z).
ob j(x) ⊃ (∃y) occupy(x, y).
3.4. Remaining work
In this section we discuss the design of modules of the PhysicalWorld Ontology that have
not been axiomatized yet.
3.4.1. The Attachment Ontology
The Attachment Ontology consists of definitions, based on relations specified by the
Shape Ontology and Multidimensional Mereotopology, for describing different types of
physical attachments and joints.
Currently, two types of attachment are included in the ontology, namely strong at-
tachment and weak attachment. We define two boxes to be strongly attached if they are
connected and have a common surface (i.e., there exists an surface which is incident with
the two boxes). Two boxes are weakly attached if they are connected but do not have a
common surface.
(∀x, y)strong attach(x, y) ≡ C(x, y) ∧ (∃z) sur f ace(z) ∧ part(z, x) ∧ part(z, y).
(∀x, y)weak attach(x, y) ≡ C(x, y) ∧ ¬strong attach(x, y).
In order to specify properties of other types of joints, we require to incorporate the
notion of boundary into the PhysicalWorld Ontology. The existing theories of bound-
ary, discussed in Section 2.5, only consider boundaries in abstract regions, and cannot
be applied for representing boundaries of physical objects. It is part of the remaining
work to apply ideas from these theories, and develop an ontology of physical bound-
aries. In particular, we need to identify an axiomatic specification for boundaries of three-
dimensional objects (i.e., boxes).
3.4.2. Physics Ontology
The Physics Ontology axiomatizes fundamental concepts required for representing ki-
netic and kinematic behaviour of physical systems. These concepts include time, dis-
placement, velocity, acceleration, mass, and force. The Physics Ontology includes a mod-
ule for each of these fundamental concepts. Considering the quantitative formulation of
these concepts, the Force ontology depends on the Mass and Acceleration Ontologies,
and the Acceleration Ontology is axiomatized using the Time and Velocity Ontologies.
The Velocity Ontology itself is specified with respect to the Time and the Displacement
Ontologies. Note also that for representing displacement we require a representation for
physical location, that is, the Displacement Ontology depends on the occupation relation
specified by the Occupation Ontology.
In addition to axiomatizing fundamental concepts, the Physics Ontology includes
a module, called Units of Measure, that specifies how units of measure corresponding
to each concept is manipulated. More specifically, the ontologies explicitly axiomatize
how units can be added, subtracted, and multiplied. Moreover, the Units of Measure
Ontology utilizes existing ontologies for time, mereotopology, location, and constitution
to axiomatize the relationship between units of measure and the concept being measured.
4. Summary
Any ontology that supports reasoning about the design and manufacturing of products
must be rooted in a set of more foundational ontologies that represent the commonsense
intuitions about the physical world. Starting with the idea that solid physical objects
are self-connected objects that are made of matter, have a shape with boundaries, and
are located in space, we have designed a suite of ontologies which are modules of an
overarching ontology that we refer to as the PhysicalWorld Ontology. The current status
of the development of the PhysicalWorld Ontology and its modules is summarized in
Table 1.
Concept Ontology Development Phase
Connection and Parthood Multidimensional Mereotopology Axiomatized
Location Occupation Ontology Verified
Qualitative Shape Shape Ontology Axiomatized
Joints and Attachment Attachment Ontology Under development
Kinematic and Kinetic Behaviour Physics Ontology Under development
Table 1. Current status of the development of modules of the PhysicalWorld Ontology.
In addition to supporting automated reasoning about manufacturing and product de-
sign, the PhysicalWorld Ontology also provides a possible foundation for the ontological
analysis of relevant existing standards and to integrate the ontologies within those stan-
dards, in particular ISO 18629 (PSL), OWL-Time, ISO 10303 (STEP), and ISO 15531
(MANDATE).
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