Its central tenet is that the object-oriented and deductive paradigms for modeling, organizing, and processing data complement each other, rather than competing, and that problems involving massive volumes of complex data can best be solved by integrating the best of … Such a clause can be trans-formed into the following equivalent logical formula: where ⇒ is the implies symbol. The following data expresses the genders of all of the people in our database. Relationships include things like the parenthood, ancestry, office assignments, office locations, and so forth. As an example, consider the sentences shown below. For example, the person relation is true of a person Y if there is an X such that X is the parent of Y or if Y is the parent of some person Z. We simply invent a new 0-ary relation, here called illegal, and define it to be true in any extension that does not satisfy our constraints. As we will see in our examples below, there is a simple way of expressing this other meaning without writing unsafe rules. In what follows, we write negative literals using the negation sign ~. Database: It is a collection of interrelated data . These can be used as binary predicates with the same functional syntax as other predicates—for example, by writing, Recall from Section 6.6 that a formula in the relational calculus is a condition that includes predicates called, All variables in the formula are universally quantified. This approach works particularly well for consistency constraints like the one stating that a person cannot be his own parent. The model that has been used to specify active database rules is referred to as the Event-Condition-Action (ECA) model. Deductive Databases and the Database Community. Predicates for illustrating relational operations. There are two main methods of defining the truth values of predicates in actual Datalog programs. In the mid–1980s, the database community, motivated by developments in deductive databases, initiated projects to develop prototype systems and implementation algorithms. These typically include arithmetic functions (such as +, *, max, min), string functions (such as concatenation), comparison operators (such as < and >), and equality (=). In some cases, constraints involve multiple relations. C:\Program Files\MySQL\MySQL Server 5.5\my.ini . As an example, consider the program above and assume we had a database containing p(a,b), p(b,a), q(a), and q(b). 73-88, ISSN 1571-0661, May, 2012. SELECT_ONE_A_EQ_C_AND_B_LESS_5(X, Y, Z ) :– REL_ONE(C, Y, Z ), Y<5. Notice that if the Datalog model is based on the relational model and hence assumes that predicates (fact relations and query results) specify sets of tuples, duplicate tuples in the same predicate are automatically eliminated. , it also requires recursion in computing its result. A logic program is a finite set of atoms and rules as just defined. Rule-defined predicates (or views) are defined by being the head (LHS) of one or more Datalog rules; they correspond to virtual rela tions whose contents can be inferred by the inference engine. It can be shown that any formula can be converted into clausal form. In the second rule, the result is not infinite, since the values that Y can be bound to are now restricted to values that are the salary of some employee in the database— presumably, a finite set of values. Starting with the base relations, we can define various interesting view relations. The dependency graph for this program contains nodes for p, q, r, and s. Due to the first rule, there is a positive arc from p to r and a positive arc from q to r. Due to the second rule, there is a positive arc from r to s and a negative arc from s to itself. The first rule states that a person X is childless if X is a person and it is not the case that X is a parent. Arithmetic functions such as +, –, , and / can be used as arguments in predicates in Prolog. In practical logic programming languages, it is common to "build in" commonly used concepts. The problem with unstratified logic programs is that there is a potential ambiguity. The second restriction is called stratified negation. The contents of a fact-defined predicate can be computed by directly retrieving the tuples in the cor-responding database relation. In my.ini file, if we search the keyword basedir, we can get the path of the MySQL server installation.. conclude additional facts) based on rules and facts stored in the (deductive) database. Additionally, because the predicate subordinate depends onSUPERIOR, it also requires recursion in computing its result. In order to simplify our definitions and analysis, we occasionally talk about infinite sets of rules. Note that the order of arguments in such sentences is arbitrary. Other comparison operators for numbers, such as <, <=, >, and >=, can be treated as binary predicates. Active Database Management System: An active database management system (ADBMS) is an event-driven system in which schema or data changes generate events monitored by active rules. The declarative semantics is based on preferred minimal models. The earliest two groups were ECRC in Europe in 1984 directed by Nicolas; and MCC in the U.S. in 1984, by Tsur and Zaniolo. A simple atom is called a positive literal, The negation of an atom is called a negative literal. We could equally well have interpreted the arguments in other orders. Defining isparent and using its negation