Timing Statistics - Rendering OWL in LaTeX for Improved Readability: Extensions to the OWLAPI

5.2 Results

5.2.3 Timing Statistics

We tracked the amount of time it took for each participant to complete each test section.

In the hypothesis, we contend that an ontology rendered in a FOL syntax allows a user

MS DL FOL Mean 9:10 6:42 9:51 Median 9:31 5:27 9:22

Table 5.5: Time Taken was measured per test-section.

MS-DL MS-FOL DL-FOL

Readability 0.0304 0.0516 0.5943

significant not significant not significant

Correctness 0.3972 0.3734 0.0400

not significant not significant significant

Timing 0.0476 0.7074 0.1978

significant not significant not significant

Table 5.6: We use Student’s t-Distribution to measure the pair-wise significance of our results.

Table 5.5. From these data, we conclude via Student’s t-distribution that only the relative improvement between MS and DL renderings is significant with p ≈ 0.048 < 0.05 which substantiates our first hypothesis.

These results fail to substantiate the second hypothesis. To this point, we note that timing understanding is a nebulous in concept in general, and thus difficult pinpoint a single point of failure. For example, our test set had varied levels of understanding of each of the syntaxes- does this variety have a disproportionate affect over different syntaxes? In future studies, it will be necessary to have a more controlled population of participants.

6 Conclusion

The Semantic Web is a field of research dedicated to modeling complex concepts in a machine readable way, as well as an eponymous extension of the World Wide Web. One of the most prominent tools available to a Semantic Web research is the ontology, a codified way of expressing complex concepts in terms of simpler concepts.

As one of the goals of the field is to be able to model any arbitrary concept in a ma-chine readable way, ontology engineering is an inherently multidisciplinary process. Thus, ontologies are usually developed in tandem with Semantic Web researchers and domain experts. This collaborative approach necessitates that there be multiple vehicles for vi-sualizing an ontology under development allowing the team to more fully understand the nascent structure.

Furthermore, we wish to lower the barrier for entry to domain experts in order to increase adoption, thus growing the Semantic Web as an artifact. To do this, there are already many tools that are attempts to improve the ontology engineering process (OEP).

For example, a visual notation for OWL and new ways to input axioms into Prot´eg´e.

In this thesis, we have described the development of two tools to add to the OEP tool set. These tools are powered by a number of changes made to the OWLAPI in order to provide human readable renderings of ontologies in Description Logic and a First

Or-der Predicate Logic Rule-like syntaxes. While the Description Logic syntax was already present as the OWLAPI’s L^ATEX rendering framework, it suffered from a number of signif-icant problems in correctness and readability.

Hypotheses:

• When presented in a Description Logic Syntax, users will more quickly and more correctly understand an ontology compared to renderings in Manchester syntax.

• When presented in a FOPL-Rule-like (FOL¹) Syntax, users will more quickly and more correctly understand an ontology compared to renderings in Description Logic syntax.

The results from the evaluation, with respect to above hypotheses, were, at best, in-conclusive. However, we contend that the key take away is that there is need for a tool set optimized for rendering an ontology in a human readable manner, whether the target is Manchester Syntax, Description Logic, or a FOL-rule-like syntax. This take away is substantiated by the fact that, in general, DL or FOL renderings resulted in statistically significant improvements over MS. As noted, though, this may be due to the usage of ex-actlythe output of the converter tool, which did not utilize shortform notation for any class names.

Future Work

There are three major points discussed in this thesis that can be targeted for improvement in future work.

First and foremost, we would like to create a tool for creating First Order Logic rules.

As previously mentioned, simply extending the OWLAPI is infeasible as it is out of scope.

Thus, it will be necessary to create a standalone tool with the OWLAPI as a dependency.

We imagine such a tool translating the ontology’s underlying data structure into an analo-gous first order logic data structure. At this point, the FOL can be manipulated in such a way that we can generate rules for those axioms that are translatable. In addition, we may borrow the hybridized syntax from [9] in order to maintain the intuitiveness of rules. It would then be our position that FOL-rules are the most readable of the available syntaxes.

