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Dat,alog and Recursion
Objectives
After completing this unit, you’ll be able:
Learn about datalog and recursion.
Define the datalog program evaluation
Discuss the difference between generalization and specialization.
Introduction
Although relational algebra is able to provide a range of useful operations for relationships, there are a few
computations that are not able to be written in the form of an expression for relational algebra. Common type of
processing the data we are unable to communicate in the form of relational algebra is an infinite process, recursively
A defined series of expressions that are similar to each other.
10.1 Datalog , Recursion and
We are now defining a relationship called Components which defines the parts that make up each.
Look over the following programs, or the collection of rules
These are rules that are part of Datalog the relational query language that is influenced by Prolog The well-known logic
programming language. In fact the notation is based on Prolog. The first rule must be understood as
follows: Colombia Emails Database.
In all cases, for the values Part, Subpart and Qty,
If there’s a Tuple in the Assembly,
There must be a Tuple in Components.
The second rule can be translated as follows:
In all cases, Part of Part2, Part2, Subpart and Qty
If there’s a Tuple in Assembly and
A triplication in Components,
Then there has to be a Tuple in Components.
The right-hand side of the symbol is known as”the rule’s body and the one that is left of the symbol is called
The rules head. The symbol signifies the logical implications; If the tuples in the
If the body is within the databases, it’s implied that the tuple listed in the first paragraph of the rule should be present in the database as well.
Be in the database.
Thus, if presented with a set of Assembly as well as Components tuples, every rule is able to be used to
Deduce, or infer, new tuples which belong to Components. This is why databases are able to infer, or deduce, new tuples.
Support Datalog rules are commonly known as deductive database systems.

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Every rule is an inference-making template by assigning constants the variables that
In a normal case that is, we can draw certain Components tuples. For instance when we set Part=trike
Subpart=wheel and Qty=3, we can conclude that is contained in Components. In analyzing
every tuple of Assembly is a tuple at a time, and the first rule permits us to determine the succession of tuples created through
projecting to project Assembly onto its initial two fields can be done by using Components.
The second rule permits us to mix Components that we have previously found with
Assembly tuples to determine the tuples of Components that are new. It is possible to apply the second rule by examining
the cross-products from Assembly and (the currently running example of) Components, and assigning values to
the variables used in your cross-product rule. Repeat the process for each row taking one row at. Take note of how
Repeated use of the variable Part2 stops specific rows from being a part of the cross product.
any new tuples. In the end, it specifies an equality join requirement on Assembly and Components.
The tuples that result from one of the applications of this rule can be seen on Figure 10.1. (In addition,
Components includes the tuples that are obtained through the application of the first rule. are not displayed.)
The tuples that result from another use of the rule is displayed in figure 10.2. Be aware that every
The tuple in the figure 10.1 is a reinferred tuple. Only the two tuples in Figure 10.1 are completely new.
The second rule is applied three times will not result in any additional tuples. The set of
Components tuples in Figure 10.2 contains all the tuples which can be inferred from using the
Two Datalog rules for defining Components as well as the specific Assembly. There are two Datalog rules that define Components and the given Assembly. The components
of a trike may now be identified by selecting all Components tuples having the trike’s value in the
First field.
Every application of the Datalog rule is explained in terms of relational algebra. The first rule
In our example program, it simply adds projection on the Assembly relation, and then adds the resultant
Tuples are added to the Components relationship that is initial empty. The second rule connects Assembly
by using Components. Then it creates by projecting. The results of each rule’s application is merged
by using the existing set Components tuples by using union.

