1. Semantic Web in Depth Rules
Professor Steffen Staab Many slides courtesy by Dr. Nick Gibbins

2. The Semantic Web layer cake
Proof
Trust
User Interface and Applications
XML + Namespaces
URI
Unicode
Signature
Encryption
RDF
RDF Schema
OWL
Identity
Standard syntax
Metadata
Ontologies + Inference
Explanation
Attribution
SPARQL (queries)
Rules

3. The Role of Rules
The KR formalisms of the Semantic Web have expressive limitations which can be overcome by rule-based knowledge
For example, we cannot assert a new fact in OWL by checking three other relations, like:
triangle(?x,?y,?z) :- knows(?x,?y),knows(?y,?z),knows(?z,?x).
“Three nodes are called a triangle if all three nodes know each other.”
OWL does not allow for stating constraints:
Inconsistent :- hasChild(?x,?y), hasAge(?x,?n), hasAge(?y,?m), ?n < ?m.
“A parent cannot be younger than his/her child.”

4. Rule Format
The majority of rules in rule-based systems are of the form: A ⇐ B1 ∧ B2 ∧ … ∧ Bn
A is known as the consequent or head of the rule
B1…Bn are known as the antecedents or body of the rule
Also known as Horn Clauses (disjunction with at most one positive literal)

5. Rule Format A ⇐ B1 ∧ B2 ∧ … ∧ Bn
A is known as the consequent or head of the rule
B1…Bn are known as the antecedents or body of the rule
Rule systems differ in what kind of heads and antecedents they allow
Propositional: P, Q, …
Relational: Pk(?X1,…,?Xn)
(nested) Function Symbols: Pk(f(?X1),…,g(?Xn-1, f(?X1),?Xn))
Negation (for the antecedent): not Pk (?X1,…,?Xn)

6. Rules – One Word for Two Things
Declarative, but rather procedural knowledge
Traditional Expert Systems
CLIPS, JESS, OPS,…
Database triggers, ECA rules (Event-Condition-Action), Production rules
Rules are active in time
The order of processing is key to the effect of rules
Declarative, (truely) logical knowledge
Datalog (part of many DBs)
Answer set programming: DLV, Potassco
F-Logic: Florid, Ontobroker, Flora-2 / Ergo Suite …
Rules describe logical constraints. Either used to derive data views (F-Logic) XOR logical consistency (ASP)

7. Rules – One Word for Two Things
Declarative, but rather procedural knowledge
Traditional Expert Systems
CLIPS, JESS, OPS,…
Database triggers, ECA rules (Event-Condition-Action), Production rules
Rules are active in time
The order of processing is key to the effect of rules
Declarative, (truely) logical knowledge
Datalog (part of many DBs)
Answer set programming: DLV, Potassco
F-Logic: Florid, Ontobroker, Flora-2 / Ergo Suite …
Rules describe logical constraints. Either used to derive data views (F-Logic) XOR logical consistency (ASP)
Some important languages sit in the middle:
Prolog, RIF,...

8. Rules and the Semantic Web
Several proposed rule languages for use with the SW:
RuleML
N3 Rules
Jena Rules
Semantic Web Rule Language (SWRL)
Rule Interchange Format (RIF)
SPIN

9. ECA-like Rules:
Given Empty default graph PREFIX dc: my: < Rule my:hasCreated(?X,?Y) :- dc:creator(?Y,?X).
Sequence of Actions
INSERT DATA { < dc:creator "A.N.Other" . }
DELETE DATA { < dc:creator "A.N.Other" . }
What is now returned in Step 3?
CREATE ?X ?P ?Z. WHERE {?X ?P ?Z.}
"A.N.Other“ my:hasCreated <
An event happened here that added a statement which was never retracted by another rule.

10. Declarative Logical Rules:
Given Empty default graph PREFIX dc: my: < Rule my:hasCreated(?X,?Y) :- dc:creator(?Y,?X).
Sequence of Actions
INSERT DATA { < dc:creator "A.N.Other" . }
DELETE DATA { < dc:creator "A.N.Other" . }
What is now returned in Step 3?
CREATE ?X ?P ?Z. WHERE {?X ?P ?Z.} {}
Here, data and logical rules are questioned to determine what holds at time of querying.

11. Issues with Semantics of Logical Rules
Recursion
Infinite structures
Undecidability
Multiple semantics
Negation
Function symbols
Negation-as-failure
Non-monotonicity

12. Non-monotonicity
Given: Person(nicola). Man(?X) :- Person(?X), not Woman(?X). Infers: Man(nicola). But add another fact: Woman(nicola) Then the inference Man(nicola) needs to be retracted.
OWL and 1st order predicate logics are monotonous: More facts always lead to more inferences, never to less.