in the definition of childless allows us to express this universal quantification. We have included an extensive bibliography of work in deductive databases, recursive query processing, magic sets, combination of relational databases with deductive rules, and GLUE-NAIL! Formal Analysis and Design of Software Systems (FADoSS) Departamento de Ingeniería del Software e Inteligencia Artificial (DISIA) Design of Gui. The sentences below constitute a database describing six instances of the parent relation. For example, if we know p(a,b) and we know that q(b) is false, then, using this rule, we can conclude that r(a,b) must be true. Recall that literals can be positive literals or negative literals. If there is at least one cycle, we call the rule set recursive. If we take s(a,b) to be false and s(b,a) to be true, then the second rule is again satisfied. Our examples will use the base relations (fact-defined predicates) REL_ONE, REL_TWO, and REL_THREE, whose schemas are shown in Figure 26.16. For example, the rule above states that r is true of any object X and any object Y if p is true of X and Y and q is not true of Y. The second type of interpretation is called the model-theoretic interpretation. However, it is definitely not the case in Prolog, so any of the rules in Figure 26.16 that involve duplicate elimination are not correct for Prolog. department. For example the following rule defines the number of a person's grandchildren using the countofall relation in this way. UNION_ONE_TWO(X, Y, Z ) :–  REL_ONE(X, Y, Z ). Deductive Database with Datalog, SQL, RA, TRC, DRC. We can express gender with two unary relation constants male and female. A functional term is an expression consisting of an n-ary function constant and n terms. The second rule says that isparent is true of X if X is the parent of some person Y. Note that in this case the conditions are disjunctive (at least one must be true), whereas the conditions in the grandfather case are conjunctive (both must be true). When a query involves rule-defined predicates, the inference mechanism must compute the result based on the rule definitions. A deductive database is a finite collection of facts and rules. In this case, if we let X be a and Y be b and Z be anything other than c, then both subgoals true, and we can conclude t(a,b). Interpretations of Rules Naqvi , … We can define the property of being childless with the rules shown below. One definition of Datalog considers both rules to be safe, since it does not depend on a particular inference mechanism. By applying the rules of a deductive database to the facts in the database, it is possible to infer additional facts, i.e. Nonetheless, it is generally advisable to write such a rule in the safest form, with the predicates that restrict possible bindings of variables placed first. Together, these two rules enforce the mutual exclusion on male and female. minus takes a sentence as argument and is true if and only if the user specifies that sentence as an addition in a transaction. In the context of logic programs, a term is defined as an object constant, a variable, or a functional term, i.e. The dependency graph for a logic program is a directed graph with two type of arcs, positive and negative. 3. For example, the the binary addition operator + is often represented by the the ternary relation constant plus. The inference mechanism is a computational procedure and hence provides a computational interpretation of the meaning of rules. A query that includes only nonrecursive predicates is called a nonrecursive query. The interpretation shown in Figure 26.13 is a model for the two rules shown, since it can never cause the rules to be violated. The result is generation of an infinite number of Y values, even though these, after a certain point, cannot lead to a set of true RHS predicates. Although … This can be accomplished by generating a relational expression involving relational operators as SELECT, PROJECT, JOIN, UNION, and SET DIFFERENCE (with appropriate provision for dealing with safety issues) that, when executed, provides the query result. All of the examples above are safe. In this case, the rule is still theoretically safe. Similarly, we can enforce the inclusion dependency on parent and adult by writing the following rule. The facts are ground axioms that are given to be true. 378 – 387. 8. This would define X to be childless if X is a person and there is some Y such that X is ~parent(X,Y) is true. For example, we might write parent(art,bob) to express the fact that Art is the parent of Bob. operation with duplicate elimination, we must rewrite them as follows: However, the rules shown in Figure 26.16 should work for Datalog, if duplicates are automatically eliminated. r(X,Y) is true if p(X,Y) and q(Y) are true. Each function constant and relation constant has an associated arity, i.e. Whenever the inference mechanism needs to compute the fact set corresponding to a nonrecursive rule-defined predicate p, it first locates all the rules that have p as their head. We can also take them both to be true. Clausal Form and Horn Clauses For example, a query such as. This system is not targeted as a complete deductive database, so that it does not provide transactions, security, and other features present in current database systems. (with appropriate provision for dealing with safety issues) that, when executed, provides the