J.-M. Nicolas. Logic for improving integrity checking in relational databases. Acta Informatica, 18(3):227-253, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....predicates should appear. Again, in a deductive database context we could generate the rule #Q j # # y # Q j # y #fR 1 # y j #; R s # y j #g, with only intentional versions of the extensional predicates or built in predicates in the residues only. Example 8. motivated by [7]) In a company database the table Supply#x;y;z# stands for Company x supplies to department y the item z . The IC 8#x;y;z##Supply#x;y; I 1 # # Supply#x;y; I 2 ## says that If a company supplies to a department item I 1 , then necessarily it also supplies item I 2 . Its version in the ....

....We can see that the operator can be used to be sure that some of the answers obtained by direct querying of the inconsistent database are correct, all we need is to see if they appear in the answer set to the transformed query obtained by application of the T operator. Example 10. motivated by [7]) Consider a database with the following IC, telling that C is the only supplier of items of class T 4 : 8#x;y;z##Supply#x;y;z#Class#z;T 4 # # x =C#, which transformed into the standard format is 8#x;y;z;w##:Supply#x;y;z# :Class#z;w# w 6= T 4 x =C#: The following rule can be generated: ....

J.-M. Nicolas. Logic for Improving Integrity Checking in Relational Data Bases. Acta Informatica, 18:227--253, 1982.

....that mentions only built in predicates. 2 Notice that in these ICs, constants, if needed, can be pushed into . Notice, as well, that equality is allowed in . Because of implementational issues we shall negate the ICs in standard format, representing ICs as denials, that is range restricted [18] goals of the form ( l 1 Delta Delta Delta l n ; 2) where each l i is a literal and variables are assumed to be universally quantified over the whole formula. We must emphasize the fact that this is just notation and from now on we shall speak of ICs assuming they are in denial form in the ....

....constraints, IC, is fact oriented if there is a tuple a and a literal name L, such that IC ffl L(a) 2 The following definition describes the class of ICs for which QUECA behaves properly. Definition 8 (Binary Integrity Constraint BIC) A binary integrity constraint (BIC) is a range restricted [18] denial of the form (2) that is, 8 ( l 1 (x 1 ) l 2 (x 2 ) x) where 8 represents the universal closure of the formula, l 1 and l 2 are database literals and is a formula that only contains built in predicates. 2 Usually ICs are not fact oriented. BICs account for an important class of ....

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J.-M. Nicolas. Logic for Improving Integrity Checking in Relational Data Bas es. Acta Informatica, 18(3):227-- 253 (1982).

....I = fp(a; b) q(a)g and OE = 8x8y(p(x; y) q(x) OE is false because p(a; a) q(a) is false. We get No as the answer of the query because there is a refutation of false p(x; y) and p(x; y) q(x) For PCL, we also consider range restricted PCNFs. The following definition can be found in [N82]: a PCNF OE in S is range restricted iff If x 2 uVar(OE) and x is in a positive literal of a clause C (in head(C) in M (OE) then x must also appear in a negative literal of C (in body(C) If x 2 eVar(OE) and x is in a negative literal of a clause C (in body(C) in M (OE) then there is ....

J.-M. Nicolas, Logic for Improving Integrity Checking in Relational Data Bases, Informatica, 1982, Springer-Verlag.

....rules or even constraints change. Such a change is called an update to the database. We restrict ourselves to updates consisting of ground atoms, representing the insertion of a new fact. A database is called consistent if it obeys all its specified integrity constraints. Following J.M. Nicolas [2] we suppose that the deductive database is consistent before the update. Throughout this paper we will use the following deductive database for illustration purposes. Example 1 Let D be the deductive database consisting of the following facts, rules and inconsistency indicator. F 1 : father(1; ....

J.M. Nicolas, Logic for Improving Integrity Checking in Relational Databases, Acta Informatica, Vol 18, no 3 (1982) 227-253.

