1. Reasoning of database consistency
through Description Logics
1Ahmad Karawash

2. Overview
Introduction
Data models and Description Logics
Description Logics and database querying
Data integration
Conclusion
Ahmad Karawash

3. Reasoning of database consistency through Description Logics
Definitions :
The object of knowledge representation is to express the problem in
computer-understandable form
Description Logics (DL) are a family of knowledge representation
languages called description languages.
Data model is essentially a language or set of concepts for describing
a class of certain kinds of databases.
Entity Relationship (ER) model used to describe the structure of data
stored in the database.
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Ahmad Karawash

4. Reasoning of database consistency through Description Logics
what is ER?
ER is the most widespread semantic data model, and it has become
a standard, extensively used in the design phase of commercial
applications.
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Ahmad Karawash

5. Reasoning of database consistency through Description Logics
ER elements:
- Entities set: set of objects that have common properties.(ex: object person have
name, phone, age).
- Relationships: set of tuples (instances), each of which represents an association among a
different combination of instances of the entities that participate in the relationship.
- Attributes: express the Elementary properties whose values belong to one of several
predefined domains, such as Integer, String, or Boolean.
- An IS-A relation between two entities is denoted by an arrow from the more specific to
the more general entity
-ER-role: is introduced since each entity can participate in a relationship more than once
,The arity of a relationship is the number of its ER-roles.
- Cardinality constraints can be attached to an ER-role in order to restrict the number of
times each instance of an entity is allowed to participate.
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Ahmad Karawash

6. Reasoning of database consistency through Description Logics
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
ER symbols:
- Domain symbol (D)  has predefined domain DB
D
- Entity symbol (E) -> set of attribute symbol (A) each has a unique domain
- Relationship symbol (R) -> N ER-role symbols
- Cardinality constraint -> - cminS from ER-role -> nonnegative integer
- cmaxS from ER-role -> all positve integer (+infinity)
String, integer,
…
E
AA
R E2E1
ER-roleER-role
Ahmad Karawash

7. Reasoning of database consistency through Description Logics
Database (B) correspond to ER (S)
- Expressed by nonempty finite set ΔB & function .B (as in algebra f : E-> R)
-.B : D -> DB
D (maps to predefined domain string, integer, …)
- .B : E -> EB (maps from E to instance of E)
- .B : A -> AB (maps to instance of attribute that connects entity to domain)
.B : R -> RB (maps to instance of relationship that connect ER-roles to entities
T : ER-roles -> ΔB
<u1:o1,..,un:on>->T[ui]=oi )
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
R1
R2
E
U1
U2
O1
O2
EB AB RB are instances of E, A, R
Ahmad Karawash

8. Reasoning of database consistency through Description Logics
Database (B) is legal to ER (S) if it satisfy :
- For each pair E1,E2 with E1 Is-a E2 => E1B C E2B
(all individuals that satisfies E1 also satisfies E2)
- For each pair R1,R2 with R1 Is-a R2 => R1B C R2B
- For each entity E : e belong EB there is only one a(e,d) belong to AB such that e
connect entity E to domain D.
- For each relation R of arity N : all instance has the form <U1:O1,…,Un:On>
- For each ER-role U of R with E : cmin(U) <= |{r belong R / r[U]=e }|<= cmax(U)
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Ahmad Karawash

9. Reasoning of database consistency through Description Logics
How to transform from ER to DLR knowledge?
DLR is an expressive Description Logic (DL) with n-ary relations,
particularly suited for modeling database schemas and queries.
To transform from ER to DLR, a mapping function (Ø) should be
introduced .
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Ahmad Karawash