query result. On the con-trary, Datalog returns results set-at-a-time. ~1985 Datalog and deductive databases 1995 Prolog interpreter embedded in NT PROLOG is the FORTRAN of Logic Programming • Prolog is the only widely used logic programming language. In this section, we show how some of the standard relational operations can be specified as Datalog rules. When we think about the world, we usually think in terms of objects and relationships among these objects. A person X is the grandparent of a person Z if X is the parent of a person Y and Y is the parent of Z. 4. Fact-defined predicates (orrelations) are defined by listing all the combinations of values (the tuples) that make the predicate true. Such capabilities would take the place of application programs that would be used to ascertain such information otherwise. DIFFERENCE_TWO_ONE(X, Y, Z ) :–  REL_TWO(X, Y, Z ) NOT(REL_ONE(X, Y, Z ). For our purposes, we are mainly interested in the form of the individual clauses, each of which is a disjunction of literals. Abstract. This example shows that is possible for a relation to appear in its own definition. In relational algebra, it is the query: which can be answered by searching through the fact-defined predicate. Download Datalog Educational System for free. The second sentence defines mother in terms of parent and female. The general theoretical problem of determining whether a set of rules is safe is undecidable. Whenever the inference mechanism needs to compute the fact set corresponding to a nonrecursive rule-defined predicate, operation. The dependency graph indicates all predicates, ,  we     must                 first  compute      both, . This may or may not be true, depending on the Datalog inference engine. This interpretation assigns a truth value (true or false) to every possible combination of argument values (from a finite domain) for the two predicates. 6. Evaluation of Nonrecursive Datalog Queries. The main problem with this is that many people incorrectly interpret that negation as meaning there is no Z for which q(Y,Z) is true, whereas the correct reading is that q(Y,Z) needs to be false for just one binding of Z. Hence, the. The formulas (1) and (2) are equivalent, meaning that their truth values are always the same. One situation where we get unsafe rules that can generate an infinite number of facts arises when one of the variables in the rule can range over an infinite domain of values, and that variable is not limited to ranging over a finite relation. Keywords: Relational Databases, Deductive Databases, SQL, Datalog, Expressive-ness 1 Introduction Deductive database systems extend (“relational”) database management systems (DBMS’s) by including a more powerful query language based on logic. Update rules are rules that define pos and neg in terms of pluss and minus and the current state of the database. The main function of an inference mechanism is to compute the facts that correspond to query predicates. In what follows, we use individual capital letters as variables, e.g. Unfortunately, the language of rules, as defined so far, allows for logic programs with some unpleasant properties. Figure 26.14 shows the fact-defined predicates EMPLOYEE, MALE,FEMALE, DEPARTMENT, SUPERVISE, PROJECT, and WORKS_ON, which correspond to part of the relational database shown in Figure 3.6. However, this is generally true only for rules with a simple structure. It can be used from most common Prolog interpreters over any … This inference mechanism would define a. Use of Relational Operations Persistent Object: a specialized object that has the property of continuous state, which means it is available at all times. Section 26.1.4 discusses possible applications of active databases. In the model-theoretic approach, the meaning of the rules is established by providing a model for these rules. Introduction to Deductive Databases Overview of Deductive Databases Prolog/Datalog Notation Datalog Notation Clausal Form and Horn Clauses Interpretation of Rules Datalog Programs and Their Safety ... Dbt Unit v Notes. The combined age of X and Y is S if the age of X is M and the age of Y is N and S is the result of adding M andN. The deductive axioms can be used to con-struct proofs that derive new facts from existing facts. For example, all parents are adults; in other words, if an entity appears in the first column of the parent relation, it must also appear as an entry in the adult relation. For example, consider the interpretation in Figure 26.13, and assume that the SUPERVISE predicate is defined by a set of known facts, whereas the SUPERIOR predicate is defined as an interpretation (model) for the rules. It is a statement that the conclusion of the rule is true whenever the conditions are true. There is a negative arc from one node to another if and only if the former node appears in a negative subgoal of a rule in which the latter node appears in the head. Here, r(X,Y) is the head, p(X,Y) & ~q(Y) is the body; and p(X,Y) and ~q(Y) are subgoals. To avoid programs of this sort, it is common in deductive databases to add a couple of restrictions that together eliminate these problems. , whose schemas are shown in Figure 26.16. The first dictates that the system remove a sentence of the form male(X) whenever the user adds a sentence of the form female(X). If the user adds a sentence of the form parent(X,Y), then the system also adds a sentence