Secondly, any subsequent evaluation would require a more carefully chosen and pre-pared set of test subjects. While each participant was a graduate student and familiar with knowledge representation in general, we noted that varying levels of familiarity may have had a significant impact on the results.

Finally, we will investigate making further changes to the OWLAPI to support a “hu-man readable” rendering of Manchester Syntax

Bibliography

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Appendices

Appendix A: Semantic Trajectory (OWL)

<?xml v e r s i o n =”1.0”? >

< r d f : RDF x m l n s =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y #”

xml : b a s e =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y ”

x m l n s : r d f =” h t t p : / / www. w3 . o r g / 1 9 9 9 / 0 2 / 2 2 − r d f −s y n t a x −n s #”

x m l n s : owl =” h t t p : / / www. w3 . o r g / 2 0 0 2 / 0 7 / owl #”

x m l n s : xml =” h t t p : / / www. w3 . o r g /XML/ 1 9 9 8 / n a m e s p a c e ” x m l n s : c p a n n o t a t i o n s c h e m a =” h t t p : / / www.

o n t o l o g y d e s i g n p a t t e r n s . o r g / s c h e m a s / c p a n n o t a t i o n s c h e m a . owl #”

x m l n s : x s d =” h t t p : / / www. w3 . o r g / 2 0 0 1 / XMLSchema#”

x m l n s : r d f s =” h t t p : / / www. w3 . o r g / 2 0 0 0 / 0 1 / r d f −schema #”

x m l n s : t r j =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y #”

x m l n s : dc =” h t t p : / / p u r l . o r g / dc / e l e m e n t s / 1 . 1 / ” >

<owl : i m p o r t s r d f : r e s o u r c e =” h t t p : / / www.

o n t o l o g y d e s i g n p a t t e r n s . o r g / s c h e m a s /

c p a n n o t a t i o n s c h e m a . owl ”/ >

The 1990 World C h e s s C h a m p i o n s h i p e v e n t t h a t was h e l d i n two

i n f o r m a t i o n t o t h e f i x e s . < / c p a n n o t a t i o n s c h e m a : h a s C o n s e q u e n c e s >

</ owl : O n t o l o g y >

<!−−

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

/ /

/ / A n n o t a t i o n p r o p e r t i e s / /

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

−−>

<!−− h t t p : / / p u r l . o r g / dc / e l e m e n t s / 1 . 1 / c r e a t o r −−>

<!−−

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

/ /

/ / O b j e c t P r o p e r t i e s / /

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

−−>

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # a t P l a c e −−>

< r d f s : r a n g e r d f : r e s o u r c e =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # P l a c e ”/ >

< r d f s : comment>C o n n e c t s a n y t h i n g ( i n c l u d i n g f i x e s i n t h i s p a t t e r n ) t o P l a c e . < / r d f s : comment>

< r d f s : l a b e l >a t P l a c e </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # a t T i m e −−>

< r d f s : r a n g e r d f : r e s o u r c e =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T i m e E n t i t y ”/ >

< r d f s : comment>C o n n e c t s a n y t h i n g ( i n c l u d i n g f i x e s i n t h i s p a t t e r n ) t o T i m e E n t i t y </ r d f s : comment>

< r d f s : l a b e l >a t T i m e </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # e n d s A t −−>

< r d f : t y p e r d f : r e s o u r c e =” h t t p : / / www. w3 . o r g / 2 0 0 2 / 0 7 / owl # F u n c t i o n a l P r o p e r t y ”/ >

< r d f s : comment>C o n n e c t s a s e g m e n t t o t h e f i x i t e n d s a t . < / r d f s : comment>

< r d f s : l a b e l >e n d s A t </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y #

h a s A t t r i b u t e −−>

< r d f s : comment>C o n n e c t s a f i x o r a s e g m e n t t o an a d d i t i o n a l i n f o r m a t i o n a s r e p r e s e n t e d by an i n s t a n c e o f A t t r i b u t e . < / r d f s : comment>