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The one and only Datalog operation that is not relationship algebra would be the repetition of the application of
the Components rules until the time that no new tuples are created. The repeated application of
A set of rules is known as the fixpoint operation.
This section concludes by writing the Datalog description of Components in terms of an extended
SQL uses the syntax that was proposed by the draft SQL:1999, and currently supported by IBM’s DB2
Version 2 DBMS Version 2:
The WITH clause creates the relation as part of the query definition. The relationship is similar to
to a view, however the scope of a relationship that is created with WITH is specific in relation to the definition of the query. It is a relation that belongs
RECURRENT keyword indicates it is a sign that tables (in our case Components) is defined recursively.
The form in the definition resembles Datalog rules. Datalog rules. It is also true that if we wanted to
identify the elements of a specific part such as trike, then we just replace the previous line
that includes the following:
Evaluation of the Datalog Program
We categorize the relationships within Datalog programs Datalog program as output relations or input relationships.
Output relations are defined using rules (e.g. Components) Input relations come with a set tuples
explicitly identified (e.g., Assembly). Based on the relation between the input relations, we have to calculate instances
for the output relationships. The definition of the term “datalog” is determined by the output relations. Datalog program is typically described in two distinct ways.
methods, both of which basically define the relation instances for output relations. Technically,
A query is a decision in one of the input relationships (e.g. All Components tuples C ) with
C.part = trike). But, the meaning of a query is obvious when we know how the relation
instances are linked to the output relations of the Datalog program.
The initial approach to define what is a Datalog program is called the semantics of the least model
and allows users to get a better understanding of the program, without having to consider how the program will be used
to be carried out. This means that the meaning is declarative, just like the logic of relational calculus and
Not operational as a the semantics of relational algebra. This is significant due to the absence of
Recursive rules can make it difficult to comprehend the program from an assessment strategy.
The second method, referred to as the semantics of the lowest fixpoint provides a conceptual strategy for evaluating
to calculate the desired relation instances. This provides the foundation for to compute the desired query instances.
within an DBMS. The most efficient evaluation methods are implemented in the actual implementation, however, they do not have the same efficiency. Colombia Email Listings.
The accuracy of the approach is demonstrated by their compatibility with the least fixpoint method. The
Fixpoint semantics are therefore operational and plays a part like that of relational algebra.
semantics for non-recursive queries.

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Least Model Semantics
We want our users to be able to comprehend the Datalog program, by comprehending each rule
independent of any other rules, having the meaning that if the body is true, then the head is also true. This
A quick and intuitive read of the rule implies that, given specific instances of relation names, there are name of the relationship
which appear within the body of a regulation, the instance of a relation for the relation in the body of a rule.
The rule should contain the requisite list of tuples. If the name of a relationship R is found on the minds of more than one
rules that the relation instance for R must meet the intuition-based interpretation of all these rules. However,
We don’t wish to include tuples in the R instance unless they are needed for one reason or another.
of the rules that define R. This means that we will only compute tuples of the rules defining R that are backed by one or more
rules for R.
To understand these concepts in a precise manner it is necessary to explain concepts about models and at the very least, models. A
Models are collections of relations instances one instance for every relation in the program which
It meets the following conditions. Each rule of the program, we make a change, we will replace every rule.
In the rule, if a variable is represented by a constant that is corresponding to it The following is true:
1. If each tuple of the body (obtained by replacing variables by constants) is in
the relation instance that is corresponding,
2. Then the tuple that was generated by the head (by the assignment of constants to variables )
The head appears) is also present in the related relation case.
Note that the examples for input relations are provided, as is the definition of the term model is given.
The main goal is to limit the number of instances of output relations. This basically restricts the instances of the output.
Take a look at the rule
Components(Part, Subpart) :- Assembly(Part, Part2, Qty),
Components(Part2, Subpart).
Imagine that we replace Part with the constant wheel Part2 by tire Qty by 1 and
Subparts by rim:
Components(wheel, rim) :- Assembly(wheel, tire, 1),
Components(tire, rim).
Consider A as an example in Assembly and C is an instance of Components. If A is a tuple,
and C is the Tuple Then C must contain the tuple rim> for an instance A or C form an example. Of course, both instances A and C
Must meet the inclusion requirements as illustrated above for each assignment of constants
The rules’ variables the following way: If the tuples of the body of rule are B and A, then the head tuple must be in A.
to be C.
Safe Datalog Programs
Take a look at the following program:
Complex Parts(Part) Complex Parts(Part) Assembly(Part, Subpart Qty) Qty > 2.
As per this rule, a complex part is defined as a part with greater than 2 copies
Any one subpart. Each part that is that is mentioned in the Assembly relation, we are able to quickly determine if it’s an assembly or a
Complex component. Contrary to this, think about this program
This variation aims to connect the price to each intricate element. But the variable Price
The rule does not mention it inside the rules body. This implies that an infinity of tuples are required.
Included in the models that is part of the program! To understand this imagine that we replace Part with the variables Part by
the constant trike SubPart by wheel and Qty divided by the constant trike, SubPart by wheel, and Qty by. This is a variation of the rule that includes
the only remaining variable is price:
Price Parts(trike,Price) Price Parts (trike, Price) Assembly(trike wheel, trike, 3) 3 > 2.