....then the program actions on the database are rolled This work is partially supported by the French Projects PRC BD3 and PRC IA. 1 back. The weakness of this approach is twofold: checking integrity constraints is expensive although ecient methods have been proposed for static constraints [Ni] and no support is provided to the user or application programmer. Commercial database management systems do not provide constraint checking mechanisms except for very restricted classes of constraints like keys or referential integrity. Thus, integrity enforcement management remains the task of ....

Nicolas, J.-M.: Logic for improving integrity checking in relational databases. Acta Inform. 18, 227-253 (1982).

....example in a later chapter. 3 deductive databases, only ground atoms without function symbols are used. Second, in order to guarantee domain independence, the permitted formulas are required to be range restricted. We use the common definition of range restrictedness as introduced in [11]. Subsequently, variables are denoted by x; y; z and a ground atom is called a fact. Rules are restricted to definite Horn clauses. Then, a possible world is a triple W : W facts ; W rules ; W constr ) where W facts is a set of facts, W rules is a set of rules defining the derived predicates, ....

J.-M. Nicolas. Logic for improving integrity checking in relational data bases. Acta Informatica, 18, 1982. 227-253.

....should be specialized at the time of checking using instances of application specific assertions in a RBAC 3 theory. As we will see, these sets of assertions are represented using base tables in the SQL representation of the security theory, and enable us to exploit Nicolas Simplification Method [13] when checking constraints on RBAC theories. To represent constraints on RBAC security theories we choose to make use of triggers; triggers are proposed for inclusion in the SQL3 standard and are already supported in commercial RDBMSs. Of course, ASSERTION statements may be used to represent ....

Nicolas, J., Logic for Improving Integrity Checking in Relational Databases, Acta Informatica, 18, 1982.

....to semantic integrity constraints in databases, which are far beyond the scope of this paper. Nevertheless, we will point some interesting references related to the issues we dealt with in this paper. For the decomposition and simplification of integrity constraints we among others refer to [7, 53]. Satisfiability and redundancy of integrity constraints is addressed in [35, 69] An analysis of aggregate constraints is presented in [61] The textbooks [3, 52] among others, include a general discussion on integrity enforcement by triggers. A general overview of semantic integrity constraints ....

J.-M. Nicolas. Logic for Improving Integrity Checking in Relational Data Bases. Acta Informatica, 18(3):227--253, 1982.

....we could then modify the resulting transaction by applying simplification algorithms to wpc(T ; ff) thus recapturing many of the benefits of approaches based on validity checking. This is the fundamental idea underlying many algorithms for the automatic maintenance of integrity constraints [29, 21, 22, 31, 28]. Given the attractiveness of this approach to integrity maintenance, it is important to understand the tradeoffs involved in designing transaction and specification languages with respect to our ability to express weakest preconditions. In this paper, we will concentrate on the basic principles ....

....which is equivalent to the original one, and then 29 try to test its safety. As mentioned in the introduction, we are interested in transforming a verifiable transaction T into a safe transaction if wpc(T ; ff) then T else abort which will maintain ff as an invariant. As pointed out in [31, 21, 22, 28, 29], assuming that ff is always true, it may be possible to find a Delta, which is much simpler than wpc(T ; ff) such that ff ( Delta wpc(T ; ff) Using this we can transform T to if Delta then T else abort which is more efficient. We are interested in studying classes of transactions for ....

J.-M. Nicolas. Logic for improving integrity checking in relational data bases. Acta Informatica, 18:227--253, 1982.

....KL One like knowledge representation languages [BBMR89] it is our final goal to integrate these aspects in the same framework as presented here. 2. Relational Simplification Techniques Simplification techniques for integrity constraints within relational databases have first been proposed by [NICO82] The method was then extended to deductive databases [DECK86,BDM88] All of these approaches base on some form of the range restricted property [NICO82] which ensures the truth of a formula to be independent of relations not occuring in the formula. The purpose of this section is to recall the ....

