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5. Semantics of Web Services
XML, Google: The syntactic web Web Services and WSDL Classical procedure invocation based on: Procedure names Parameter types Routing information Strong coupling of subsystems required In particular in ecommerce scenarios, a loose coupling can be expected In ecommerce scenarios, agents use different conceptual data models Problems with syntactic approaches to information retrieval and type-checking for calling procedures Enable system designers to express the meaning of the names in the conceptual data model
Description Logics and Semantic Web
Description Logics:
A Logical Foundation of the
Semantic Web
Volker Haarslev Concordia University, Computer Science Department 1455 de Maisonneuve Blvd. W. Montreal, Quebec H3G 1M8, Canada http://www.cs.concordia.ca/~faculty/haarslev/ [email protected]
Typical Information Retrieval Example
Suppose you are a salesperson, who wishes to find a
Ms. Cook you met at a trade conference last year
you don’t remember her first name but you remember she worked for one of your clients and her daughter is a student of your alma mater
An intelligent search agent can
ignore pages relating to cooks, cookies, Cook Islands, etc. find pages of companies your clients are working for follow links to or find private home pages check whether a daughter is still in school match with students from your alma mater
If you already have the Semantic Web
Basic Web Technology
Uniform Resource Identifier (URI)
foundation of the Web identify items on the Web uniform resource locator (URL): special form of URI
Extensible Markup Language (XML)
send documents across the Web allows anyone to design own document formats (syntax) can include markup to enhance meaning of document’s content machine readable
Resource Description Framework (RDF)
make machine-processable statements triple of URIs: subject, predicate, object intended for information from databases
A Logical Foundation for the Semantic Web
Systems can understand basic concepts such as
subclass inverse relation, etc.
Even better
state (any) logical principle permit computers to reason (by inference) using these principles an employee sells more than 100 items per day ⇒ bonus follow semantic links to construct a proof for your conclusions exchange proofs between agents (and human users)
OWL is a syntactic variant of a well-known and very
expressive description logic
Description Logics: Introduction
Important syntactic feature: variable-free notation
constructors: », «, ¬, Ô, Ó standard description logic ALC
Description of concept parent
parent 7 person » Ôhas_child.person
We add two concepts
woman 7 female » person mother 7 female » parent
What type of inferences are interesting?
satisfiability of (named) concepts subsumption of (named) concepts
Inference Service: Concept Subsumption
Consider the question "Is a mother always a woman?"
Does the concept woman subsume the concept mother?
Description logic reasoners offer the computation of a
subsumption hierarchy (taxonomy) of all named
concepts
person female parent woman mother parent 7 person » Ôhas_child.person woman 7 person » female mother 7 parent » female parent 7 person » Ôhas_child.person woman 7 person » female mother 7 parent » female
yes, woman subsumes mother
(see also proof on previous slide)
Description Logics: Semantics (1)
Translation to first-order predicate logic usually possible
Declarative and compositional semantics preferred
Standard Tarski-style interpretation I = (Δ
I
I
Syntax Semantics A A I ⊆ Δ I , A is a concept name ¬C Δ I \ C I C » D C I ∩ D I C « D C I ∪ D I ÓR.C { x ∈ Δ I | Óy: (x,y) ∈ R I ⇒ y ∈ C I } ÔR.C { x ∈ Δ I | Ôy ∈ Δ I : (x,y) ∈ R I ∧ y ∈ C I } R R I ⊆ Δ I x Δ I , R is a role name C ≤ D C I ⊆ D I C 7 D C I = D I Concepts Roles Axioms →
Description Logics: Concept Examples woman 7 person » female parent 7 person » Ôhas_child.person mother 7 parent » female person ≤ Óhas_child.person mother_having_only_female_kids 7 mother » Óhas_child.female mother_having_only_daughters 7 woman » parent » Óhas_child.woman equivalent grandma 7 woman » Ôhas_child.parent great_grandma 7 woman » Ôhas_child.Ôhas_child.parent ← →
Description Logics: Semantics (2)
Interpretation domain can be chosen arbitrarily
Distinguishing features of description logics
domain can be infinite open world assumption
A concept C is satisfiable iff there exists an
interpretation I such that C
I
I is called a model of C
Subsumption can be reduced to satisfiability
subsumes(C,D) ⇔ ¬sat(¬C » D) denoted as C ≥ D or D ≤ C
Example Taxonomy top female woman mother mother_having_only_daughters mother_having_only_female_kids parent person grandma great_grandma ←
Description Logics: Individuals
How can we assert knowledge about individuals?
Assertional axioms
concept assertion for an individual a a:C satisfied iff aI^ ∈ CI example: elizabeth:mother role assertion for two individuals a and b (a,b):R satisfied iff (aI,bI) ∈ RI example: (elizabeth,charles):has_child
Unique name assumption
Different names denote different individuals a I ≠ b I
Description Logics: ABox (2)
New basic inference service: ABox satisfiability
asat(A)
All other inference services can be reduced to asat
instance checking: instance?(a,C,A) ≡ ¬asat(A ∪ {a:¬C}) concept satisfiability: sat(C) ≡ asat({a:C}) concept subsumption: subsumes(C,D) ≡ ¬sat(¬C » D) ≡ ¬asat({a:¬C » D})
Open world assumption
A = {andrew:male, (charles,andrew):has_child} Does instance?(charles,∀has_child.male, A) hold? No. Why?
Description Logics: ABox Example
(male ≤¬female)
queen_mum : woman
(queen_mum,elizabeth) : has_child
elizabeth : woman
(elizabeth,charles) : has_child
(elizabeth,anne) : has_child
charles : parent » male
anne : woman
(charles,andrew) : has_child
andrew : person » male
queen_mum elizabeth charles anne andrew additional axiom ensuring disjointness