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Any change in a constant’s Price will result in an tuple that can be used in the output relationship.
Price Parts. In this case, for example substituting Price with 100 will give us the Tuple Price Parts(trike,100). If you are able to calculate the
the simplest model of an application is not finite, even for one of its input relationships, then we can say that the
The program is not safe.
Database systems prohibit dangerous programs because they require that every variable within the head of the program be accounted for.
rules must be included within the rule must also be reflected in the. The rules are referred to as limited in their range, and each
Range-restricted Datalog program is an infinite minimum model when the instances of the input relation are
finite.
Negative and Recursive Queries
The two rules could be viewed as a way of dividing into parts (those which are listed in the
The first column in the Assembly table) divided into two classes: the Big and Small classes. The first rule categorizes the term “big” to
It is the group of components that comprise at minimum three copies of the subpart and are not classified as small.
parts. The second rule is to define Small as the group of parts that aren’t considered to be big.
In the particular instance of Assembly depicted in Figure 10.3 The trike is the only component.
that is composed of at minimum three copies of the subpart. If the tuple could be described as the category of Small or Big? If we
Apply the first rule first and the second rule. This Tuple will be in the Big. In order to follow the first rule, we
Take a look at the tuples when you are in Assembly Select those that have Qty > 2. (which is basically ) Remove those
that are present in the current version of Small (both Small and Big were initially empty) Add the
Tuples left to the Big. So applying the first rule will add to Big. To Big.
In the same way, we can also see that, if we apply the second rule used prior to the first one, is an addition to Small
instead of Big
This program contains two fixpoints, neither one of which is less than the other, as is shown in
Figure 10.4. The first fixpoint contains an enormous tuple, which is not present at the fixpoint that is second Therefore,
It’s not bigger in comparison to the first fixpoint. The second fixpoint contains an a Small tuple which doesn’t
The first fixpoint is the one that appears that is why it’s not less than the first fixpoint. It is therefore not less than the first. The the order is the order in which 
We apply the rules to determine which fixpoints are computed, and the result is disappointing.
We hope that users are able to comprehend their questions without having to think about what the
Evaluation results. Colombia Email Leads.
What causes the issue is the usage of the word not. If we apply the first rule, certain inferences are
not allowed due to Tuples within Small. Parts that meet the other requirements of
The rule’s body can be used to add to Big. We take the parts of Small from
This set of candidates. Therefore, certain inferences can be made if Small has no value (as it is prior to the
Second rule applies) are prohibited second rule is applied. Small is a tuple (generated through the
Second rule preceding the second rule before the). This is the issue in the event that it is not used to add Tuples to an
Relationships can block the possibility of inference from other relationships. This situation cannot ever occur.
The addition of more tuples an existing relation will never impede an inference from other tuples
Negation and Range-Restriction