< r d f s : l a b e l >h a s A t t r i b u t e </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s F i x −−>

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s S e g m e n t ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # e n d s A t ”/ >

</ owl : p r o p e r t y C h a i n A x i o m >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s S e g m e n t ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # s t a r t s F r o m ”/ >

</ owl : p r o p e r t y C h a i n A x i o m >

< r d f s : comment>R e l a t i n g t h e t r a j e c t o r y t o e a c h o f i t s f i x e s . < / r d f s : comment>

< r d f s : l a b e l >h a s F i x </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s S e g m e n t

−−>

< r d f s : comment>R e l a t i n g t h e t r a j e c t o r y t o e a c h o f i t s s e g m e n t s . < / r d f s : comment>

< r d f s : l a b e l >h a s S e g m e n t </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s T r a j e c t o r y −−>

< r d f s : r a n g e r d f : r e s o u r c e =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T r a j e c t o r y ”/ >

< r d f s : comment>A n y t h i n g t h a t h a s a t r a j e c t o r y c a n u s e t h i s p r o p e r t y t o c o n n e c t i t t o t h e t r a j e c t o r y i n s t a n c e . < / r d f s : comment>

< r d f s : l a b e l >h a s T r a j e c t o r y </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # n e x t F i x −−>

< r d f s : comment>R e l a t e s one f i x t o t h e i m m e d i a t e l y f o l l o w i n g f i x i n t h e s e q u e n c e . < / r d f s : comment>

< r d f s : l a b e l >n e x t F i x </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # s t a r t s F r o m

−−>

< r d f : t y p e r d f : r e s o u r c e =” h t t p : / / www. w3 . o r g / 2 0 0 2 / 0 7 / owl # F u n c t i o n a l P r o p e r t y ”/ >

< r d f s : comment>C o n n e c t s a s e g m e n t t o t h e f i x i t

s t a r t s f r o m . < / r d f s : comment>

< r d f s : l a b e l >s t a r t s F r o m </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # t r a v e r s e d B y

−−>

< r d f s : comment>C o n n e c t a s e g m e n t t o t h e moving o b j e c t t h a t t r a v e r s e s i t . < / r d f s : comment>

< r d f s : l a b e l >t r a v e r s e d B y </ r d f s : l a b e l >

</ owl : O b j e c t P r o p e r t y >

<!−−

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

/ /

/ / C l a s s e s / /

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

−−>

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # A t t r i b u t e

−−>

< r d f s : comment>C a p t u r e s a d d i t i o n a l i n f o r m a t i o n t h a t e n r i c h e s some f i x o r s e g m e n t . < / r d f s : comment>

< r d f s : l a b e l >A t t r i b u t e </ r d f s : l a b e l >

</ owl : C l a s s >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # E n d i n g F i x

−−>

<owl : i n t e r s e c t i o n O f r d f : p a r s e T y p e =”

C o l l e c t i o n ”>

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x ”/ >

</ owl : C l a s s >

</ owl : R e s t r i c t i o n >

</ r d f s : s u b C l a s s O f >

< r d f s : comment>D e s c r i b e s a f i x , w h i c h i s an a d o r n e d s p a t i o t e m p o r a l p o i n t . A s e q u e n c e o f f i x e s f o r m t h e t r a j e c t o r y . < / r d f s : comment>

< r d f s : l a b e l >F i x </ r d f s : l a b e l >

</ owl : C l a s s >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # M o v i n g O b j e c t −−>

< r d f s : comment>T h i s i s t h e hook t o an o n t o l o g y /

p a t t e r n t h a t d e s c r i b e s t h e moving o b j e c t , i f any , w h i c h moves a l o n g t h e t r a j e c t o r y . < / r d f s : comment>

< r d f s : l a b e l >M o v i n g O b j e c t </ r d f s : l a b e l >

</ owl : C l a s s >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # P l a c e −−>

