ISO/IEC Standards and Ontologies in Information Technology

ISO/IEC 21383-2: Basic Formal

Ontology

Alan Ruttenberg and Barry Smith

JOWO, Graz, September 24, 2019

These slides: 

1

International Standards Organization (ISO)

International Electrotechnical Commission (IEC)

2

3

4

ISO/IEC define 

connectors

International Standards Organization (ISO)

International Electrotechnical Commission (IEC)

5

ISO/IEC Joint Technical Committee JTC1:

Information technology

6

iso.org/standard/71954.html

iso.org/standard/74572.html

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iso.org/standard/71954.html

iso.org/standard/74572.html

ISO 21838-1: 3.14, 3.17 and 3.18

ontology 

=def.  collection of 

terms

, 

relational expressions

 and

associated natural-language 

definitions

 together with one or

more 

formal theories

 designed to capture the intended

interpretations of these definitions

domain 

=def. collection of 

entities

 of interest to a certain

community or discipline

domain ontology 

=def. 

ontology

whose 

terms

 represent 

classes

or 

types

 in some 

domain

8

ISO 21838-1: 3.19 and 3:20

category 

=def. general 

class

 or type that is shared across many

different 

domains

 and is represented by a domain-neutral 

term

top-level ontology (TLO) 

=def. 

ontology

 that is created to

represent the 

categories

 that are shared across a maximally

broad range of 

domains

9

Requirements for being a top-level ontology

Shall include no domain-ontology content (contra

SUMO)

Shall cover all entities (be maximally general)

Shall comprise a collection of three information

artefacts:

1.

textual artefact

2.

OWL axiomatization

3.

CL axiomatization

10

Requirements for being a top-level ontology

Shall cover all entities

Space and time

Actuality and possibility

Classes and types

Time and change

Parts, wholes, unity and boundaries

Space and place

Scale and granularity

Qualities and other attributes

Quantities and mathematical

entities

Processes and events

Constitution

Causality

Information and reference

Artefacts and socially constructed

entities

Mental entities; imagined entities;

fiction; mythology; religion

11

Requirements for being a top-level ontology

Shall cover all entities (be maximally general)

Shall comprise a collection of three information

artefacts:

1.

textual artefact

2.

OWL axiomatization

3.

CL axiomatization

12

Requirements for being a top-level ontology

1.

exists as a textual artefact

A TLO shall include a textual artefact represented by a natural language

document providing:

(1)

a list of domain-neutral terms and relational expressions,

incorporating identification of primitive terms, and

(2)

definitions of the meanings of the terms and relational expressions

listed.

13

Requirements for being a top-level ontology

2. OWL axiomatization

The TLO shall be made available via at least one machine-

readable axiomatization in OWL 2 with the direct semantics [9]

or in some description logic that is designated by W3C as a

successor of OWL 2.

The signature of the OWL axiomatization shall a subset of the set

of natural language terms and relational expressions that is

specified in the textual artifact.

14

Requirements for being a top-level ontology

3. CL axiomatization

The TLO shall be made available via an axiomatization in a

language conforming to ISO/IEC 24707 Common Logic [1].

The axiomatization shall be proven consistent using standard

automated theorem provers.

It shall be shown that BFO-ISO-OWL is derivable from BFO-ISO-CL

How will CL help?

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Infectious Disease Ontology (IDO)

infectious organism 

=def. An organism that has an infectious

disposition

can be expressed in OWL

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infectious disposition (5-place relation)

=def.  A pathogenic disposition that inheres in an 

organism 

and is

a 

disposition

 for that organism

(1)

to be transmitted to a 

host

,

(2) to establish itself in the host,

(3) to initiate 

processes

 that result in a 

disorder

 in the host, and

(4) to become part of that disorder.

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infection (8-place relation)

•

=def A part of an extended 

organism 

that itself has as part a 

population

of one or more 

infectious agents 

and that

•

(1) exists as a result of 

processes 

initiated by 

members 

of the infectious

agent population and is

•

(2) clinically abnormal in virtue of the presence of this infectious agent

population, or

•

(3) has a 

disposition 

to bring 

clinical abnormality 

to 

immunocompetent

organisms 

of the same 

species 

as the 

host 

through 

transmission 

of a

member 

or 

offspring 

of a member of the infectious agent population.

