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 of several ontologies selected from the TONES repository (reference?). For each experiment one or more axioms containing nominal schemas were added to each ontology. 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 lhis 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, and also shows that even the grounding approach can be used for small use cases or for initial testing.

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

The section also includes java code to ground axioms containing nominal schemas to a given ontology. After the grounding reasoning tasks can be performed with the ontology using any reasoner available just as usual (This 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

Ontology	Classes	Annotation P.	Data P.	Object P.	Individuals
Fam	4	0	1	11	5
Swe	189	1	6	25	22
Bui	686	15	0	24	42
Wor	1842	6	0	31	80
Tra	445	2	4	89	183
FTr	22	2	6	52	368
Eco	339	2	8	45	482

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 per 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	Plain		1 different ns				2 different ns				3 different ns
Name	Ontology		2 app		8 app		2 app		4 app		2 app
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 (42)	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
FTr (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 per Ontology

For every experiment several axioms was added to each ontology including 1 or 2 different nominal schemas each.

Name	No axioms added		20 axioms, 1 ns		10 axioms, 2 ns
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