< r d f s : comment>T h i s i s t h e hook t o o t h e r p a t t e r n /

</ owl : R e s t r i c t i o n >

o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s A t t r i b u t e

a n o t h e r f i x . I f t h e p a t t e r n i s u s e d t o model t h e

r e s o u r c e =” h t t p : / /

< r d f s : comment>The hook t o c l a s s / p a t t e r n / o n t o l o g y t h a t m o d e l s t i m e , t h i s c l a s s p r o v i d e s t h e

t e m p o r a l e x t e n t o f t h e t r a j e c t o r y . One e x a m p l e o f t i m e model i s t h e W3C Time O n t o l o g y . < / r d f s :

comment>

< r d f s : l a b e l >T i m e E n t i t y </ r d f s : l a b e l >

< r d f s : s e e A l s o r d f : r e s o u r c e =” h t t p : / / www. w3 . o r g / 2 0 0 6 / t i m e ”/ >

</ owl : C l a s s >

<!−− h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T r a j e c t o r y

−−>

< r d f s : s u b C l a s s O f >

<owl : someValuesFrom r d f : r e s o u r c e =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # Segment

”/ >

</ owl : R e s t r i c t i o n >

< r d f s : l a b e l >T r a j e c t o r y </ r d f s : l a b e l >

</ owl : C l a s s >

<!−−

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

/ /

/ / G e n e r a l a x i o m s / /

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

−−>

< r d f s : s u b C l a s s O f r d f : r e s o u r c e =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # Segment ”/ >

</ owl : R e s t r i c t i o n >

<owl : someValuesFrom r d f : r e s o u r c e =” h t t p : / / w3id . o r g /

d a s e l a b / o n t o / t r a j e c t o r y # A t t r i b u t e ”/ >

d a s e l a b / o n t o / t r a j e c t o r y # T r a j e c t o r y ”/ >

< r d f : t y p e r d f : r e s o u r c e =” h t t p : / / www. w3 . o r g / 2 0 0 2 / 0 7 / owl # A l l D i s j o i n t C l a s s e s ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # A t t r i b u t e ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # M o v i n g O b j e c t ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # P l a c e ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # Segment ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T i m e E n t i t y ”/ >

< r d f : D e s c r i p t i o n r d f : a b o u t =” h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T r a j e c t o r y ”/ >

</ owl : members>

</ r d f : D e s c r i p t i o n >

</ r d f : RDF>

<!−− G e n e r a t e d by t h e OWL API ( v e r s i o n 4 . 2 . 5 . 2 0 1 6 0 5 1 7 − 0 7 3 5 ) h t t p s : / / g i t h u b . com / o w l c s / o w l a p i −−>

Appendix B: Semantic Trajectory (Manchester Syntax)

O n t o l o g y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y >

I m p o r t : < h t t p : / / www. o n t o l o g y d e s i g n p a t t e r n s . o r g / s c h e m a s / c p a n n o t a t i o n s c h e m a . owl>

D a t a t y p e : r d f : P l a i n L i t e r a l

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # a t P l a c e >

Range :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # P l a c e >

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # a t T i m e >

Range :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T i m e E n t i t y >

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # e n d s A t >

C h a r a c t e r i s t i c s : F u n c t i o n a l

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s A t t r i b u t e >

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s F i x >

S u b P r o p e r t y C h a i n :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s S e g m e n t >

o < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # e n d s A t >

S u b P r o p e r t y C h a i n :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s S e g m e n t >

o < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # s t a r t s F r o m >

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s S e g m e n t >

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s T r a j e c t o r y >

Range :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T r a j e c t o r y >

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # n e x t F i x >

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # s t a r t s F r o m >

C h a r a c t e r i s t i c s :

F u n c t i o n a l

O b j e c t P r o p e r t y : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # t r a v e r s e d B y >

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # A t t r i b u t e >

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # E n d i n g F i x >

E q u i v a l e n t T o :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x >

and ( n o t ( i n v e r s e (< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # s t a r t s F r o m >) some < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # Segment >) )