18

Documentation of hub and spokes approach to the

creation of suites of interoperable ontology modules

hub

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iso.org/standard/74572.html

Contents of ISO/IEC 21838-2: BFO

•

Textual artifact (terms, relational expressions, definitions)

•

Demonstration of status as top-level (= domain-neutral) ontology

•

Link to OWL and CL content on ISO 389 Software Maintenance

Portal (currently at 

https://buffalo.app.box.com/v/bfo-iso-owl-cl

)

•

Guide to creation of BFO-conformant ontology content

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https://buffalo.app.box.com/v/bfo-iso-owl-cl

OWL

1. bfo-iso.owl – OWL in rdf/xml format

2. bfo-iso.ofn – OWL in a variant of a functional syntax with URIs

3. bfo-iso-labeled.ofn – bfo-iso.ofn with the URIs replaced with

the associated labels, a version more appropriate for reading

Two versions provided, one with full set of temporalized

relations

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https://buffalo.app.box.com/v/bfo-iso-owl-cl

MODEL

three versions of the model used to prove consistency of the

CL formalization: in prover 9, CLIF, and Clausetester formats

CL

CL axiomatization of BFO-ISO

PDF

complete set of modules of the CL axiomatization of BFO-ISO

is provided in the traditional first-order logic (FOL) syntax.

25

https://buffalo.app.box.com/v/bfo-iso-owl-cl

BFO-ISO

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BFO 2.0

27

pr

ocess

profile

N

N

R

R

R

X

BFO-ISO

28

X = Deprecated; 

N = New,  R = Renamed

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1.

Bug fixes, including improved set of natural-language definitions

2.

FOL / CL

formalization and consistency proof

•

More expressive, more intuitive for human use in ontology design

•

Provides basis for multiple different OWL versions

•

BFO-ISO-OWL1 

core version

•

BFO-ISO-OWL2 version with full set of temporalized relations

Other changes

Rollout strategy for BFO-ISO

1.

Publication of ISO/IEC 21838 Parts 1 and 2 in spring

2020

2.

Revise BFO 2.0 Spec to conform to BFO-ISO and

publish for critical review

3.

Replace BFO 2.0 by BFO-ISO as official version of

BFO

4.

Create software to enable (semi-)automatic update

of BFO 2.0-based ontologies to BFO-ISO

conformance

30

Initial impact

•

ISO 29303: Interoperability Reference Framework

•

ISO/CEN Materials Testing

•

Joint AI Center (JAIC) ISO standard for AI

•

IC and Military Ontology Suites

•

BFO-Based Engineering Ontologies - NCOR Wiki

•

IOF

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32

https://www.industrialontologies.org/

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BFO-Based Engineering Ontologies

34

BFO-Based Engineering Ontologies

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BFO-Based Engineering Ontologies

https://mitpress.mit.edu/building-ontologies

36

37

Next steps with BFO

1.

Sites – protein sites, oral cavity, thoracic cavity, [interior of] exhaust

pipe – vs. spatial regions (determined by frame of reference)

2.

Units of measure – how to deal with things like this. What sort of

entity is a joule per second squared  (1 m

2

 kg / s

4

)?

3.

What is a system in BFO?

4.

Process qualities – BFO recognizes only qualities of independent

continuants – what about rates (heart beat, flow, frequency, …).

What about qualities of processes as recognized by PATO (the

quality ontology)

For example: velocity, frequency, rate (of heart beat, of flow)

38

specifically_depends_on

Continuant

Occurrent

process, event

Independent

Continuant

thing

Specifically 

Dependent

Continuant

quality

 ....  .....    .......

temperature depends

on bearer

39

The problem with process qualities

Occurrent

(Process)

Independent

Continuant

(

molecule, 

cell, organ,

organism

)

quality 

.....  .....     ....  .....

40

rate … 

inheres-in

inheres-in

Occurrent

(Process)

Independent

Continuant

(

molecule, 

cell, organ,

organism

)

PATO:

quality 

.....  .....  ....  .....

41

inheres-in

inheres-in

The problem with process qualities

Proposed solution

Occurrent

(Process)

Independent

Continuant

(

molecule, 

cell, organ,

organism

)

BFO:

quality 

.....  .....  ....  .....