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If the rules allow be incorporated into the body, then the scope-restriction definition must be
It is extended to ensure that range-restricted programs are secure. If a relationship is found in
The body or rule that is preceded by not, we consider this negated event. Relationships that occur in
Body that is not negated are referred to as positive occurrences. A program is restricted in its range in the event that each
Variable in the rule’s head occurs in a positive to the body.
10.4 Modifying Complex Data Semantics
Data modeling, using an specific type of data model and as an exclusive method of storing data collection.
The design of the system is usually associated with Charles Bachman (1969) who presented the Data
The Structure Diagram to be one of the earliest, extensively used data models for designing databases in networks.
A variety of alternative data models were suggested shortly after The most famous of them is
The relational model was swiftly criticised for being flat which means that every information can be
The representation is an array of tables that have the atomic values of each cell. The definition of a well-formed relational
models demand that you have complex attributes types (hierarchic, multi-valued, composite, and models that are derived)
Be converted into atomic attributes and relations normalized. Inter-entity (inter-relation)
relations are difficult to visualize and the resultant set of relationships, making it difficult to manage the
Completeness and accuracy of the model is difficult. The relational model easily maps to the
physical properties that are characteristic of digital storage mediums and , as such, is an excellent tool for designing an
Physical database.
The model based on relationships between entities had two major goals one was to visualise
inter-entity relationships , and secondly to break down relationships between entities and secondly to separate the DB designing process in two distinct phases:
1. Record, within the ER model, is the entity as well as inter-entity relations are required “by the
enterprise”, i.e. owned by the user or owner of the application or system. This is the phase that must be completed by the owner/user of the information system or application
The model and the resulting model must and the resulting model should DBMS tool that will be used
Realizing the DB.
2. Convert the ER model into the model of data supported by the DBMS to be used
implementation.
This design is two-phase and supports the independence of data, i.e. it is possible to DB structure modifications
at the physical level , without having to change the user or enterprise perspective of DB the content.
10.5 Specialization
The term “specialization” is a limitation on the scope of a procedure that is, a process p1 can be described as an example of a
Specialization of a procedure the process p0 when every instance of p1 is an example of the p0 however, it is not always.
and vice and vice versa. The definition is reformulated to include the frame of reference. There are two
instances to be considered:
1. The two processes can be described in the same reference frame. In this case , extensions are used.
All of the of the processes of the processes are described in the same terms and are able to be directly compared. So p1 is
A specialization of p0 only if and only it is the case that an extension to p1 can be described in the frame
Of reference refers to a portion of extension of p0 that is similarly described.
2. The process is described in different frame of reference however there is an underlying “common”
Frame of Reference (which is a refined version of both). In this particular case the frame of reference is p1. It’s a particularization
of p0 only of p1 if the refinement is a particularization to the refinement of p0 in the conditions of
common frame of common frame of. Therefore, this second instance reduces to the one one by way of
refinement.

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One possible method of expressing this concept of specialization is to think in the context of the concept of a set
of transformations to any specific process representationthat can be applied to a particular process
description, generate the description of a specificization of the procedure. The two-part definition of
Specialization suggests that two types of transformations will be required:
A specialization transformation is an action that, when applied to a procedure that is described with
A given representation, and a reference frame is able to produce a new description of the process under
the frame of reference that correspond to an additional version of the original
process. The specialization of transformations can alter the duration of a process , while keeping the
frames of reference.
A refining transformation is an operation that alters the frame of reference of an
process, while also preserving its extension and generating a description of the same procedure
in an entirely different framework of reference.
For every type of transformation , there’s an inverse type of transformation that is an generalizing transformation
is based on a description of the process that is based on a process description to generate a generalization the original procedure and thus is the
the reverse of a specializing transformation. In the same way, an abstracting transform is the reverse of a specializing transformation.
of refining the process of refining, resulting in a fresh description of the refining process within the framework
of reference in that frame, which is of reference for which the original frame is.
In the event that refining or abstracting transformations do not limit the duration of an operation, it follows
From what we define as process specificization as a specialization transformation that is composed of
refining or abstracting transformations in any order results in an additional specialization. Similar to
statement can be used to describe general transformations.
The set of refinement/abstracting or refining transformations is considered to be complete if, for any procedure p it is was described Colombia Database 
within a frame of reference the description of the procedure in the other reference frame could
It is possible to obtain the set p a finite number transformations taken out of the collection.
A set of specialization transformations can be considered locally complete when they are in every frame
and any other process described in that reference frame or any particularization of the process that is described
Within that framework of reference can be achieved by applying to p a finite amount of transformations
taken from drawn from. This is the first portion of the definition of process specificization.
given above.
There is also a concept of completeness that is a reference to the second portion of this definition. A set
of specializing transformations as well as refining or abstracting transformations is believed to be global
full if for any particular process p, there is a particularization of p, for which the common frame of reference is used
existence can be obtained by applying p to the number of transformations taken out of the collection.
The proposition is that A should be an entire set of refining/abstracting transforms, and S be a local
A complete set of specialization transformations. Then A [[union]] is global.