.... Simplification Techniques Simplification techniques for integrity constraints within relational databases have first been proposed by [NICO82] The method was then extended to deductive databases [DECK86,BDM88] All of these approaches base on some form of the range restricted property [NICO82] which ensures the truth of a formula to be independent of relations not occuring in the formula. The purpose of this section is to recall the main properties of the simplification method. The theoretical background is presented in the above papers and in [JK90] where simplification is extended ....

Nicolas,J.-M. (1982). Logic for improving integrity checking in relational databases. Acta Informatica 18(3), Dec. 1982.

....based on a first order theory of object bases. This layer corresponds to a modified view of databases as systems for managing a model of knowledge about the world in an accessible and accurate manner for users. Some basic optimization techniques for the logical layer are simplification methods [NICO82,BCL89], recursion optimization [BR86] and semantic query optimization [JARK84,CGM90] They have in common that optimized formulas are obtained by partially evaluating either integrity constraints or update specifications with queries. The bottom layer contains the implementations of the logical ....

....when following references. This section presents object bases to be special cases of deductive databases (EDB,IDB,IC) EDB is the extensional database of base relations, IDB is a set of deductive rules, and IC is a set of integrity constraints. The formulas in IDB [ IC have to be range restricted [NICO82] which is a widely accepted sufficient condition for domain independence (see [BRY88,ML90] for more details) To ensure unique perfect models, we also assume that the set IDB is stratified [CGT90] The next subsection defines the extensional database for deductive object bases. Then, the ....

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Nicolas,J.-M. (1982). Logic for improving integrity checking in relational databases. Acta Informatika 18.

....problem was proved in [FS] Other lower bounds [M2] R94] have been proved using these methods. Other work on dynamic complexity for databases includes the theory of maintaining materialized views upon updates ( J92] GMS93] Io85] and in integrity constraint simplification ( LST87] [N82]) The design of dynamic algorithms is an active field. See, for example, E 92] E2 92] R94] CT91] F85] F91] among many others. There is also a large amount of work in the programming language community on incremental computation, see for example [RR93, LT94] 2 This paper is organized ....

J-M. Nicolas, "Logic for Improving Integrity Checking in Relational Databases," Acta Informatica, (18:3) (1982), 227-253.

....I = fp(a# b)#q(a)g and OE = 8x8y(p(x# y) q(x) OE is false because p(a# a) q(a) is false. On the other hand, wegetNo as the answer of the query q(x)# not(p(x# y) because q(a)#not(p(a# b) is false. For PCL, we also consider range restricted PCNFs. The following definition can be found in [N82] a PCNF OE in S is range restricted iff If x 2 uVar(OE) and x is in a positive literal of a clause C (in head(C) in M(OE) then x must also appear in a negative literal of C (in body(C) If x 2 eVar(OE) and x is in a negative literal of a clause C (in body(C) in M(OE) then there is a ....

J. M. Nicolas, Logic for Improving Integrity Checking in Relational Data Bases, Informatica, 1982, Springer-Verlag.

....and = 8x8y(p(x; y) q(x) is false because p(a; a) q(a) is false. However, we get No as the answer of the query q(x) not(p(x; y) because there is a refutation of false p(x; y) and p(x; y) q(x) For PCL, we also consider range restricted PCNFs. The following de nition can be found in [N82]: a PCNF in S is range restricted i If x 2 uVar( and x is in a positive literal of a clause C (in head(C) in M( then x must also appear in a negative literal of C (in body(C) If x 2 eVar( and x is in a negative literal of a clause C (in body(C) in M( then there is a clause D ....

J.-M. Nicolas, Logic for Improving Integrity Checking in Relational Data Bases, Informatica, 1982, Springer-Verlag.

