1. +
RDFS Semantics,
Inference techniques and
Sesame
Mariano Rodriguez-Muro,
Free University of Bozen-Bolzano

2. +
Disclaimer

License

This work is licensed under a
Creative Commons Attribution-Share Alike 3.0 License
(http://creativecommons.org/licenses/by-sa/3.0/)

3. +
Reading material

Foundations of Semantic Web Chapter 3.

Semantic Web for the Working Ontologist. Chapter 8
http://proquest.safaribooksonline.com/book/-/9780123859655

4. +
Core concepts

Systems that perform inference are often called reasoning
engines or reasoners.

Reasoner engine
a system that infers new information based on the contents of a
knowledgebase. This can be accomplished using rules and a rule
engine, triggers on a database or RDF store, decision trees,
tableau algorithms, or even programmatically using hard-coded
business logic

A reasoner must be compliant to the semantics of the ontology
language it supports

Hence, an ontology language must state it’s semantics in a
formal way

5. +
Giving semantics to RDFS

Implementing semantics for RDFS

Overview

Using RDFS inference with Sesame

6. +
RDFS rule-based semantics

7. +
RDFS rule-based semantics

Example: Type propagation through rdfs:subClassOf described
as a rule
[IF]
?class1 rfds:subClassOf ?class2 AND ?instance rdf:type ?class1
[THEN]
?instance rdf:type ?class2

Subclass transitivity as a rule
[IF]
?class1 rfds:subClassOf ?class2 AND ?class2 rfds:subClassOf ?class3
[THEN]
?class1 rdf:type ?class3

8. +
RDFS rule-based semantics

The RDFS specification defines RDFS semantics in terms of 26
rules grouped as follows:

RDFS entailment rules core rules, simple “reasonable” entailments
(incomplete w.r.t. domain/range/subPropertyOf and subClassOf)

RDFS rdfsensional rules complete the rule set w.r.t. to
domain/range/subPropertyOf and subClassOf

Datatype entailment rules covers inference related to datatype’s
lexical forms

See http://www.w3.org/TR/rdf-mt/#rules

See Section 3.3 of Foundations of Semantic Web

9. RDFS Entailment Rules
+
Name
Condition
Conclusion
rdfs1
uuu aaa lll.
_:nnn rdf:type rdfs:Literal .
where lll is a plain literal
(with or without a language tag).
where _:nnn identifies a blank node
allocated to lll by rule rule lg.
rdfs2
aaa rdfs:domain xxx .
uuu aaa yyy .
uuu rdf:type xxx .
rdfs3
aaa rdfs:range xxx .
uuu aaa vvv .
vvv rdf:type xxx .
rdfs4a
uuu aaa xxx .
uuu rdf:type rdfs:Resource .
rdfs4b
uuu aaa vvv.
vvv rdf:type rdfs:Resource .
rdfs5
uuu rdfs:subPropertyOf vvv .
vvv rdfs:subPropertyOf xxx .
uuu rdfs:subPropertyOf xxx .
rdfs6
uuu rdf:type rdf:Property .
uuu rdfs:subPropertyOf uuu .
rdfs7
aaa rdfs:subPropertyOf bbb .
uuu aaa yyy .
uuu bbb yyy .

10. RDFS Entailment Rules (cont.)
+
Name
Condition
Conclusion
rdfs8
uuu rdf:type rdfs:Class .
uuu rdfs:subClassOf rdfs:Resource .
rdfs9
uuu rdfs:subClassOf xxx .
vvv rdf:type uuu .
uuu rdf:type xxx .
rdfs10
uuu rdf:type rdfs:Class .
uuu rdfs:subClassOf uuu .
rdfs11
uuu rdfs:subClassOf vvv .
vvv rdfs:subClassOf xxx .
uuu rdfs:subClassOf xxx .
rdfs12
uuu rdf:type
rdfs:ContainerMembershipProperty .
uuu rdfs:subPropertyOf rdfs:member .
rdfs13
uuu rdf:type rdfs:Datatype .
uuu rdfs:subClassOf rdfs:Literal .

11. RDFS extensional entailment rules
+
Name
Condition
Conclusion
ext1
uuu rdfs:domain vvv .
vvv rdfs:subClassOf zzz
uuu rdfs:domain zzz .
ext2
uuu rdfs:range vvv .
vvv rdfs:subClassOf zzz .
uuu rdfs:range zzz .
ext3
uuu rdfs:domain vvv .
www rdfs:subPropertyOf uuu .
www rdfs:domain vvv .
ext4
uuu rdfs:range vvv .
www rdfs:subPropertyOf uuu .
www rdfs:range vvv .
ext5
rdf:type rdfs:subPropertyOf www .
www rdfs:domain vvv .
rdfs:Resource
rdfs:subClassOf vvv .
ext6
rdfs:subClassOf rdfs:subPropertyOf www .
www rdfs:domain vvv .
rdfs:Class rdfs:subClassOf
vvv .
ext7
rdfs:subPropertyOf rdfs:subPropertyOf www .
www rdfs:domain vvv .
rdf:Property
rdfs:subClassOf vvv .
ext8
rdfs:subClassOf rdfs:subPropertyOf www .
www rdfs:range vvv .
rdfs:Class rdfs:subClassOf
vvv .
ext9
rdfs:subPropertyOf rdfs:subPropertyOf www .
www rdfs:range vvv .
rdf:Property
rdfs:subClassOf vvv .