S u b C l a s s O f :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x >

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x >

S u b C l a s s O f :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # a t P l a c e >

some < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # P l a c e > ,

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # a t T i m e >

some < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T i m e E n t i t y > ,

i n v e r s e (< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s F i x >) some < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T r a j e c t o r y > ,

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y #

h a s A t t r i b u t e > o n l y < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # A t t r i b u t e > ,

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # n e x t F i x >

o n l y < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # M o v i n g O b j e c t

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # P l a c e >

e l ” P l a c e ”

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # Segment>

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # t r a v e r s e d B y

> o n l y < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # M o v i n g O b j e c t >

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # S t a r t i n g F i x >

E q u i v a l e n t T o :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x >

and ( n o t ( i n v e r s e (< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # e n d s A t >) some < h t t p : / / w3id . o r g /

d a s e l a b / o n t o / t r a j e c t o r y # Segment >) )

S u b C l a s s O f :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x >

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T i m e E n t i t y >

C l a s s : < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T r a j e c t o r y >

S u b C l a s s O f :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s S e g m e n t >

some < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # Segment > ,

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s F i x >

o n l y < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x

> ,

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # h a s S e g m e n t >

o n l y < h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # Segment>

D i s j o i n t C l a s s e s :

< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # A t t r i b u t e >,<

h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # F i x >,< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # M o v i n g O b j e c t >,< h t t p

: / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # P l a c e >,< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # Segment >,< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T i m e E n t i t y >,< h t t p : / / w3id . o r g / d a s e l a b / o n t o / t r a j e c t o r y # T r a j e c t o r y >

Appendix C: Semantic Trajectory (First Order Logic)

Classes

Attribute

AllDifferent(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

EndingFix

EndingFix(x₁) → Fix(x₁) ∧ ∀x₂(startsFrom(x₂, x₁) → ¬Segment(x₂)) Fix(x1) ∧ ∀x₂(startsFrom(x₂, x₁) → ¬Segment(x₂)) → EndingFix(x₁)

EndingFix(x1) → Fix(x1)

Fix

Fix(x₁) → ∃x₂(atPlace(x₁, x₂) ∧ Place(x₂)) Fix(x1) → ∀x₂(nextFix(x₁, x₂) → Fix(x₂)) Fix(x₁) → ∃x₂(atTime(x₁, x₂) ∧ TimeEntity(x₂)) Fix(x₁) → ∀x₂(hasAttribute(x₁, x₂) → Attribute(x₂)) Fix(x1) → ∃x₂(hasFix(x₂, x₁) ∧ Trajectory(x₂))

AllDifferent(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

MovingObject

AllDifferent(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

Place

AllDifferent(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

Segment

Segment(x₁) → ∃x₂(startsFrom(x₁, x₂) ∧ Fix(x₂)) Segment(x1) → ∃x₂(endsAt(x₁, x₂) ∧ Fix(x₂))

Segment(x₁) → ∀x₂(hasAttribute(x₁, x₂) → Attribute(x₂)) Segment(x₁) → ∀x₂(startsFrom(x₁, x₂) → Fix(x₂))

Segment(x1) → ∃x₂(hasSegment(x₂, x₁) ∧ Trajectory(x₂)) Segment(x₁) → ∀x₂(traversedBy(x₁, x₂) → MovingObject(x₂)) Segment(x₁) → ∀x₂(endsAt(x₁, x₂) → Fix(x₂))

AllDifferent(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

StartingFix

StartingFix(x1) → Fix(x₁) ∧ ∀x₂(endsAt(x₂, x₁) → ¬Segment(x₂)) Fix(x1) ∧ ∀x2(endsAt(x2, x1) → ¬Segment(x2)) → StartingFix(x1)

StartingFix(x₁) → Fix(x₁)

TimeEntity

AllDifferent(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

Trajectory

Trajectory(x₁) → ∃x₂(hasSegment(x₁, x₂) ∧ Segment(x₂)) Trajectory(x1) → ∀x₂(hasFix(x₁, x₂) → Fix(x₂))