10. Reasoning of database consistency through Description Logics
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Ø(S) -> gives the knowledge base of ER S
- Set of atomic concept of Ø(S)={set of entity & domain symbol of S}
- Set of relation concept of Ø(S)={
- R in S -> PR in Ø(S) [relation symbol between E and R]
- A in S -> PA in Ø(S) [attribute symbol between E and Domain] }
- Set of axiom : - E1 Is-a E2 => E1 C E2
- R1 Is-a R2 => PR1 C PR2
- For each attribute A with domain D of an entity E,
E C (forall[$1](PA ^ ($2:D))) ^ =1 [$1]PA
- For each relationship R of arity n with ER-roles
PR C ($μ R(U1):E1) ^ …••• ^($μ R(Un):En)
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11. Reasoning of database consistency through Description Logics
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
ER
DLR
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12. Reasoning of database consistency through Description Logics
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
What benefits can be derived from having established
relationships?
Reasoning:
- Entity satisfiability, i.e., whether for every concept C, S admits a model in
which it has a nonempty extension. If C must always have an empty
extension then there is an inconsistency
- Relation satisfiability, i.e., whether S admits a model in which a certain
relation has a nonempty extension.(similar to above)
- Consistency of the ER schema, i.e., whether S admits a finite model.
Without this, there is no database that satisfies the schema, so
inconsistent if infinite model.
Ahmad Karawash

13. Reasoning of database consistency through Description Logics
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Reasoning (continue):
Redundancy of the ER schema. Various forms of redundancy in the ER
schema can be detected: e.g., if A, B are entities and both A v B and B v A
hold, we can conclude that one of the entities is redundant.
- Stronger constraints on relationship roles.
- Entity subsumption, i.e., whether the extension of one concept B is a
subset of the extension of another concept A in every model of S. This
property suggests that the designer check for the possible omission of an
explicit IS-A relationship between B and A.
- Relation subsumption, i.e., whether the extension of one relation is a
subset of the extension of another relation in every model of S. (Similar to
the above.)
Ahmad Karawash

14. Reasoning of database consistency through Description Logics
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Description Logics as query languages:
- the query description can be compared to the inconsistent description. If
they are equivalent, then there is surely a mistake
- The query can be classified with respect to the concepts in the schema.
This can be used to help users pose queries in an unfamiliar domain.
- Queries can also be classified with respect to each other into a
subsumption hierarchy. In an environment where several people are
asking exploratory questions about the data over a long period of time
(e.g., data mining by humans), it is very useful to have the questions
organized
Ahmad Karawash

15. Data Integration
 Integrating different data sources is one of the fundamental problems
faced by the database community.
 The goal of a data integration system is to provide a uniform interface to
various data sources [Levy,2000].
 The design of a data integration system is a very complex task, which
comprises several different aspects.
Reasoning of database consistency through Description Logics
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
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16. Conclusion
 The greatest advantage of DL models is not representing
information model only but reasoning with the model.
 The subsumption relationship can be used for semantic query
optimization.
 DLs are useful in heterogeneous or federated databases.
 The meaning of the DL model is unambiguous and precise and is
capable to check the consistency of any entire model.
Reasoning of database consistency through Description Logics
Introduction - Data models & DL - DL & database querying - Data integration - conclusion
Ahmad Karawash 7

17. Any question?
Ahmad Karawash
Ahmad_karawash@hotmail.com
Ahmad Karawash

18. References
 Krötzsch, M., Simacikˇ, F., Horrocks, I.: A Description Logic Primer. CoRR.
abs/1201.4, 1–16 (2012).
 Lutz, C.,Toman, D.: Conjunctive Query Answering in the Description Logic EL using a
Relational Database System. International Joint Conferences on Artificial Intelligence.
pp. 2070–2075 (2009).
 Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity
of query answering in description logics. Artif. Intell. 195, 335–360 (2013).
 Motik, B., Horrocks, I., Sattler, U.: Integrating Description Logics and Relational
Databases. Science (80-. ). 1–44 (2006).
 Bertossi, L.: Consistent query answering in databases, (2006).
 Borgida, A., Lenzerini, M., Rosati: Description Logics for Data Bases. Description
Logic Handbook. pp. 472–494 (2002).
 …..
Ahmad Karawash