42

PATO:

characteristic… 

has-characteristic

inheres-in

‘characteristic’ is an abbreviation (defined class,

convenience class)

John is running at 3 miles per minute at 

t

means:

–

John has quality at 

t

: running at 3 miles per minute

–

John participant_in running r

1 

at 

t

–

 r

1 

has characteristic (rate) 3 miles per minute at 

t

43

‘characteristic’ is an abbreviation (defined class,

convenience class)

Example: running 

r 

at 

t 

has velocity 

v

r

 has characteristic (rate) 

v 

at 

t =

def.

there is some 

x

, 

x 

is an independent continuant

& x

 participant_in 

r 

at 

t

& x has quality at 

t

: running at 3 miles per minute

44

Continuant

Occurrent

Independent

Continuant

Specifically 

Dependent

Continuant

Quality

Disposition

e.g. Functioning

Function

Role

Realizable

Dependent

Continuant

45

Occurrent

Independent

Continuant

Specifically 

Dependent

Continuant

Quality

Disposition

Function

e.g. Disease

Role

Realizable

Dependent

Continuant

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Disease Course

Occurrent

Independent

Continuant

Specifically 

Dependent

Continuant

Quality

Disposition

Function

e.g. Disease

Role

Realizable

Dependent

Continuant

47

Disease Course

Disorder

has material basis

realized

 in

Specifically Dependent Continuants

Specifically

Dependent

Continuant

Quality, Pattern

Realizable 

Dependent 

Continuant

if any bearer ceases to exist,

then the quality or function

ceases to exist

the color of my skin

the function of my heart

48

Generically Dependent Continuants

Generically

Dependent

Continuant

Information 

Object

Sequence

if one bearer ceases to exist, then

the entity can survive, because

there are other bearers

(copyability)

the pdf file on my laptop

the DNA (sequence) in this

chromosome

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Information objects

pdf file

poem

symphony

algorithm

symbol

sequence

molecular structure

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Generically dependent continuants such as

plans, laws …

are concretized in specifically dependent

continuants

(the plan in your head, the protocol being

realized by your research team, the law

being implemented by this government

agency)

51

T

h

e

s

a

m

e

d

a

t

u

m

c

a

n

e

x

i

s

t

i

n

m

a

n

y

c

o

n

c

r

e

t

i

z

a

t

i

o

n

s

Generically

Dependent

Continuant

Information 

Artifact

excel file 

doc file

instances

52

Continuant

Independent

Continuant

Specifically 

Dependent

Continuant

Quality

Disposition

Information 

Artifact

Role

Realizable

 Dependent

Continuant

53

Generically

Dependent

Continuant

Gene 

Sequence

Continuant

Independent

Continuant

Specifically 

Dependent

Continuant

Quality

Information 

Artifact

54

Generically

Dependent

Continuant

Gene 

Sequence

Material 

Entity

Information 

Bearing 

Entity

Continuant

Independent

Continuant

Specifically 

Dependent

Continuant

Quality

Information 

Artifact

55

Generically

Dependent

Continuant

Material 

Entity

Information 

Bearing 

Entity (your

hard drive

Information 

Quality Entity 

(pattern on 

your hard drive)

specifically

depends_on

Continuant

Independent

Continuant

Specifically 

Dependent

Continuant

Quality

Information 

Artifact

56

Generically

Dependent

Continuant

Material 

Entity

Information 

Bearing 

Entity

Information 

Quality

Entity

 (Pattern) 

specifically

depends_on

concretized_by

`

Alan Ruttenberg

These slides: 

https://buffalo.box.com/v/BFO-ISO-JOWO

58

1.

First-Order Logic / Common Logic formalization and consistency

proof

•

More expressive, more intuitive for human use in ontology

design

•

Provides basis for multiple different OWL versions

•

BFO-ISO-OWL1 without temporalized regions

•

BFO-ISO-OWL2 full set of temporalized relations

2.

Definitive set of natural-language definitions and examples

3.

A clear basis for evaluating criticisms or extensions of BFO

What BFO-ISO brings to the table

These slides: 

https://buffalo.box.com/v/BFO-ISO-JOWO

BFO-ISO axiomatization compared to BFO2 Reference

captures the content of the 2015 BFO 2.0 Reference and User’s Guide, with some

changes:

1.

Revised labels in some cases

2.

Some new relations

3.

Remove sub-properties of inheres-in

4.

Clarification of the temporal theory

5.

Bug fixes (including errors in axioms)

6.

Normalization of spatiotemporal relations to remove redundancy

7.

Some changes to time-indexed relations

8.

