John Bateman Till Mossakowski Oliver Kutz Joana Hois
description
Transcript of John Bateman Till Mossakowski Oliver Kutz Joana Hois
![Page 1: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/1.jpg)
Ontology Structuring Mechanisms and Ontological Modularity
ongoing research and targeted applications
John Bateman Till Mossakowski
Oliver KutzJoana Hois
http://www.sfbtr8.uni-bremen.dehttp://www.fb10.uni-bremen.de/ontology
BREMEN ONTOLOGY RESEARCH GROUP
University of Bremen + DKFI, Bremen
![Page 2: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/2.jpg)
I1-[OntoSpace]
2Bateman/Mossakowski/Kutz/Hois 2008
Overview of our topics today
● General orientation and our position on ontologies
● The formal framework within which we are working
● Examples of ontological modularities and re-use
● Conclusions
![Page 3: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/3.jpg)
I1-[OntoSpace]
3Bateman/Mossakowski/Kutz/Hois 2008
Several Research Areas currently under Investigation
● Mobility support
● Spatially-embedded tasks
● Exploration, Route Planning
● Navigation
● Interaction with diverse user groups
● Disabilities
● Age
![Page 4: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/4.jpg)
I1-[OntoSpace]
4Bateman/Mossakowski/Kutz/Hois 2008
Problem foci
● Spatial assistance systems● Route planning and navigation● Real-world environments
involving ‘common-sense’ entities● Interfacing with geographic information● Interfacing with language technology● Interfacing with visual presentations (maps)● Interfacing with robotic sensor data● Embodied systems● Human-Robot Interaction
![Page 5: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/5.jpg)
I1-[OntoSpace]
5Bateman/Mossakowski/Kutz/Hois 2008
Problem
● Many different kinds of knowledge are required to get people into the loop in a way that is empowering and enriching rather than restricting
![Page 6: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/6.jpg)
I1-[OntoSpace]
6Bateman/Mossakowski/Kutz/Hois 2008
Voronoi map From Voronoi map From SFB/TR8 project: SFB/TR8 project: A1-[RoboMap]A1-[RoboMap]
Voronoi calculation on a scanned floor plan
“where are you?”
![Page 7: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/7.jpg)
I1-[OntoSpace]
7Bateman/Mossakowski/Kutz/Hois 2008
Sources of relevant knowledge
Location-based services
Geographic Information Systems
Commonsense objects and activities
Spatial awareness and understanding
Natural language capabilities
Robot perception
Use
r K
now
ledg
e U
ser
(dis
)abi
litie
s
![Page 8: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/8.jpg)
I1-[OntoSpace]
8Bateman/Mossakowski/Kutz/Hois 2008
Problem restated
● Getting these diverse areas of expertise to talk to each other is a serious issue● different communities● different interests● different representations
● The kinds of knowledge maintained by such systems are very different
![Page 9: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/9.jpg)
I1-[OntoSpace]
9Bateman/Mossakowski/Kutz/Hois 2008
Essential idea…
● Providing channels to ontologies provides access to detailed contextual ‘world-knowledge’ that does not then have to be worked out again…
Application
Ontology
![Page 10: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/10.jpg)
I1-[OntoSpace]
10Bateman/Mossakowski/Kutz/Hois 2008
Many perspectives on ‘reality’: many ontologies
event
time
space-1
space-2
event
Ontologically diverse
![Page 11: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/11.jpg)
I1-[OntoSpace]
11Bateman/Mossakowski/Kutz/Hois 2008
Example of communication problems: When is a road not a road?
● Community 1:● transit system designers● roads and highways as connections between
destinations (cities, towns, etc.)