....to specify integrity constraints, and provide techniques that decide which constraints (out of a set of constraints) have to be checked for a given update. Moreover, the proposed algorithms simplify the constraints to be checked, if possible. This approach was originally proposed by Nicolas in [10], and later extended and modified by many researchers (most notably by [5] Recently, rule based programming paradigms gained some popularity for databases. These efforts found their expression in two directions: in deductive databases which augment the query processing capabilities of database ....

....in the future. Finally, constraint (7) evaluates to T, which means that this constraint need not be checked for the particular update. In summary, for the particular update only a single constraint ( 3 ) has to be checked. So far our algorithm looks quite similar to the one proposed by Nicolas [10] for static constraints. The remainder of this section will focus on complications that arise in our enforcement algorithm due to the special nature of temporal constraints and activation patterns. Due to the lack of space we will discuss these complications informally. The first complication ....

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Nicolas J.-M.: "Logic for Improving Integrity Checking in Relational Databases", Acta Informatica 18, 1982, pp. 227-253.

....their system as the backend. Qian 88] describes techniques for distributing global constraints among sites in a way that reduces communication at run time. These techniques can be used to preprocess constraints in our architecture. Similarly, efficient constraint checking techniques discussed in [Nicolas 82, Bry 92] can be used by both local constraint managers and the global constraint manager. Distributed constraint checking can also be made more efficient by using the demarcation protocol [Barbara 92] or by generating queries that are sufficient to allow us to infer that a constraint has not been ....

Nicolas, J.M., "Logic for Improving Integrity Checking in Relational Data Bases," Acta Informatica, 18(3), pp. 227--253, 1982.

....run time. These techniques can be used at the preprocessing phase at the GCM. Similarly the optimizations that result from instantiating constraints by updates made to the database can be used by both local constraint managers and the global constraint manager. Such optimizations are discussed in [Nic82, KSS87, LST87, SV86, BMM92]. Distributed constraint checking can also be made more efficient by using the demarcation protocol [BGM92] or by generating queries that are sufficient to allow us to infer that a constraint has not been violated [BBC80, BCL89, Elk90, GU92] In Section 4.2 we discuss how these ideas are used in ....

.... phase derives local tests for every invalidating operation and stores them in the local catalog of the corresponding site (Figure 2) Local tests can be derived for a large class of constraints using conjunctive query containment techniques [GU92] Related techniques are also discussed in [Nic82, KSS87, LST87, BCL89, BGM92, BMM92] Local checks are a very useful optimization in the distributed scenario because they often avoid the remote communications associated with global validation [GW93] For instance, suppose the designer adds a new column col 1 of weight 10 tons on floor f l 1 . In order to ensure that there is a ....

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J. M. Nicolas. Logic for Improving Integrity Checking in Relational Data Bases. Acta Informatica, 18(3):227--253, 1982.

....systems. Consistency means that the database must be semantically correct. It is classically ensured by the definition of integrity constraints, which are assertions defined on the database, which must be satisfied at the end of each transaction. Much work has been devoted to this problem [Nic82,CW90,GW93,CFPT94,GW97] and many DBMS provide now this functionality [IBM89,Syb89,ES97] Good surveys describing the various approaches are given in [GA93,FMP97] In the great majority of cases, consistency management systems are designed for simple and classical flat transaction models and very few solutions have been ....

....Consistency is generally assured by integrity constraints (IC) which are logical assertions that must always hold in the database. A database state is consistent if and only if all constraints are satisfied. Much work concerning the checking of integrity constraints has already been done [Nic82,CW90,GW93,CFPT94,GW97]. Good surveys describing the various approaches are given in [GA93,FMP97] Some approaches are adapted for on line transactions, such as active rules and triggers [WC96] where the user is in charge of determining the events raising the checking of a given constraint. Other solutions use ....

J.-M. Nicolas. Logic for Improving Integrity Checking in Relational Data Bases. Acta Informatica, 18(3):227--253, 1982.