Uniform treatment of access to time-indexed relations from OWL

9.

Object aggregates can, at some times, have only a single member

10.

Removal of reference to space and time (SpaceR and TimeR) in definitions

11.

OWL version relation to FOL version clarified.

The Reference and User’s Guide will be revised to capture these changes, and

to incorporate a large body of new examples of usage

59

Friendlier labels for boundary terms

‘0-D continuant fiat boundary’ renamed: ‘fiat point’

‘1-D continuant fiat boundary’ renamed: ‘fiat line’

‘2-D continuant fiat boundary’ renamed: ‘fiat surface’

60

is quality of, is role of, is function of

We don’t define these in the formal theory because

•

They are trivial to define if you want them

•

They duplicate the type: If B is function of C then B is a

function.

•

All these properties are sub-properties of inheres-in

•

All the information you need is in the inheres in relation and

type of subject

•

Doing so makes the model smaller

61

Temporal theory extended

four new relations added

•

first instant of (temporal instant, temporal region)

•

last instant of (temporal instant, temporal region)

•

concretizes at (quality or process, gdc, temporal region)

•

Is carrier of at (quality, gdc, temporal region)

As well as their inverses

part-of split into (binary) occurrent-part-of and (time-indexed continuant-part-of-at)

62

More on temporal theory later

Spatiotemporal relations

•

Remove many same-type relations e.g

temporal region occupies temporal region

•

Occupation relations

range: spatiotemporal

•

Location relation

range: independent continuants,

but not spatial regions

•

Existence relation

range: temporal region

Note: ternary relations in diagram have

arrow “at” branching off arrow relating

first two relata

63

Spatiotemporal relation extent

•

Exists-at is partial

•

exists-at(x,t) means x exists at least at t

•

Instance-of is partial

•

instance-of(x,U,t) means x  instantiates U for at least t

•

Occupy relations are exact

•

occupies-temporal-region(p,t) means p doesn’t occupy anything other than t.

•

Projection relations are exact

•

projects-onto-temporal-region(st,t) means the projection is to exactly t.

64

These slides: 

https://buffalo.box.com/v/BFO-ISO-JOWO

Five relations lose temporal index

•

Rationale:

•

If some B specifically depends on some C, then B depends on C

at any time B exists. Thus the time index can be carried by ‘exists

at’. a temporal index doesn’t carry additional interesting

information.

•

It was clarified that if a process realizes a role, it realizes it the

whole time the process exists. Again no choice so no necessity

for temporal index.

•

Usage in OWL is simpler. At-some-time and at-all-times versions

of these relations unnecessary.

65

Concretizes 

gains

 a temporal index

•

There is 

now

 an aggregate of people

•

They form a shape (quality)

•

The aggregate bears the shape

•

The shape concretizes the logo

but only for now

•

After a while the aggregate moves around

•

The shape changes

•

Same GDC, same quality particular (the shape changes type)

•

Now the shape doesn’t concretize the logo

•

Implication: because qualities can change, it matters 

when

 the quality is

understood to concretize a GDC

66

Object aggregates can have a single member

at some times

•

“An entity b is an object aggregate at t if and only if there is a mutually

exhaustive and pairwise disjoint partition of b into object

s

 at t”

•

Elsewhere that is formalized with n >= 2

•

Rationale: Organizations are object aggregates

•

What if a two person organization loses one of it’s members? Does the

organization cease to exist? Not necessarily

•

So: An entity 

b

 can be an object aggregate 

even if 

it has only one

member BUT at some time it must have more than one member.

67

These slides: 

https://buffalo.box.com/v/BFO-ISO-JOWO

Object aggregates can temporarily coincide

•

Rationale: Organizations are object aggregates, albeit with specific kinds

of roles.

•

Consider a small town fire company, which changes members

periodically

•

Some members are also part of the school committee

•

Suppose, that during a high turnover period it happens the members of

the two organizations are exactly the same. There are still two

organizations.

•

This mereology not extensional. Accordingly antisymmetry is modified

so it applies not to every moment, but to the history as a whole.