● Community 2:● environment and wildlife department● species have habitats● habitats have divisions separating them
![Page 12: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/12.jpg)
I1-[OntoSpace]
12Bateman/Mossakowski/Kutz/Hois 2008
Ontologically mediated inter-operability
city A
city B
Hwy 456
nodenode
transit system
graph ontology
environment
species A
region ontology
![Page 13: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/13.jpg)
I1-[OntoSpace]
13Bateman/Mossakowski/Kutz/Hois 2008
Ontologically mediated inter-operability
city A
city B
Hwy 456
nodenode
transit system
graph ontology
environment
region ontology
species A
![Page 14: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/14.jpg)
I1-[OntoSpace]
14Bateman/Mossakowski/Kutz/Hois 2008
Methodological starting point
● There is no sense in which a simple ‘merging’ of the ontologies involved is a sensible strategy to follow
![Page 15: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/15.jpg)
I1-[OntoSpace]
15Bateman/Mossakowski/Kutz/Hois 2008
Solution we are pursuing
● High degree of interoperability between diverse knowledge-rich systems is to be achieved by ontological engineering, taking in:
● knowledge of the human world (commonsense)● knowledge of the robot world (programmed, emergent)● geo-knowledge (GML, other standards)● spatial knowledge (spatial calculi)● knowledge of language (linguistics)
![Page 16: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/16.jpg)
I1-[OntoSpace]
16Bateman/Mossakowski/Kutz/Hois 2008
Ontological diversity inter-ontology mappings
description
time
landmarks
choremes
event types
CASL
CASLCASL
route graphs
CASL
CASL
![Page 17: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/17.jpg)
I1-[OntoSpace]
17Bateman/Mossakowski/Kutz/Hois 2008
Perspectives / Viewsrather than inheritance
lake
geographical region
Alternate theories / ontologies
obstacle
recreational area
source of pure water
link in transport network
![Page 18: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/18.jpg)
I1-[OntoSpace]
18Bateman/Mossakowski/Kutz/Hois 2008
Inter-ontology mappings
● ... can only work if there is sufficient content to get hold of!
● That is: not a relationship between ‘terms’ but a relationship between ‘theories’.
● For this, need deep ontologies, so-called ‘axiomatized ontologies’
![Page 19: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/19.jpg)
I1-[OntoSpace]
19Bateman/Mossakowski/Kutz/Hois 2008
Choosing between types of ontologies
● ‘Light’ ontologies: semantic web?
● ‘Heavy’ ontologies:● Rich axiomatization● Formal principles ● Well-defined design criteria
![Page 20: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/20.jpg)
I1-[OntoSpace]
20Bateman/Mossakowski/Kutz/Hois 2008
Our ontological starting point
Leo Obrst
![Page 21: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/21.jpg)
I1-[OntoSpace]
21Bateman/Mossakowski/Kutz/Hois 2008
Theories...
● We all have theories...● theories of the world● theories of how buildings are● theories of the best way to get from A to B● theories of how to persuade your boss for a
raise
● ‘A-ontologies’ set such theories out in an explicit specification.
![Page 22: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/22.jpg)
I1-[OntoSpace]
22Bateman/Mossakowski/Kutz/Hois 2008
Prerequisites for success
● unless you can reason with the axioms: non-starter
● unless you can chunk your axioms: non-starter
● unless you can parameterize and re-use theories: non-starter
● unless you can state relations between the meanings of chunks: non-starter
logic
building theories
structured logic support
inter-theory mappings
![Page 23: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/23.jpg)
I1-[OntoSpace]
23Bateman/Mossakowski/Kutz/Hois 2008
Essential ingredients we are drawing on in Bremen
● Existing ontologies
● DOLCE (Masalo/Borgo/Guarino) (for cross-category binding and axiomatization)
● BFO (Barry Smith) (for sites, niches and places and for SNAP/SPAN)
● GUM (John Bateman) (for linguistic semantics and natural language processing)
● State of the art logical tools● CASL + Hets Tool
![Page 24: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/24.jpg)
I1-[OntoSpace]
24Bateman/Mossakowski/Kutz/Hois 2008
Ontology construction
● Axioms are grouped into logically appropriate theories● Theories may be extended via parameterization to
achieve semantic re-use● Theories may be created and related by views: theory
morphisms
Only with this re-use factor can the complexity of distinct axiomatized ontologies really be harnessed and used to scale-up.
![Page 25: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/25.jpg)
I1-[OntoSpace]
25Bateman/Mossakowski/Kutz/Hois 2008
Approaches to ‘simplifying’ the ontologist’s life...
● Making sure that each component of a library of theories only specifies the axioms which are relevant at that point (cf. John Sowa: “That is the whole point of Ockham's razor: eliminate any axioms that are not absolutely essential to the task at hand.”)
● Making sure that unnecessary detail is hidden in ‘upstream’ libraries: CASL
● Possibilities for ‘common subsets’:
● packages such as our spatial calculi
● packages such as DOLCE’s ‘constitution’, ‘participation’, ‘quality spaces’, BFO’s ‘sites’
● language-based generic ontology (GUM)
![Page 26: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/26.jpg)
I1-[OntoSpace]
26Bateman/Mossakowski/Kutz/Hois 2008
This is essential: because in analysis there are a lot of pieces to put back together!!