of the form adult(X). In Datalog, rules are expressed as a restricted form of clauses called Horn clauses, in which a clause can contain at most one positive literal. A childless person is one who has no children. p(a,b) and q(b,c). The Datalog expression (8) can be considered as an integrity constraint, where all the predicates must be true to satisfy the query. In general, the minimal model that corresponds to a given set of facts in the model-theoretic interpretation should be the same as the facts generated by the proof. We write data in mathematical notation. SUPERIOR(X, Y ) :–  SUPERVISE(X, Z ), SUPERIOR(Z, Y ). In logic programming, these problems are avoided by requiring all rules to be safe. The development of database technology has currently reached the stage of deductive database systems which use Horn clauses for defining relations. • As a Logic Programming language, it has a number of advantages – … Here, we use prefers to represent the fact that the first person likes the second person more than the third person. sets of simple facts. A program or a rule is said to be safe if it generates a finite set of facts. In many database texts, constraints are written in direct form - by writing rules that say, in effect, that if certain things are true in an extension, then other things must also be true. In addition, some notes on performance are taken. But what can we say about s? connectives only. REL_ONE(U, V, W ), REL_THREE(W, X, Y, Z ). Since the latter two depend only on the fact-defined predicates EMPLOYEE, SALARY, and SUPERVISE, they can be computed directly from the stored database relations. Here, an infinite number of Y values can again be generated, since the variable Y appears only in the head of the rule and hence is not limited to a finite set of values. 282, pp. In general, the rule body defines a number of premises such that if they are all true, we can deduce that the conclusion in the rule head is also true. Another use of this update mechanism is to maintain materialized views. Unfortunately, if a user forgets to include an addition or deletion required by the constraints, this can lead to errors. Consider the example shown in Figure 26.11, which is based on the relational data-base in Figure 3.6, but in a much simplified form. These can be stored in the form of As an example of these concepts, consider a small interpersonal database. Uploaded by. This remains a model for the rules shown, but it is not a minimal model, since changing the truth value ofSUPERIOR(james,bob) from true to false still provides us with a model for the rules. The restrictions are easy to satisfy in most applications; and, by obeying these restrictions, we ensure that our logic programs produce finite, unambiguous answers for all questions. The logic program just shown is not stratified with respect to negation because there is a cycle involving a negative arc. The process of proving whether a certain fact (theorem) holds is known as, The second type of interpretation is called the. Such a clause can be trans-formed into the following equivalent logical formula: (implies) symbol. After that, we introduce logic programs, i.e. It helps to combine the RDBMS with logic programming. Introduction A deductive database is a finite collection of facts and rules. However, the programmer cannot affect the control part of a deductive database system. (BS) Developed by Therithal info, Chennai. In this case, we can conclude that every corresponding instance of the head is true. For example, consider the interpretation shown in Figure 26.13 for the predicates SUPERVISE and SUPERIOR. Hence, it is not necessary to include the universal quantifiers (for all) SELECT_ONE_A_EQ_C_OR_B_LESS_5(X, Y, Z ) :– REL_ONE(C, Y, Z ). Then we could write the update rules to maintain this materialized view. 7. This concludes our introduction to deductive databases. Whenever a predicate A is specified in the body (RHS) of a rule, and the head (LHS) of that rule is the predicate B, we say that B depends on A, and we draw a directed edge from A to B. positive literals. (A materialized view is a defined relation that is stored explicitly in the database, usually to save recomputation.). A Deductive Database is a type of database that can make conclusions or we can say deductions using a sets of well defined rules and fact that are stored in the database. A deductive database uses two main types of specifications: facts and rules. A variable X is limited in a rule if (1) it appears in a regular (not built-in) predicate in the body of the rule; (2) it appears in a predicate of the form X=c or c=Xor (c1<<=X and X<=c2) in the rule body, where c, c1, and c2 are constant values; or (3) it appears in a predicate of the form X=Y orY=X in the rule body, where Y is a limited vari-able. A negation in a logic program is said to be stratified with respect to negation if and only if there is no negative arc in any cycle in the dependency graph. Rules are called deductive axioms, since they can be used to deduce new facts. Exercise: Click here to test your understanding of the concept of stratified negation. The upshot is that there is ambiguity about s. By concentrating exclusively on programs that are stratified with respect to negation, we avoid such ambiguities. In this section, first we discuss the two theoretical interpretations. 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