68

SpaceR, TimeR

•

In BFO 2 conceived as maximal temporal region/spatial region of

which all other regions were parts

•

This is in direct opposition to what we know of relativity

•

Instead:

•

Spatiotemporal regions primary

•

All temporal regions project from a spatiotemporal region

•

All spatial regions project from a spatiotemporal region

These slides: 

https://buffalo.box.com/v/BFO-ISO-JOWO

Miscellaneous

•

Processes exist at least on an interval

•

a specifically dependent continuant can inhere in more than one

independent continuant

•

Relational quality = quality that inheres in more than one thing

70

These slides: 

https://buffalo.box.com/v/BFO-ISO-JOWO

Axiomatization

What’s an axiomatization?

•

An axiomatization is an expression of a theory in a logical system

•

We have BFO axiomatization is expressed in first order logic

•

Renderings in common logic, different prover formats, typeset

•

Examples for: TransitiveObjectProperty(temporalPartOf)

•

   f

https://buffalo.app.box.com/v/bfo-iso-owl-cl

72

•

(forall (a b c)

(if (and (temporal-part-of a b) (temporal-part-of b c))

(temporal-part-of a c)))

Things you can do with FOL

•

Is this set of formulas consistent?

•

What is a model of this set of formulas?

•

Is this model I have satisfying?

•

Is this conclusion correct?

•

Am I justified in adding this assertion to OWL?

•

A new set of tools to apply to our problems.

https://buffalo.app.box.com/v/bfo-iso-owl-cl

73

The BFO-FOL axiomatization

•

Goal to make something useful (to an ontology engineer)

•

Make as much implicit understanding explicit

•

Clarify underspecified areas of the spec

•

Expose and fix bugs

•

Make sure it is reasonable as a logical theory – consistent, models intended

•

There are tools available to use it in a practical way

•

Create a baseline against which future extensions can be measured

•

Fix it when necessary, strengthen it over time

•

Have it be a basis for adjudicating questions of appropriateness of different

OWL approaches

•

Use it to help build BFO-OWL

•

Make it “good enough to be wrong” ™

74

Working with OWL

Using BFO from OWL

•

We understand the world, in part, by framing it within BFO

•

Take BFO as expressed in FOL as authoritative

•

To write OWL we need to understand what it means by expressing it

in FOL

•

The authoritative BFO is not frozen – It is a start

•

If BFO is problematic in some area, let’s try to fix BFO

https://buffalo.app.box.com/v/bfo-iso-owl-cl

76

How to base an ontology on BFO

•

When using BFO terms, use the BFO URIs

•

Import as strong a version of BFO as is practical

•

Understand that even without BFO axioms in your ontology, your

ontology still needs to be consistent with BFO.

•

Use FOL tools to do QC of the ontology or parts of it and the complete

BFO

•

Don’t reinvent parts of BFO in your ontology

•

If something 

can 

be expressed using BFO or specialized from it, 

do

 so.

https://buffalo.app.box.com/v/bfo-iso-owl-cl

77

BFO considered semantic extension of OWL

•

A semantic extension defines entailments which are valid under that

extension

•

Semantic extensions may impose special syntactic conditions

•

Entailment regimes must be monotonic in the sense that if A simply entails

B then A also entails B under any extended notion of entailment

•

A semantic extension cannot "cancel" an entailment made by a weaker

entailment regime, although it can treat the result as a syntax error.

•

However, a set of OWL assertions could become inconsistent when

interpreted according to the extension

https://buffalo.app.box.com/v/bfo-iso-owl-cl

78

BFO-OWL

•

We ignore (for the moment) OWL data expressions

•

There is a well-defined translation (WDT)  from vanilla OWL to first

order logic (FOL)

•

BFO-OWL is a semantic extension of OWL

•

We document a WDT from BFO-OWL (BFOT) to FOL

•

What does it mean for the translation to work?

•

BFO-OWL artifact defined as any OWL assertion that is BFO-FOL valid.