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The proof: Take a look at the process p0 as well as the specialization p1 which is the common frame of reference is used.
exists. Since A is complete one could apply a finite number of transformations from A to
It is then possible to refine it within its common reference frame. With local completeness, one can create its refinement.
Apply specialized transformations to create the refined version of p1 (since the latter is an specificization of
the refinement of p0 using the assumption). In the end, through the totality of A, one is able to change the
The refinement of p1 in the p1.
We suggest that one effective method of expressing this concept of specialization is by referring to it in the context of the concept of a set
of transformations to any specific of process representations can be applied to a specific process
description, create an explanation of a particularization of the process, and then produce a description of a specialization of that. The two-part definition of
Specialization suggests that two types of transformations are required:
A specialization transformation is an action that, when applied to a procedure described in
A given representation, and a particular frame of reference result in a brand new process description in
the frame of reference that correspond to the specialization of the original
process. The specialization of transformations can alter the duration of a procedure while maintaining the
frames of reference.
A refining transformation is a process that alters the frame of reference of an
process, while also preserving its potential for extension, and generating an explanation of the exact process
with an entirely different framework of reference.
For every kind of transformation, there is an inverse type that is related to it: generalizing transformation
uses a description of a process to create a generalization of the original procedure and, as such, is the
the reverse of a specializing transformation. Similar to an abstracting transformation, it is the reverse of a specializing transformation.
of refining of refining, resulting in a fresh description of the refining process within the context of a frame
of reference, for that frame, which is an improvement.
In the event that refining or abstracting transformations allow for the extension of the process, it is logical to follow
From the definition we have of process specificization as a specialization transformation that is composed of
refining/abstracting transforms within any sequence results in the possibility of a specificization. The similar
statement is applicable to generalizing transformations.
A set of refining or abstracting transformations is considered complete if there is a the process defined
within the frame of reference the description of that process in another frame is possible.
It is possible to obtain the set p a finite number transformations that are drawn out of the collection.
A set of transformations that specialize is considered to be locally complete in the reference frame
and any other process described in that reference frame and any other specificization of the process that is described
Within that framework of reference can be obtained by applying the p-value a finite number of transformations
that are drawn from drawn from. This is the first portion of the definition of process specialization.
given above.

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There is also a concept of completeness that is a reference to the second portion in the definition. A set
of specialized in transformations and refining/abstracting them is said to be global
Complete if, for any process p, there is a particularization of p, for which is a common frame of reference is used
existence can be determined through applying to p an infinite number of transformations by the sets.
Propogation: Let A comprise an entire set of refining/abstracting transforms, and S be a local
Complete set of specialized transformations. Then A [[union]] is global.
A proof: Think of an p0 process and the specialization p1 which is the common frame of reference is used.
exists. Because A is complete, it is possible to apply a finite number of transformations from A to
It is then possible to refine it within it’s common framework of reference. Through local completeness, one could create its refinement.
Utilize specializing transformations for the refinement of p1 (since the latter is an particularization of
the improvement of p0 through the assumption). In the end, through the totality of A, one is able to change the
The refinement of p1 in refinement of p1 into.
Generalization buy Colombia email database.
The generalization hierarchy can be described as an organized collection of entities that have the same characteristics. It
is a highly effective and widely utilized method of identifying common traits among entities
while keeping their distinctions. The relationship that exists between an individual and one or more
refined versions. The thing being refined is known as the supertype, and each refined version is
named the subtype.
Generalization hierarchies are recommended when (1) the majority in a group appear
similar type, (2) attributes are the same for different entities the same type, or (3) models are constantly updated.
evolving. Generalization hierarchies enhance the reliability of the model by permitting changes to
Only be distributed to individuals who are relevant to the change and make the model simpler by cutting down on the
Number of entities within the model.
Making the Generalization Hierarchy
To create the generalization structure, every of the common traits are assigned the Supertype.
The supertype also has an attribute known as an discriminator, and whose values define the
categories of subtypes. Unique attributes to a category belong to the relevant
subtype. Each subtype is also inherited from the primary key from the supertype. Subtypes with only one key.
The primary key must be removed. Subtypes can be linked to supertypes by a one-to-one
relationship.

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Different types of Hierarchies
A generalization hierarchy could be disjoint or overlapping. In an overlapped hierarchy,
An entity instance may be an element of many subtypes. For instance, it could represent students at the university
You have found the top-level entity PERSON with three subtypes: FACULTY STAFF,
and as a STUDENT. It is possible for a person to belong to multiple subtypes or for example, a employee
member who is an active student.
The fundamental rule of hierarchy of generalization is that every instances of the entity supertype should
are present in the subtype in at minimum. similarly instances of the subtype should be as a supertype.
Subtypes may be element of only one Generalization Hierarchy. In other words, a type cannot be associated with another subtype.
to multiple supertypes. Generalization hierarchies can be nested through having
The subtype of one hierarchy could may be the supertype of another.
Subtypes can include the primary entity of an existing relationship, but not the child. If it was allowed it would be the
Subtypes could have two primary keys.
10.7 Summary
The goal for data modeling is create an appropriate data structure for the database to be as perfect as possible.
it is possible to do so with a relevant world, typically associated with an organization as possible with a relevant world, often associated with
information is needed.
In general, there is a connection between a data model and a component of the existing
The world is not perfect, but it’s quite possible to imagine that a model of data may have a connection with an imagined world.
abstract world.
10.8 Keywords
Datalog: Program for datalogging is either input or output relations.
Modeling of data: Data modelling employing a particular type of data model, and as an exclusive activity in
information system design.
Specialization: an extension restriction of a procedure.