13. Multiple Semantics
Given: Person(nicola). Man(?X) :- Person(?X), not Woman(?X). Woman(?X) :- Person(?X), not Man(?X). What should be inferred? Possibility 1: Nothing (e.g. well-founded semantics) Possibility 2: Two competing solutions that are never true at the same time (e.g. answer-set semantics) a. Man(nicola) b. Woman(nicola)

14. Infinite Structures
Number(0). Number(succ(?X)) :- Number(?X). Number holds for 0, succ(0), succ(succ(0)),... Even(0). Even(0) Even(succ(succ(?X))) :- Even(?X). Even(2),Even(4),... Odd(succ(?X)) :- Even(?X). Odd(1),Odd(3),.. Magic :- EXISTS ?X Number(?X) and not Even(?X) and not Odd(?X). Magic requires to check all infinitely many numbers

15. Description Logics and Rules
Some work on designing DLs which include trigger rules of the form: C ⇒D (if an individual is a member of C, then it must be a member of D

16. Description Logics and Rules
C ⇒D is (often) not the same as saying C ⊑ D (every instance of C is an instance of D)
C ⊑ D is equivalent to saying ¬D ⊑ ¬C (contrapositive)
The procedural trigger rule C ⇒D is not equivalent to ¬D ⇒ ¬C
DLs with rules include an epistemic (modal) operator K:
KC can be read as “the class of things which are known to be of class C”
C ⇒D is equivalent to KC ⊑ D
Used as a foundation for SWRL, etc

17. SPIN

18. SPARQL CONSTRUCT
PREFIX foaf: < PREFIX vcard: < CONSTRUCT { ?x vcard:FN ?name . ?x vcard: ?mail . } WHERE { ?x foaf:name ?name . ?x foaf:mbox ?mail . }
CONSTRUCT matches graph patterns and returns a new graph
We could implement a simple rule-based system using CONSTRUCT queries to represent rules

19. SPARQL CONSTRUCT is not a rule language
From the Data Access Working Group Charter:
“While it is hoped that the product of the RDF Data Access Working Group will be useful in later development of a rules language, development of such a rules language is out of scope for this working group. However, any serializations of a query language must not preclude extension to, or inclusion in, a rules language. The group should expend minimal effort assuring that such an extension be intuitive and and consistent with any query language produced by the group.”
Spin goes this way.

20. Constraints
# must be at least 18 years old ASK WHERE { ?this ex:age ?age . FILTER (?age < 18) . } Put this boolean condition on a class.

21. Class constraint in SPIN
ex:Parent a rdfs:Class ; rdfs:label "Parent"^^xsd:string ; rdfs:subClassOf ex:Person ; spin:constraint [ a sp:Ask ; rdfs:comment "must be at least 18 years old"^^xsd:string ; sp:where ([ sp:object sp:_age ;  variable ?age sp:predicate ex:age ;  property ex:age sp:subject spin:_this  variable ?this ] [ a sp:Filter ; sp:expression [ a sp:lt ; sp:arg1 sp:_age ; sp:arg2 18 ] ]) ].
Spin encodes the syntax tree of SPARQL queries using blank nodes.

22. Spin encodes the syntax tree of SPARQL queries using blank nodes.
Unreadable
Unless it is made readable by a tool
Constraint/rule can be stored together with data and executed to indicate consistency or inferred data

23. SPARQL Construct Query
CONSTRUCT { ?this ex:grandParent ?grandParent . } WHERE { ?parent ex:child ?this . ?grandParent ex:child ?parent .

24. SPARQL Construct Query Turned into SPIN Rule
ex:Person a rdfs:Class ; rdfs:label "Person"^^xsd:string ; rdfs:subClassOf owl:Thing ; spin:rule [ a sp:Construct ; sp:templates ([ sp:object sp:_grandParent ; sp:predicate ex:grandParent ; sp:subject spin:_this ]) ; sp:where ([ sp:object spin:_this ; sp:predicate ex:child ; sp:subject sp:_parent ] [ sp:object sp:_parent ; sp:subject sp:_grandParent ]) ] .

25. Jena Rules

26. Jena Rules
Jena RDF/OWL library contains support for forward- and backward-chaining rules
Only implemented in Jena
Syntax:
[rule name: antecedents -> consequent ]
Antecedents expressed as triple patterns (unfortunately not in a SPARQL-like syntax)

27. Jena Rule Example
# Example rule file @prefix ont: < @include <RDFS>. [rule1: (?x ont:parent ?t) (?t ont:brother ?z) -> (?x ont:uncle ?z)]
can include other rulebases – these
are the entailment rules for RDFS

28. Semantic Web Rule Language

29. SWRL Member Submission to W3C in 2004
Based on RuleML subset and OWL
XML and RDF-based serialisations (also, human-readable abstract syntax)
Obeys constraints put on OWL re: disjointness of instances and datatype values
Two types of variable in expressions
I-variable – matches class instances
D-variable – matches datatype values

30. SWRL Rule Example In abstract syntax:
hasParent(?x1,?x2) ∧ hasBrother(?x2,?x3) ⇒ hasUncle(?x1,?x3)
In abstract syntax:
Implies(Antecedent(hasParent(I-variable(x1) I-variable(x2)) hasBrother(I-variable(x2) I-variable(x3))) Consequent(hasUncle(I-variable(x1) I-variable(x3))))