https://buffalo.app.box.com/v/bfo-iso-owl-cl

79

Soundness and completeness

•

Properties of a reasoner/logical language

•

Soundness = conclusions a reasoner finds aren’t mistaken

•

Completeness = the reasoner will compute all possible conclusions

•

OWL-DL is sound and complete

•

OWL Reasoning with BFO-OWL 

should

 be sound, may not be

complete

•

That’s not surprising – consider that OWL is a semantic extension of

RDF but that an RDF reasoner won’t find conclusions an OWL

reasoner would

https://buffalo.app.box.com/v/bfo-iso-owl-cl

80

Soundness

•

If an OWL reasoner draws a conclusion, then a FOL reasoner should

draw the same conclusion based on the translation from OWL

•

If not, OWL isn’t being helpful – you can’t trust it’s reasoner

81

Completeness

•

A first order prover might find a conclusion that the OWL reasoner would not

•

This is the added value – by using a stronger reasoner we get additional

conclusions

•

Correspondingly, the stronger reasoner gives us understanding of where BFO-

OWL will be incomplete

82

Validating BFO-OWL

•

BFO-OWL is BFO-Sound if every conclusion of the OWL reasoner is a

valid conclusion from BFO-FOL

•

Every BFO-OWL assertion is provable from BFO-FOL

•

OWL reasoning is sound, i.e. every conclusion an OWL reasoner

makes is provable

•

Therefore BFO-OWL is BFO-sound

83

Compositionality

•

If in OWL, assertion 1 is true and assertion 2 is true, then

(assertion 1 and assertion 2) is true

•

The same must go for the translations via BFOT* (soundness)

*BFOT = translation of BFO-OWL in FOL syntax

84

Temporal regions

Temporal theory

•

A time-indexed relation captures relations which may change in time

•

BFO has many such relations – parthood, location, participation

•

But what is this 

time 

you speak of? Underspecified.

•

What are 0-dimensional and 1-dimension temporal regions?

a continuant-part-of b at time t

•

OWL only supports binary relations. What to do?

Temporal regions

•

BFO ISO make decisions about the structure of temporal theory, which

were previously not clear.

•

Hard requirements are

•

Must have two sorts of temporal regions: instants and intervals

•

Minimal extensional mereology

•

Don’t disagree with known science

•

Quantification should be over temporal regions.

•

Common choices in temporal theories

•

Dense – between any two instants there’s another instant

•

Discrete – there is successor and predecessor relations

•

Infinitely extends forward and or backwards

•

Current science is unclear which of these, if any, is true of time

•

So BFO does not adopt any of them

•

Bonus: There are finite models

Structure through first and last instant

first and last instant may or may not be part of the region they bound

temporal instants form a total order using the precedes relationship

with gaps

Temporal region dimensionality

•

Interpretation of zero- and one-dimensional temporal regions wasn’t clear

•

zero dimensional temporal region: A sum of only temporal instants

•

Mereological sum of of now and an hour ago.

•

one dimensional temporal region: A sum including an temporal interval

•

Can be weird stuff such as disjoint sums of intervals and points

•

Every temporal region is part of an interval.

•

If you want to ignore special relativity you can assert that there is a unique interval all temporal

regions are part of.

Temporal region is a disjoint union of zero- and one-dimensional regions. The only class asserted as

disjoint union in BFO.

•

Note: Spatial regions deserve similar treatment, but that’s not yet

developed

89

Temporal region hierarchy

90

No parts other than self

No gaps between beginning

 and end

Disjoint sums of regions including at least an interval

Disjoint sums of instants

Didn’t seem worth naming

Intervals have no gaps

•

Define temporal intervals as having no gaps using first and last instant

•

If there’s a temporal interval B whose first instant is 

F

1 and last

instant is 

L

1, and temporal region C whose first instant is 

F

2 and last

instant 

L

2 and 

F

2 > 

F

1 and 

L

2 < 

L

1, then C is temporal part of B

L

1

91

Interval parts cover the interval

•

If an interval has parts, it has to be at least a sum of intervals that

cover the larger interval

B, D, E are intervals

C is a instant

Yup

92

OWL time-indexed relations

Challenges in developing an OWL BFO

•

We want BFO OWL to be BFO-understandable in terms of BFO-FOL

•

BFO’s instance-of relation is time-indexed. The cognate rdf:type is

binary.

•

Many other relations are ternary, but OWL supports only binary

relations

•

Easy:

•

Is-a, translates directly to rdfs:subclassOf

•

Classes are directly transferable to OWL

Origins: Class relations

In ”Relations in Biomedical Ontologies” a pattern is developed for how to interpret

class-class relations. For example, A part of B, were A and B are continuant is to be

interpreted as

(forall (x t)

  (if (instance-of x A t)

    (and (exists (b) (instance-of b B t))

             (part-of a b t)))

For occurrents

(forall (x t)

  (if (instance-of x A t)

    (and (exists (b) (instance-of b B))

             (part-of a b)))

Note that that for the continuant case, even though there is a time-indexed instance of, the relation

defined has no time index

First attempts at BFO-OWL, and their failure

•

Since OWL supports only binary relations, the binary class relations

were used in OWL

•

The problem: Those related classes but OWL relates individuals

•

So the semantics is wrong.