![Page 27: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/27.jpg)
I1-[OntoSpace]
27Bateman/Mossakowski/Kutz/Hois 2008
Combining theories for semantic interpretation
driving along
the road to Bremen
on the right
is a church
![Page 28: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/28.jpg)
I1-[OntoSpace]
28Bateman/Mossakowski/Kutz/Hois 2008
Combining theories for semantic interpretation
driving along
the road to Bremen
on the right
is a church
o>
hp
oriented path
route graph
half-planes
physical object occupying a region
![Page 29: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/29.jpg)
I1-[OntoSpace]
29Bateman/Mossakowski/Kutz/Hois 2008
OK, go towards the mountains along the main road
until you reach a large wooden house.
Be careful, the road gets a bit narrow where the old church sticks out.
Turn right at the house and,
then, at the third intersection, turn right leaving the city limits.
Then turn downhill towards the river.
At the river, take the ferry over to the café.
![Page 30: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/30.jpg)
I1-[OntoSpace]
30Bateman/Mossakowski/Kutz/Hois 2008
OK, go towards the mountains along the main road
until you reach a large wooden house.
Be careful, the road gets a bit narrow where the old church sticks out.
Turn right at the house and,
then, at the third intersection, turn right leaving the city limits.
Then turn downhill towards the river.
At the river, take the ferry over to the café.
theory of landmarks: mountain
theory of destinations: the house
theory of structural landmarks / constraints on movement and decisions: (along) the main road
Theories needed for interpretation
theory of shapes of physical objects: narrow road, old church (sticking out)
theories of orientation: towards
theory of landmarks: the house
theories of orientation: right
theory of ordered sequencestheories of orientation: right
theories of regions (administrative): city
theories of orientation: towardstheories of topography: slopestheory of landmarks: the river
theory of structural landmarks: intersections
theory of structural landmarks: (over) the rivertheory of landmarks: river
theory of destinations: the café
![Page 31: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/31.jpg)
I1-[OntoSpace]
31Bateman/Mossakowski/Kutz/Hois 2008
Theories...
● Each of these contributions to the meaning of what is being said is considered to draw on a range of more or less related theories of the world…
● axiomatised ontologies set such theories out in an explicit specification.
![Page 32: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/32.jpg)
I1-[OntoSpace]
32Bateman/Mossakowski/Kutz/Hois 2008
John Sowa(email/web discussion)
IEEE StandardUpper OntologyWorking Group
![Page 33: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/33.jpg)
I1-[OntoSpace]
33Bateman/Mossakowski/Kutz/Hois 2008
John Sowa(email/web discussion)
IEEE StandardUpper OntologyWorking Group
![Page 34: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/34.jpg)
I1-[OntoSpace]
34Bateman/Mossakowski/Kutz/Hois 2008
John Sowa(email/web discussion)
IEEE StandardUpper OntologyWorking Group
• What kinds of ‘modules’ are these?
• What is the nature of relationships that can hold between them?
• How do these relate to different communities’ theories of the world?
![Page 35: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/35.jpg)
I1-[OntoSpace]
35Bateman/Mossakowski/Kutz/Hois 2008
A general approach…
In the next section of the talk we discuss how we are formalizing these notions of ontological modularity and inter-module relationships.
● Formal framework: CASL● Generic framework for describing how
ontologies and modules can be related: ‘alignments’
● Some examples
![Page 36: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/36.jpg)
I1-[OntoSpace]
36Bateman/Mossakowski/Kutz/Hois 2008
CASL - Common Algebraic Specification Language
• Standardised first-order specification language;
• designed by CoFI “Common Framework Initiative for algebraic specification and development” since 1995
• approved by IFIP WG 1.3 “Foundations of Systems Specifications” (1998), extensive documentation (LNCS 2900, 2960)
• various extensions and sublanguages, including higher-order dialects, modal logic, OWL-DL;
• supports structured specifications including imports, hiding, renaming, union, extensions, etc.