31. SWRL Rule Example
Artist(?x) ∧ artistStyle(?x,?y) ∧ Style(?y) ∧ creator(?z,?x) ⇒ style/period(?z,?y)
Implies(Antecedent(Artist(I-variable(x)) artistStyle(I-variable(x) I-variable(y)) Style(I-variable(y)) creator(I-variable(z) I-variable(x))) Consequent(style/period(I-variable(z) I-variable(y))))
Class membership

32. SWRL Rule Example
Artist(?x) ∧ (≤1 artistStyle)(?x) ∧ creator(?z,?x) ⇒ (≤1 style/period)(?z) Implies(Antecedent(Artist(I-variable(x)) (restriction(artistStyle maxCardinality(1))) (I-variable(x)) Style(I-variable(y)) creator(I-variable(z) I-variable(x))) Consequent((restriction(style/period maxCardinality(1)) (I-variable(z))))
Use of restrictions and other OWL features

33. SWRL XML Syntax
<ruleml:imp> <ruleml:_rlab ruleml:href="#example1"/> <ruleml:_body> <swrlx:individualPropertyAtom swrlx:property="hasParent"> <ruleml:var>x1</ruleml:var> <ruleml:var>x2</ruleml:var> </swrlx:individualPropertyAtom> <swrlx:individualPropertyAtom swrlx:property="hasBrother"> <ruleml:var>x2</ruleml:var> <ruleml:var>x3</ruleml:var> </swrlx:individualPropertyAtom> </ruleml:_body> <ruleml:_head> <swrlx:individualPropertyAtom swrlx:property="hasUncle"> <ruleml:var>x1</ruleml:var> <ruleml:var>x3</ruleml:var> </swrlx:individualPropertyAtom> </ruleml:_head> </ruleml:imp>
Based on OWL XML Presentation Syntax (with RuleML)

34. SWRL RDF Syntax
<swrl:Variable rdf:ID="x1"/> <swrl:Variable rdf:ID="x2"/> <swrl:Variable rdf:ID="x3"/> <ruleml:Imp> <ruleml:body rdf:parseType="Collection”> <swrl:IndividualPropertyAtom> <swrl:propertyPredicate rdf:resource="&eg;hasParent"/> <swrl:argument1 rdf:resource="#x1" /> <swrl:argument2 rdf:resource="#x2" /> </swrl:IndividualPropertyAtom> <swrl:IndividualPropertyAtom> <swrl:propertyPredicate rdf:resource="&eg;hasSibling"/> <swrl:argument1 rdf:resource="#x2" /> <swrl:argument2 rdf:resource="#x3" /> </swrl:IndividualPropertyAtom> </ruleml:body> …

35. Rule Interchange Format

36. Rule Interchange Format
W3C Working Group chartered in late 2005
More expressive language than SWRL
Common core with extensions
Reached Recommendation in June 2010

37. Rule Interchange Format
Defines XML syntax and non-XML presentation syntax (c.f. OWL)
Latest version from:

38. RIF Dialects Two dialects (building on a common core):
RIF Basic Logic Dialect
Monotonic condition and conclusion
Statements are either true or false
The values of predicates cannot be changed, you can only add new statements
RIF Production Rule Dialect
Non-monotonic condition and conclusion
Values of predicates can be changed

39. RIF Basic Logic Dialect
Definite Horn rules
Disjunction with exactly one positive literal A :- B and C and D
N-ary predicates (sugared syntax)

40. RIF Structure Rules occur in Groups: Groups occur in Documents:
Group( (Forall ?x Q(?x) :- P(?x)) (Forall ?x Q(?x) :- R(?x)) )
Groups occur in Documents:
Document( Group( (Forall ?x Q(?x) :- P(?x)) (Forall ?x Q(?x) :- R(?x)) ) Group( (Forall ?y R(?y) :- S(?y)) ) )

41. RIF Example
Document( Prefix(cpt Prefix(ppl Prefix(bks Group ( Forall ?Buyer ?Item ?Seller ( cpt:buy(?Buyer ?Item ?Seller) : cpt:sell(?Seller ?Item ?Buyer) ) cpt:sell(ppl:John bks:LeRif ppl:Mary) ) )

42. RIF Example
Document( Prefix(dbp Prefix(my Prefix(rdfs Group ( Forall ?mname ?aname ?movie ?actor my:actorIn(?aname ?mname) : And( dbp:starring(?movie ?actor) rdfs:label(?movie ?mname) rdfs:label(?actor ?aname) ) ) )

43. RIF Example
Document( Prefix(dbp Prefix(my Prefix(rdfs Group ( Forall ?mname ?aname ?movie ?actor my:actorIn(?aname ?mname) :- And( ?movie[dbp:starring -> ?actor rdfs:label -> ?mname] ?actor[rdfs:label ?aname] ) ) )

44. Reflection

45. Reflection on Rules Current subjective assessment of rules
Much used in Knowledge representation and Databases
More used than Description Logics
Rules are not exchanged much on the Web
Suggested solution for the time being:
Define your rules locally
Use whatever rule mechanism and syntax you like
Apply with data from the Web