Download presentation

Presentation is loading. Please wait.

Published byBrisa Knightly Modified over 2 years ago

1
Relational Schemas and Predicate Logic: Notation

2
Relations Let E1,..,En be sets of entities or objects (we may have Ei = Ej). The Cartesian product E1 x … x En is the set of tuples of the form (e1,..,en) where ei is in set Ei. A relation R on E1,..,En is a subset of the Cartesian product E1 x … x En. We say that n is the arity of the relation. Note that a relation may be unary.

3
Relational Schemas A schema specifies a finite set of relations R1,..Rn with additional structure: Each column/field in a relation gets a name (can also just use position) and a domain. A subset of fields is identified as the key. The non-key fields are often called (descriptive) attributes. The values of the attributes are determined by the values of the key field. Common Notation –Student(Name:string,GPA:numeric,Age:integer) –Registered(Name:string,Course:string,grade:nume ric)

4
ER Model: Entities Entity: Real-world object distinguishable from other objects. An entity is described (in DB) using a set of attributes. Entity Set: A collection of similar entities. E.g., all employees. – All entities in an entity set have the same set of attributes. – Each entity set has a key. – Each attribute has a domain. – A key defines the values of attributes---the attributes are functions of the keys. Employees ssn name lot

5
ER Model: Relationships Relationship: Association among two or more entities. E.g., Attishoo works in Pharmacy department. Relationship Set: Collection of similar relationships. – An n-ary relationship set R relates n entity sets E1... En; each relationship in R involves entities e1,..., en Same entity set could participate in different relationship sets, or in different “roles” in same set. lot dname budget did since name Works_In DepartmentsEmployees ssn Reports_To lot name Employees subor- dinate super- visor ssn

6
Notes on ER relationships Note that relationships can have descriptive attributes too. The values of the descriptive attributes are determined once we have identified the entities involved: grade(Joe,CMPT354). The fields that identify the entities involved are callled foreign key pointers.

7
Relational Instance and Finite Models A relational instance is a relational schema + set of tuples specified for each relation. The list of relations (with tuples specified, but without field names and key constraints) is called a finite model in logic.

8
Graphical Visualization A graph on set S is a binary symmetic relation over S x S. If the relation instance contains only one binary symmetric relation, it can be visualized as a graph whose edges and nodes are annotated with the values of descriptive attributes. Classic social network analysis considers only the graph structure, not the attributes.

9
Translating Schemas Into Logic: no functions Each relation of arity n predicate symbol with n arguments. E.g., “A student with GPA 3.0 is younger than 40” Student(S,G,A) AND G = 3.0 A < 40. Pros: –Simple Translation. –Simple logic. Cons: –Loses information about key fields. –Not always natural to read.

10
Translating Schemas Into Logic: Functions Introduce one function symbol for each descriptive attribute. The arguments are the key fields. E.g., Age(S), grade(S,C). Also: S.age,Registered.grade. E.g., “A student with GPA 3.0 is younger than 40” GPA(S) = 3.0 Age(S) < 40. Pros: –Keeps information about keys and foreign keys. –Natural to read. Cons: a bit more complex mathematically.

11
Formal definitions in logic Use the function-free formulation, with predicate symbols R1,..,Rn. The language contains a set of constants and variables. A term is a constant or a variable. An atom is: –a predicate symbol with the required numbers of terms, e.g. Student(N,G,40), Student(Jack,3.0,40). –A comparison of terms, e.g. X > 3, X = Y, 5 > 1. A literal is an atom or a negated atom.

12
Clauses A clause is a set of literals. The negated literals are called the body, the positive ones the head. A clause is often written in implication form: b1 AND b2 h1. Also h1 :- b1,b2. A clause with a single positive literal is a Horn clause.

Similar presentations

OK

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke1 The Entity-Relationship Model Chapter 2.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke1 The Entity-Relationship Model Chapter 2.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on chromosomes and genes and locus Ppt on intellectual property rights Ppt on the topic online education Ppt on zener diode application Ppt on case study in psychology Ppt on ready to serve beverages recipes Ppt on condition monitoring software Ppt on teachers day greetings Ppt on nazism and hitler in germany Ppt on dubai shopping festival