![Page 37: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/37.jpg)
I1-[OntoSpace]
37Bateman/Mossakowski/Kutz/Hois 2008
CASL language constructs
![Page 38: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/38.jpg)
I1-[OntoSpace]
38Bateman/Mossakowski/Kutz/Hois 2008
CASL example: basic
Basic specification of “Services located at rooms”
![Page 39: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/39.jpg)
I1-[OntoSpace]
39Bateman/Mossakowski/Kutz/Hois 2008
CASL example: structured
Named structured specification of a distance function
![Page 40: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/40.jpg)
I1-[OntoSpace]
40Bateman/Mossakowski/Kutz/Hois 2008
CASL example: view
![Page 41: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/41.jpg)
I1-[OntoSpace]
41Bateman/Mossakowski/Kutz/Hois 2008
GenMereology
GenParthood
Lüttich & Mossakowski (FOIS 2004)DOLCE in CASL
GenParthood
Primitives
![Page 42: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/42.jpg)
I1-[OntoSpace]
42Bateman/Mossakowski/Kutz/Hois 2008
spec MEREOLOGY =PRIMITIVES
then%%Ad7, Ad8, Ad9 and Ad10 are generated by %% instantiation of GenMereology
GENMEREOLOGY [sort T]then
GENMEREOLOGY [sort S]then
GENMEREOLOGY [sort PD]end
GenMereology
GenParthoodPrimitives
Mereology
Lüttich & Mossakowski (FOIS 2004)DOLCE in CASL
![Page 43: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/43.jpg)
I1-[OntoSpace]
43Bateman/Mossakowski/Kutz/Hois 2008
The Tool HeTS
![Page 44: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/44.jpg)
I1-[OntoSpace]
44Bateman/Mossakowski/Kutz/Hois 2008
Varieties of Modules
● logically self-sufficient/independent conservativity;
● part of a larger “integrated” ontology DDLs, E-connections, etc.
● coupling through interface alignments
● tradition, convenience, elegance, etc. general structuring techniques
“Parts” of an ontology can be considered a “module” for a variety of reasons:
Realised through various theory morphisms
![Page 45: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/45.jpg)
I1-[OntoSpace]
45Bateman/Mossakowski/Kutz/Hois 2008
Shapes of Alignments
● we represent various alignments as diagrams of certain “shapes”
● connected through “interfaces”● we assume alignment mappings are given● colimits are used for an overall integration● composition of diagrams as composition of
alignments● definitional extensions do not add ‘substance’
![Page 46: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/46.jpg)
I1-[OntoSpace]
46Bateman/Mossakowski/Kutz/Hois 2008
Structuring mechanism
Arrows in Diagrams
● black: imports;● dashed black: automatically constructed imports● blue: definitional or conservative extensions;
dotted red: proof obligations; theorem links; interpretation into theory;
green: = proven “red” obligation;
Postulating links
![Page 47: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/47.jpg)
I1-[OntoSpace]
47Bateman/Mossakowski/Kutz/Hois 2008
V-alignment through interface
● cannot handle subclass alignments
![Page 48: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/48.jpg)
I1-[OntoSpace]
48Bateman/Mossakowski/Kutz/Hois 2008
W-alignment with bridge ontology
● Integration through bridge ontology
Woman Person
![Page 49: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/49.jpg)
I1-[OntoSpace]
49Bateman/Mossakowski/Kutz/Hois 2008
M-alignment: bridges and extensions
● Integration through bridge along extensions
Woman,Bank
Person,BankPerson
Person,Bank
Woman, Person, Financial_Bank, River_Bank
![Page 50: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/50.jpg)
I1-[OntoSpace]
50Bateman/Mossakowski/Kutz/Hois 2008
Bibliographical Ontology in DL
logic DL
spec Biblio_DL = Class: Researcher
SubclassOf: name some Thing
ObjectProperty: hasArticle InverseOf: hasJournal
Class: Article SubclassOf: author some Thing,
title some Thing, hasJournal some Journal
Class: Journal SubclassOf: name some Thing, hasArticle some Thing, impactFactor some Thingend
![Page 51: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/51.jpg)
I1-[OntoSpace]
51Bateman/Mossakowski/Kutz/Hois 2008
Bibliographical Database
Biblio_RS
logic RelationalScheme
spec Biblio_RS = tables person(key: id,name); author_of(person,paper); paper(key: id,title,published_in); journal(key: id,name,impact_factor)
links author_of.person -> person.id; author_of.paper -> paper.id; paper.published_in -> journal.idend
![Page 52: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/52.jpg)
I1-[OntoSpace]
52Bateman/Mossakowski/Kutz/Hois 2008
A Heterogeneous Mappinglogic CASL
view Biblio_RS_in_DL : Biblio_RS to { Biblio_DL with logic DL -> CASL then %def preds journal(j,n,f:Thing) <=> Journal(j) /\ name(j,n) /\ impactFactor(j,f);
