reasoning of database consistency through description logics

Reasoning of database consistency through Description

Logics

1Ahmad Karawash

Overview Introduction

Data models and Description Logics

Description Logics and database querying

Data integration

Conclusion

3Ahmad Karawash

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 describinga 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

4Ahmad Karawash


what is ER?ER is the most widespread semantic data model, and it has becomea standard, extensively used in the design phase of commercial applications.


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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.


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ER symbols:

- Domain symbol (D) has predefined domain DBD

- 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-role

ER-role

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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 )


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R1

R2

EU1

U2

O1

O2EB AB RB are instances of E, A, R

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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)


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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 .


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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) Ahmad Karawash



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ER

DLR

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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.

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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.)

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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

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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.



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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.



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Any question?Ahmad Karawash

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Ahmad Karawash

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). …..

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reasoning of database consistency through description logics

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