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 the new description logics extension nominal schemas . Several ontologies selected from the TONES repository (reference?) were used for this evaluation. For each experiment presented one or more axioms containing nominal schemas were added to each ontology. For this Naive implementation, 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.

Naive Implementation

Although not very time-efficient this implementation will serve as a baseline for development and testing of more optimised algorithms, and 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 experimets 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(the java program was built for testing purposes only and therefore it is not an optimised generic algorithm).

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	[1]	No mod
Swe	189	1	6	25	22	[2]	20 individuals added
Bui	686	15	0	24	42	[3]	40 individuals added
Wor	1842	6	0	31	80	[4]	80 individuals added
Tra	445	2	4	89	183	[5]	No mod
FTr	22	2	6	52	368	[6]	No mod
Eco	339	2	8	45	482	[7]	No mod

The 3 last of them are down... I have them in my computer, shall we upload them?

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.

Adding one axiom to each Ontology

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

Ontology	No axioms		1 different nominal schema				2 different nominal schemas				3 different nominal schemas
Name	added		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

Code and 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 and then modifying the text extension from ".txt" to ".owl". 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 that will be grounded with all individuals in the ontology.

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!).

Remark: all classes, properties, and namespaces in the frame need to be defined in the ontology for a correct performance of the reasoner after the grounding.

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 all axioms in the previous ontology with all possible grounded combinations of individuals for the defined frame. To ground several nominal schemas to the ontology we just have to run the program several times with the desired frames.

The program is only available for Turtle Syntax. A converter of OWL syntax is available in: [8]

Code can be downloaded from: [here] (make code available!)

Smart Grounding

In this section we present results for the empirical evaluation for nominal schema when the optimization proposed in (REFERENCE) is applied comparing the results with the 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 and the nominal schema appearances need to be "safe" as defined also in (REFERENCE).

Java code is included to automatically perform this implementation along with a tutorial to use the program.

Ontologies

We present metrics for the three EL ontologies used for the testing in this section.