paper(a,t,j:Thing) <=> Article(a) /\ Journal(j) /\ hasArticle(j,a) /\ title(a,t);
author_of(p,a:Thing) <=> Researcher(p) /\ Article(a) /\ author(p,a);
person(p,n:Thing) <=> Researcher(p) /\ name(p,n) } = logic RelationalScheme -> CASLend
![Page 53: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/53.jpg)
I1-[OntoSpace]
53Bateman/Mossakowski/Kutz/Hois 2008
Structure of bibliography example
Biblio_DL Biblio_RS
Ext_Biblio_DL
Heterogeneous mapping between ontologies
![Page 54: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/54.jpg)
I1-[OntoSpace]
54Bateman/Mossakowski/Kutz/Hois 2008
![Page 55: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/55.jpg)
I1-[OntoSpace]
55Bateman/Mossakowski/Kutz/Hois 2008
● ‘window’ in T1
‘window’ in T2
map objects in T1 to materials in T2
![Page 56: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/56.jpg)
I1-[OntoSpace]
56Bateman/Mossakowski/Kutz/Hois 2008
E-connections many sorted: extended M-alignment
![Page 57: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/57.jpg)
I1-[OntoSpace]
57Bateman/Mossakowski/Kutz/Hois 2008
Summary
● Relations between modules can be characterized in general in terms of the shapes of these alignment diagrams
● Providing support for expressing these structured relationships adds considerably to the ontologist’s toolkit
![Page 58: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/58.jpg)
I1-[OntoSpace]
58Bateman/Mossakowski/Kutz/Hois 2008
One further exploratory example…
● relating linguistic spatial information and non-linguistic descriptions
![Page 59: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/59.jpg)
I1-[OntoSpace]
Bateman/Mossakowski/Kutz/Hois 2008
Further M-Alignment Example:Linguistic and Spatial Ontology
● natural linguistic spatial interaction
linguistic ontology
spatial ontologies
specificspatial calculi
space-specificparts
![Page 60: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/60.jpg)
I1-[OntoSpace]
Bateman/Mossakowski/Kutz/Hois 2008
M-Alignment ExampleLinguistic and Spatial Ontology
orientations:(e.g. DCC-8)linguistic
ProjectionRelations
FrontProjection BackProjection RightProjection LeftProjection
● R(linguistic,spatial) : LeftProjection . placement [LeftProjection] ⇒ leftFront ∨ left ∨ leftBack
front
leftFront rightFront
right
leftBack
left
leftBack
back
![Page 61: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/61.jpg)
I1-[OntoSpace]
Bateman/Mossakowski/Kutz/Hois 2008
M-Alignment ExampleLinguistic and Spatial Ontology
orientations:(e.g. DCC-8)linguistic
ProjectionRelations
FrontProjection BackProjection RightProjection LeftProjection
front
leftFront rightFront
right
leftBack
left
leftBack
back
● R(linguistic,spatial) : LeftProjection . direction [LeftProjection]
⇒ leftFront
![Page 62: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/62.jpg)
I1-[OntoSpace]
Bateman/Mossakowski/Kutz/Hois 2008
M-Alignment ExampleLinguistic and Spatial Ontology
● R(l,s): LeftProjection.placement[LeftProjection]
⇒ leftFront ∨ left ∨ leftBack● R(l,s): LeftProjection. direction[LeftProjection]
⇒ leftFront
![Page 63: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/63.jpg)
I1-[OntoSpace]
63Bateman/Mossakowski/Kutz/Hois 2008
Relation between linguistic and non-linguistic characterisations…
combines different alignments between the linguistic semantics and the spatial characterisation
![Page 64: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/64.jpg)
I1-[OntoSpace]
64Bateman/Mossakowski/Kutz/Hois 2008
Conclusions and ongoing and future directions
● Dealing with information flexibly requires ontological treatments that are contentful
● Axiomatised ontologies are a way of approaching this
● But structured ontological specifications with well-specified possibilities for relating between ontologies/modules are then essential
● Offers us a structured path towards interoperability
![Page 65: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/65.jpg)
I1-[OntoSpace]
65Bateman/Mossakowski/Kutz/Hois 2008
Appendix
Biblio_RS
![Page 66: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/66.jpg)
I1-[OntoSpace]
66Bateman/Mossakowski/Kutz/Hois 2008
Modules based on Conservativity
Model-theoretic implies proof-theoretic conservativity, but not conversely.
model-theoretic conservativity: Every T1-model can be expanded to a T2-model.
A theory morphism is proof theoretically conservative if
![Page 67: John Bateman Till Mossakowski Oliver Kutz Joana Hois](https://reader036.fdocuments.us/reader036/viewer/2022062322/5681457e550346895db256fb/html5/thumbnails/67.jpg)
I1-[OntoSpace]
67Bateman/Mossakowski/Kutz/Hois 2008
Modules based on Conservativity