NSByGrounding

Nominal Schema Reasoning by Grounding

This page contains the implementations of nominal schema reasoning using naive and smart grounding.

Introduction

In this page we include the empirical evaluation and implementation of nominal schemas, a new description logics extension (See the Literature section). Several ontologies selected from the TONES repository [1] were used for this evaluation. For each experiment presented one or more axioms containing nominal schemas were added to each ontology, resulting in the inclusion of several regular axioms containing nominals. As stated in the paper, occurences of nominal schemas are grounded with all possible combinations of individuals contained in the knowledge bases. After the grounding reasoning times (using Pellet after grounding) are averaged over 100 runs, and load time is reported separately. We are particularly interested in finding what are the limits of this implementation varying both the number of different nominal schemas and their number of occurrences per axiom.

Testing was performed using a 64-bit Windows 7 computer with an Intel(R) Core(TM) i5 CPU processor. A java JDK 1.5 version, allocating 3GB as the minimun for the java heap and 3.5GB as the maximun, was used for each experiment.

Naive Implementation

Although not very time-efficient this implementation will serve as a baseline for development and testing of more optimised algorithms. It also shows that even the grounding approach can be used for small use cases or for initial testing.

The section includes testing data obtained from different experiments showing the feasibility of this implementation when the number of different nominal schemas per axiom is low.

Java code to ground axioms containing nominal schemas to a given ontology is also included. After the grounding reasoning tasks can be performed with the ontology using any reasoner available just as usual.

Ontologies

We present in this section the metrics of the ontologies used for the Naive implementation. Some ontologies were modified, as shown in the table, to better suit test purposes.

Ontology	Classes	Annotation P.	Data P.	Object P.	Individuals	URI	Modifications
Fam	4	0	1	11	5	[2]	No mod
Swe	189	1	6	25	22	[3]	20 individuals added
Bui	686	15	0	24	42	[4]	40 individuals added
Wor	1842	6	0	31	80	[5]	80 individuals added
Tra	445	2	4	89	183	[6]	No mod
FTr	22	2	6	52	368	[7]	No mod
Eco	339	2	8	45	482	[8]	No mod

Note that the ontologies are sorted by the number of individuals they contain. As stated in the paper the number of regular axioms grounded from an original axiom containing nominal schemas is k^n where n is the number of different nominal schemas and k is the number of individuals in the knowledge base. Consequently, the number of individuals is one of the important factors that must be taken into account in the testing results.

Testing results

This section contains two tables showing the reasoning time results for the ontologies when axioms with different combinations of nominal schemas are added. Every experiment time results are presented in two columns showing loading time for the first and checking satisfiability for the second.

Adding one axiom to each Ontology

For every experiment in this section only one axiom was added to each ontology varying the number of different nominal schemas and their number of appearances.

Ontology	No axioms added		1 different nominal schema				2 different nominal schemas				3 different nominal schemas
			2 appearances		8 appearances		2 appearances		4 appearances		2 appearances
Fam (5)	0.01	0.00	0.01	0.00	0.01	0.01	0.01	0.00	0.01	0.00	0.04	0.02
Swe (22)	3.58	0.08	3.73	0.07	3.73	0.11	3.85	0.10	3.88	0.11	10.86	1.11
Bui (42)	2.7	0.16	2.5	0.15	2.47	0.15	2.75	0.26	3.05	0.36	1'14	6.68
Wor (82)	0.11	0.04	0.12	0.05	1.48	0.87	1.1	0.55	1.88	1.03	197'12	5'15
Tra (183)	0.05	0.03	0.05	0.02	0.05	0.02	5.76	1.76	9.9	3.73	OOM	OOM
FTr (368)	0.03	4.28	0.05	5.32	0.09	5.51	35.53	42.73	1'18	9'30	OOM	OOM
Eco (368)	0.04	0.24	0.07	0.02	0.10	0.04	56.59	13.67	53.32	35.35	OOM	OOM

Adding several axioms to each Ontology

Two experiments were considered in this section:

Experiment 1: 20 axioms containing one different nominal schema per axiom with two appearances were added to each ontology.

Experiment 2: 10 axioms containing two different nominal schemas per axiom with two appearances each were added to each ontology.

Name	No axioms added		Experiment 1		Experiment 2
Fam (5)	0.01	0.00	0.01	0.00	0.02	0.01
Swe (22)	3.58	0.08	3.42	0.08	3.73	0.28
Bui (42)	2.7	0.16	2.69	0.25	5.7	3.21
Wor (80)	0.11	0.04	0.23	0.28	12.42	6.88
Tra (183)	0.05	0.03	0.32	0.15	1' 43.54'	43.63
FTr (368)	0.03	4.28	0.52	11.33	OOM	OOM
FTr (368)	0.04	0.24	0.65	0.3	OOM	OOM

Naive Safe Grounding

In this section we present results for the empirical evaluation for nominal schema when the optimization proposed in [1,2] is applied comparing the results with the standard Naive implementation. Three ontologies, also obtained from the TONES repository, are considered in this section.

To apply this Smart Grounding ontologies need to be part of the SROELVn description logics (essentially the OWL EL profile) and the nominal schema appearances need to be "safe". Intuitively, if the nominal schemas are "safe" they are independent from each other. The exact definition of safeness is described in [1]. Since the nominal schemas are independent from each other instead grounding the original axiom containing several appearances of nominal schemas we can ground several axioms with less number of different nominal schemas each. Remember that the final number of axioms is k^n where k is the number of individuals and n the number of different nominal schemas appearing per axiom. Therefore lowering this n will yield a much smaller amount of grounded axioms and a better performance of the algorithm.

Note that this implementation was done with testing purposes in mind rather than usability and the program will not be able to detect if an axiom contains "safe" nominal schemas. This has to be done, as shown in [1] by the user, and then ground all resulting axioms separately.