12. +
Datatype entailment rules
Name
Condition
Conclusion
rdfsD1
ddd rdf:type rdfs:Datatype .
uuu aaa "sss"^^ddd .
_:nnn rdf:type ddd .
where _:nnn identifies a blank node
allocated to "sss"^^ddd by rule rule lg.
rdfsD2
ddd rdf:type rdfs:Datatype .
uuu aaa "sss"^^ddd .
uuu aaa "ttt"^^ddd
rdfsD3
ddd rdf:type rdfs:Datatype .
eee rdf:type rdfs:Datatype .
uuu aaa "sss"^^ddd .
uuu aaa "ttt"^^eee .

Note, infinite number of rules!

Semantics by rules is easy to understand (most of them), but
“hacky”

13. +
Other semantics for RDFS

RDFS rule-based semantics are SYNTACTIC, easy to
understand, implemented everywhere

Syntactic rules are prone to incompleteness (several passes
were necessary to fix RDFS rule-based semantics)

Sometimes not-intuitive

RDFS also has model-theoretic semantics, clear semantics
based on set theory

Won’t see them in this course, see Chapter 3 in Foundations
of Semantic Web

14. +
Rule-based inference

Basic idea, describe all mandatory inferences as rules.

A rule describes how new information based on the current
state of the data/knowledge base.
IF a holds in the data
Then b holds in the data
Pre-condition
conclusion

Rule based inference cannot be used for ANY language., (key
factors, non-determinism and termination)

They are enough to capture the semantics of RDFS

15. +
Implementing RDFS
semantics

16. +
Implementing RDFS semantics

Most (really, almost all) reasoners that implement RDFS
semantics use one (or both) of the following techniques

Forward chaining
Deduction calculus for all the rules in the RDFS rules.

Backward chaining
Looking for all possible facts from which we may derive the
conclusion

17. +
Forward chaining

Objective: Is fact X implied by the data?

How: Pre-compute all implied facts, then just check if fact X is
there

How it works



Works at “load” time
Infers new facts based on the existing ones
Continues applying inferences until reaching a fix point (graphs are
sets)

New facts are added “immediately” to the repository

Natural match to RDFS rule-based semantics

18. +
Forward chaining

How it works

Works at “load” time

Infers new facts based on the existing ones

Continues applying inferences until reaching a fix point (graphs are
sets)

New facts are added “immediately” to the repository

Natural match to RDFS rule-based semantics
Complex interactions in forward chaining

19. +
Forward chaining, cons and pros

Pros


Rules are already given by the RDFS rule-based semantics


Easy to implement
Retrieval is FAST (also query answering)
Cons

Adds a lot of new information (maybe not necessary)

Extra space

Extra time

Updates are VERY complicated (truth maintenance)

20. +
Forward chaining (cont.)

21. +
Forward chaining, cons and pros

Pros




Cons





Easy to implement
Rules are already given by the RDFS rule-based semantics
Retrieval is FAST (also query answering)
Adds a lot of new information (maybe not necessary)
Extra space
Extra time
Updates are VERY complicated (truth maintenance)
Possible optimizations: application order, parallelism (often
incomplete)

22. +
Backward chaining

Objective: is fact X implied by the data?

How: Compute the facts that would be necessary for fact X to
be implied, verify if any of those conditions is true.

23. +
Forward chaining, cons and pros

Pros


No data is generated, no extra loading time


Easy to implement
Simple update management or truth maintenance
Cons



Retrieval is slower
Fast query time may require complex optimization techniques
Possible optimizations: caching, low level indexes

24. +
Forward or Backward

Key aspects in deciding for forward
or backward chaining:

Loading time

Query time

Space constraints

Updates

25. +
Any other ways to implement with
RDFS semantics

There are other, more efficient methods

Not implemented in common frameworks

More to come in this course

26. +
RDFS reasoning in Sesame
Easy

27. +
Sesame RDFS Sail

RDFS entailments are implemented using a SAIL

The sail is a ForwardChainingRDFSInferencer

On load time it will perform forward chaining

28. +
Sesame RDFS Sail

RDFS entailments are implemented using a SAIL

The sail is a ForwardChainingRDFSInferencer

On load time it will perform forward chaining

29. +
Setting it up

Create the repository of your choice and attach the sail
Repository myRepository = new SailRepository(
new ForwardChainingRDFSInferencer(
new MemoryStore()));
myRepository.initialize();

As with any forward chaining inference engine, load time will be
affected by the use of this sail

30. +
Sesame RDFS in the console

In the console, simply create the pre-configured repos:

in-memory-rdfs

native-rdfs-types

31. +
Sesame and reasoning

Sesame’s native support for inferences is poor, only RDFS

Performance is not great

Options on large scenarios: OWLIM