Trajectory(x₁) → ∀x₂(hasSegment(x₁, x₂) → Segment(x₂))

AllDifferent(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

Object properties

atPlace

∃x₁Thing(x1) → ∀x₂(atPlace(x₁, x₂) → Place(x₂))

atTime

∃x₁ Thing(x₁) → ∀x₂(atTime(x₁, x₂) → TimeEntity(x₂))

endsAt

→ ≤ 1x₂endsAt(x₁, x₂) ∧ Thing(x₂)

hasAttribute

hasFix

hasSegment

hasTrajectory

∃x₁ Thing(x1) → ∀x₂(hasTrajectory(x₁, x₂) → Trajectory(x₂))

nextFix

startsFrom

→ ≤ 1x2startsFrom(x1, x2) ∧ Thing(x2)

traversedBy

Data properties

Individuals

Datatypes

string

Appendix D: Semantic Trajectory (Description Logic)

Classes

Attribute

AllDisjoint(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory) EndingFix

EquivalentClasses(EndingFix, Fix u ¬(∃startsFrom⁻.Segment)) EndingFix v Fix

Fix

Fix v ∃atPlace.Place Fix v ∀nextFix.Fix

Fix v ∃atTime.TimeEntity Fix v ∀hasAttribute.Attribute Fix v ∃hasFix⁻.Trajectory

AllDisjoint(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

MovingObject

AllDisjoint(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory) Place

AllDisjoint(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory) Segment

Segment v ∃startsFrom.Fix Segment v ∃endsAt.Fix

Segment v ∀hasAttribute.Attribute Segment v ∀startsFrom.Fix

Segment v ∃hasSegment⁻.Trajectory Segment v ∀traversedBy.MovingObject Segment v ∀endsAt.Fix

AllDisjoint(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory) StartingFix

EquivalentClasses(StartingFix, Fix u ¬(∃endsAt⁻.Segment)) StartingFix v Fix

TimeEntity

AllDisjoint(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

Trajectory

Trajectory v ∃hasSegment.Segment Trajectory v ∀hasFix.Fix

Trajectory v ∀hasSegment.Segment

AllDisjoint(Attribute, Fix, MovingObject, Place, Segment, TimeEntity, Trajectory)

Object properties

atPlace

> v ∀atPlace.Place atTime

> v ∀atTime.TimeEntity endsAt

> v≤ 1endsAt.>

hasAttribute hasFix hasSegment hasTrajectory

> v ∀hasTrajectory.Trajectory nextFix

startsFrom

> v≤ 1startsFrom.>

traversedBy

Data properties Individuals Datatypes

string

Appendix E: Question Pool

For each answer, write the axiom that justifies your answer.

1. T F Only some EndingFixes are Fixes 2. T F All Fixes are StartingFixes

3. T F Fixes and Segments are equivalent concepts

4. T F Trajectories, Segments, and Fixes are mutually disjoint concepts 5. T F Trajectories may have more than one possible StartingFix 6. A Segment

A. Is not a trajectory

B. Is always connected to another segment C. Is a Fix

8. Which of the following statements is TRUE A. A Trajectory does not have Fixes B. All Segments belong to a Trajectory.

C. The domain of ‘atPlace’ is Place D. Both A & B

E. Both A & C

9. Which of the following statements is TRUE A. Only MovingObjects traverse a Segment B. A Segment has a MovingObject C. A Segment must start at a Fix.

D. A Segment must start at a Place.

E. Both A & C

10. Which of the following statements is TRUE A. A Place may have Attributes

B. If any Fix is the start of a Segment, then it is a StartingFix C. A Fix that does not begin a Segment is an EndingFix D. Any Place is also a TimeEntity

E. Both B & C

11. Which of the following statements is TRUE A. A Fix may have Attributes

B. A Segment may have Attributes C. A Trajectory may have Attributes D. Both A & B

E. A, B, & C

In document Rendering OWL in LaTeX for Improved Readability: Extensions to the OWLAPI (Page 54-107)