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Safe Datalog Programs
Take a look at the following program:
Complex Parts(Part) Complex Parts (Part) Assembly(Part and Subparts, Quality) Qty > 2.
As per this rule, a “complex part” is defined as a part with greater than 2 copies
Any one subpart. For each component that is mentioned in the Assembly relation, we are able to quickly determine if it’s an assembly or a
complicated element. Contrary to this, think about these programs:
Price Parts(Part,Price) Parts of Price: Assembly(Part Subpart Qty) Qty > 2.
This variant aims to link an amount to each element. But Price is the variable
It is not included within the text of the rule. This implies that an infinity of tuples have to be
that is included in every model in this software! To understand this imagine that we replace part with Part by
the trike that is constant, SubPart by wheel, and Qty divided by the constant trike, SubPart by wheel, and Qty by. This is a variation of the rule that includes
the only remaining variable is price:
Price Parts(trike,Price) Price Parts (trike, Price) Assembly(trike wheel, trike) 3 > 2.
Then, any assignment of a constant Price will result in the possibility of including a tuple in the output relationship.
Price Parts. In this case, for example substituting Price with 100 will give us the price tuple Parts(trike,100). If you are able to calculate the
The simplest model for the program isn’t infinite, not even for one of its input relationships, we can say that the
This program is dangerous.
Database systems block unsafe programs , requiring each variable that is in the head of an
rules must be included within the rule must also be reflected in the. These programs are believed to be restricted in their range, and each
Range-restricted Datalog program is the finite minimum model if the input relations are
finite.
The two rules could be viewed as an attempt to separate the parts (those which are included in the
First column on the Assembly table) split into two classes, the Big and Small classes. The first rule categorizes the term “big” to
It is the group of components that have at minimum three copies of the subpart and are not considered to be small.
parts. The second rule is to define Small as the group of parts that aren’t classified as large parts.
When we consider the case of Assembly depicted in Figure 10.3 Trike is the sole component.
that makes at three copies of a subpart. If the tuple Be in Big or Small? If we
Apply the first rule, and the second rule to this tuple, it is Big. In order to follow the first rule, we
Take a look at the tuples when you are in Assembly Choose those that have Qty > 2. (which is not a problem). ) Remove those
that are present in the current version of Small (both Small and Big were initially empty) and then add the
Tuples left to the Big. Thus the application of the first rule will add to Big. Moving forward
In the same way, we can also see that, if we apply the second rule used before the first is included in Small
rather than Big! Colombia email list purchase online.
The program is divided into two fixpoints, neither one of which is less than the other, as is shown in
Figure 10.4. The first fixpoint contains the Big tuple which is not present at the fixpoint that is second Therefore,
It’s not bigger that the fixpoint. The second fixpoint contains an a Small tuple which is not
The first fixpoint is the one that appears that is why it’s not bigger than the first fixpoint. Therefore, it is not smaller than the first. The the order is the order in which
We apply the rules to determine the fixpoint that is computed and this is disappointing.

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We would like users to comprehend their questions without having to think about what they are asking.
Evaluation results
The cause of the issue is in the use of the word not. If we apply the first rule, there are some inferences that are
not allowed due to Tuples Small. Parts that meet the other requirements of
The rule’s body could be added to Big. We take the parts of Small from
This set of possibilities. This means that some inferences are possible Small does not exist (as it is before
Second rule applies) are denied second rule is applied. Small is a tuple (generated through the
Second rule prior to the second rule (before the). This is the problem when it comes to using to add the tuples is an
The relation may not allow the possibility of inference from other relations. This situation will never occur;
The addition of tuples to an existing relation will never hinder an inference from other tuples.