•

In addition, the class semantics was only partially adopted. For

example class-has-part is not the inverse of class-part-of, but the

binary has-part we used in OWL

 was

 taken as the inverse of has-part

BFO-ISO axiomatization strategy

•

BFO-OWL should follow as a logical consequence of BFO-OWL.

•

Develop binary relations that indirectly 

used

 the time-indexed

relations, even if we couldn’t use the BFO primitives directly.

•

These new relations would be completely defined in terms of the BFO

primitives, and since they were binary, they could be used in OWL

•

With these we prove each assertion in the BFO OWL file from the BFO

FOL theory. In fact we *define* the BFO OWL file to be any collection

of assertions that can be proven from BFO-FOL or a conservative

extension

Strategy sets of associated relations

(forall (p q)

 (iff (

occupies-spatial-region-

at-some-time

 p q

)

  (exists (t)

   (and (exists-at p t) (exists-at q t)

    (

occupies-spatial-region 

p q t

)))))

The at-some-time gives access

to 

a

 relation that otherwise

can’t be expressed in OWL

Every time indexed relation in BFO has corresponding

at-all-times and at-some-time relations

•

concretizes

•

is concretized by

•

continuant part of

•

has continuant part

•

proper continuant part of

•

has proper continuant part

•

generically depends on

•

located in

•

has location

•

has material basis

•

material basis of

•

member part of

•

has member part

•

has participant

•

participates in

•

is carrier of

•

occupies spatial region

•

spatially projects onto at

Benefits/Caveats

•

Benefits

•

The biggest benefit is that that without these there would be no ways – directly or indirectly – to

use the BFO time-indexed relations.

•

With these definitions all assertions in the OWL version of BFO are provably consequences of BFO-

FOL.

•

However;

•

These relations are “permanent specific relations” vs the “permanent generic relations” suggested

by the Relations paper

•

They assume rigid classes in that we need a translation for rdf:type. Since rdf:type is binary it can’t

be understood as BFO’s ternary instance-of relation. We define (a rdf:type C) as (forall (t) (if

(exists-at a t) (instance-of a C t)))

•

They are over the 

existence of entities 

rather than over 

when they instantiate certain classes

.

•

Where a base relation is transitive, the at-all-times version is also transitive 

but the at-some-

time version is not

•

There is active work to develop alternative conservative extensions of BFO that give

access to the ternary primitives but which address some of the current limitations.

Temporal Quantification

Temporal quantification

•

When we write “forall 

t

”, what does 

t

 range over?

•

“Relations in Biomedical Ontology” (RBMO) paper writes:

where 

t 

ranges over temporal instances

•

What if we want 

t

 to range over temporal regions? Conflict.

102

Contradiction

•

A material entity M occupies two spatial regions S1, S2 at two times

T1, T2.

•

Material entities can occupy only one spatial region at a time

•

Suppose M exists at interval T, which is the sum of T1, T2

•

Quantifying over temporal regions would mean 

t -> 

T, T1, T2

•

Using RBMO formulation, there would need to be a spatial region S

that M occupies at each of T, T1, T2

•

Whatever you choose for s will conflict with either T1, T2, or both.

103

Contradiction

•

No matter what S? is, it will conflict

with either S1, S2 or both

104

Revised pattern

(forall (C C1)

  (iff (part-of C C1)

      (forall (c t)

        (implies (instance-of c C t)

            (exists (c1)

              (and (instance-of c1 C1 t)

                       (part-of c c1 t)))))))

(forall (C C1)

  (iff (part-of C C1)

      (forall (c t)

        (implies (instance-of c C t)

            (exists (c1 

t'

)

              (and 

(part-of t' t)

                       (instance-of c1 C1 

t'

)

                       (part-of c c1 

t'

)))))))

Pattern: forall t [use t]

Pattern: forall t 

there is a part t1  [use t1]

The second pattern has the desired meaning, for a finite (non-dense, non-infinite) temporal theory

105

All formal content of ISO/IEC 21838-2: Basic Formal Ontology 

https://buffalo.app.box.com/v/bfo-iso-owl-cl

These slides:

https://buffalo.box.com/v/BFO-ISO-JOWO