Ontologies

We present metrics for the three EL ontologies used for the testing in this section. Due to the lack of EL ontologies with their own individuals all individuals for this section were artificially builded for the given ontologies.

Ontology	Classes	Annotation P.	Data P.	Object P.	Individuals	URI	Modifications
Rex	552	10	0	6	100	[9]	100 individuals added
Spatial	106	13	0	13	100	[10]	100 individuals added
Xenopus	710	19	0	5	100	[11]	100 individuals added

Testing Results

The next table present the testing results for the ontologies considered in this section. Again results for each experiment are refered in pairs of columns showing loading and checking satisfiability times.

Ontology	No ns		1 different ns P.		2 different ns		3 different ns
Rex	0.025	0.009	0.031	0.013	1.689	0.112	OOM	OOM
Rex Optimized			0.058	0.023	0.046	0.011	0.053	0.009
Rex	0.035	0.029	0.021	0.014	1.536	0.101	OOM	OOM
Rex Optimized			0.018	0.013	0.033	0.007	0.044	0.011
Rex	0.063	0.018	0.07	0.19	1.598	0.112	OOM	OOM
Rex Optimized			0.099	0.037	0.083	0.018	0.097	0.063

Literature

1. Markus Krötzsch, Frederick Maier, Adila Alfa Krisnadhi, Pascal Hitzler, A Better Uncle For OWL - Nominal Schemas for Integrating Rules and Ontologies. In: S. Sadagopan, Krithi Ramamritham, Arun Kumar, M.P. Ravindra, Elisa Bertino, Ravi Kumar (eds.), WWW '11 20th International World Wide Web Conference, Hyderabad, India, March/April 2011. ACM, New York, 2011, pp. 645-654.
2. Adila Alfa Krisnadhi, Frederick Maier, Pascal Hitzler, OWL and Rules. In: Reasoning Web 2011, Springer Lecture Notes in Computer Science. To appear.
3. David Carral Martinez, Adila Krisnadhi, Frederick Maier, Kunal Sengupta, Pascal Hitzler, Reconciling OWL and Rules. Technical Report, Kno.e.sis Center, Wright State University, Dayton, OH, USA, June 2011.
4. David Carral Martinez, Adila A. Krisnadhi, Pascal Hitzler, Syntax Proposal for Nominal Schemas. Technical Report, Kno.e.sis Center, Wright State University, Dayton, OH, USA, June 2011.

Acknowledgements

This work was supported by the National Science Foundation under award 1017225 III: Small: TROn---Tractable Reasoning with Ontologies, and by State of Ohio Research Incentive funding in the Kno.e.CoM project. Adila Krisnadhi acknowledges support by a Fulbright Indonesia Presidential Scholarship PhD Grant 2010.

Appendix

Grounding Tutorial

This section presents java code to ground axioms with nominal schema for a given ontology. OWL API library needs to be added to the classpath for this task.

Create the frame

First the user needs to write down the frame containing the axiom we want to ground to the knowledge base and store in a .owl file. It can be created with any text editor available. This file should be placed in the same folder as our ontology.

Example of frame containing one axiom with one nominal schema and two appearances:

[

rdf:type owl:Class;

rdfs:subClassOf :frameClass1;

owl:intersectionOf(

[ rdf:type owl:Restriction;

owl:onProperty :property1;

owl:someValuesFrom

[ rdf:type owl:ObjectVariable; owl:variableId ”v1” ]

]

[ rdf:type owl:Restriction;

owl:onProperty :property2;

owl:someValuesFrom

[ rdf:type owl:ObjectVariable; owl:variableId ”v1” ]

]

)

].

The blank node [ rdf:type owl:ObjectVariable; owl:variableId "v1"] represents the nominal schema. It will be replaced and grounded with all individuals in the ontology.

Remark: for the program to work correctly nominal schemas must be typed in the same line with no other axioms, as shown above, when the user builds the frame.

Example of frame containing one axiom with two nominal schemas and two appearances each:

[

rdf:type owl:Class;

rdfs:subClassOf :frameClass1;

owl:intersectionOf(

[ rdf:type owl:Restriction;

owl:onProperty :property1;

owl:someValuesFrom

[ rdf:type owl:ObjectVariable; owl:variableId ”v1” ]

]

[ rdf:type owl:Restriction;

owl:onProperty :property2;

owl:someValuesFrom

[ rdf:type owl:ObjectVariable; owl:variableId ”v1” ]

]

[ rdf:type owl:Restriction;

owl:onProperty :property3;

owl:someValuesFrom

[ rdf:type owl:ObjectVariable; owl:variableId ”v2” ]

]

[ rdf:type owl:Restriction;

owl:onProperty :property4;

owl:someValuesFrom

[ rdf:type owl:ObjectVariable; owl:variableId ”v2” ]

)

].

For this second example the program will ground all possible pair combinations for the nominal schemas "v1" and "v2". The number of groundings is equal to the number of individuals raised to the second power (two different nominal schemas: the program will ground all possible combinations).

Remark: note that all classes, properties, and namespaces in the frame need to be previously defined in the ontology for a correct performance of the reasoner after the grounding. We assume that all predicates that are part of the rule we wanted to ground previously appeared in the ontology.

Grounding the axioms

The program will start and prompt the user for the folder's path where we have stored the frame and the ontology and then for the names of these. After execution a new file with appear with the same name as the ontology followed with the word "Grounded.owl". The new file contains the same previous ontology with all possible grounded combinations of individuals for the defined frame added at the end. To ground several nominal schemas for a given ontology we just have to run the program several times with the desired frames.

The program is currently only available for Turtle Syntax. A converter of OWL syntax is available in: [12]

Code can be downloaded from: [13]