.... Datadriven approaches can be based on the learning algorithms developed in Artificial Intelligence (AI) Many of these learning algorithms discover rules represented in languages similar to First Order Predicate Logic (FOPL) and these rules can be used to represent general integrity constraints [13, 14] and query transformation rules. For example, the representation languages used in AQ15[15] and in the conceptual clustering algorithm Cluster 2[16] are fairly close to FOPL. 2.2. Learning and Discovery techniques in AI The AI learning algorithms are based on supervised concept learning and ....

....be learned for semantic query optimization. We then show the correspondence between basic transformation rules and patterns in the data distribution, which forms the basis of the datadriven rule discovery algorithm. 3.1. Representation Language We follow a logic based representation proposed in [1, 13, 14] for queries, integrity constraints and query transformation rules. For relations P, the atomic formula will be written as P(a 1 op t 1 , a n op t n ) where a 1 , a n are some attributes of P. The operation op is a comparison operator which will include = and . Well formed ....

J. M. Nicolas, Logic for Improving Integrity Checking in Relational Databases, Acta Informatica 18 pp. 227253 Springer Verlag, (1982).

....database is updated all integrity constraints have to be checked. Clearly, for large databases with many integrity constraints this is not practical. Therefore, techniques were developed to improve the checking of integrity constraints [AIM88, BDM88, BMM92, Dec86, KSS87, LST87, LT85, LT86, MK88, Nic82] All methods assume the consistency of the database before an update and knowledge about the update. For this reason they are usually called incremental consistency checks. A well known approach keeps track of updated predicates in order to check only relevant integrity constraints [BDM88] ....

....to be taken into account [AIM88, BDM88, BMM92, Dec86, LST87] A second branch of optimization techniques not only keeps track of updated predicates but also of updated data values. These data values can be used to simplify integrity constraints before they are checked [AIM88, Dec86, HI85, LST87, Nic82] Again, let us assume the integrity constraint p(X) q(X) If the fact p(1) is asserted, we can substitute X by 1 which yields the simplified integrity constraint p(1) q(1) Furthermore, we know that the precondition (i.e. p(1) is true because we have asserted this fact. Thus, the ....

J.-M. Nicolas. Logic for Improving Integrity Checking in Relational Data Bases. Acta Informatica, 18(3):227--253, 1982.

....system has kept that promise in a satisfactory way. One of the assumptions that has discouraged people from using integrity constraints is that constraints should be checked systematically at run time, after each update. Despite the several optimisation techniques that have been proposed ([Nic79, LT85, HI85, BM86, KSS87, HCN84, WSK83, BDM88, BD95, Law95]) in order to improve dynamic checking, system performances are still greatly affected. Considering the efficiency problems that most database systems already have without having to deal with integrity constraints, one understands why integrity has more or less been left aside. The situation can ....

....transformers generate formulas that are far bigger than their input formulas. So, undertaking systematic method correction might be the best way of ensuring very low system performances. 7 Related work The study of integrity constraints in database systems has been a topic of large interest [Sto75, Nic79, GM79, CB80, LT85, HI85, BM86, KSS87, HCN84, WSK83, BDM88, SS89, Law95]. Several works concern the optimisation of checking: Nic79, HI85] for relational databases, BM86] for deductive databases, BD95] for object oriented databases, and [Law95] for deductive object oriented databases. In the context of active database systems, triggers are used to express ....

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J.M. Nicolas. Logic for Improving Integrity Checking in Relational Databases. Technical report, ONERA-CERT, 1979.

....before. Datadriven approaches can be based on the learning algorithms developed in Artificial Intelligence (AI) Many of these learning algorithms discover rules represented in languages similar to first order predicate logic (FOPL) which can be used to represent general integrity constraints [14, 15] and query transformation rules. For example, the representation languages used in AQ15[16] and in the conceptual clustering algorithm Cluster 2[17] are fairly close to FOPL. The AI learning algorithms can be classified into two categories, supervised concept learning and unsupervised discovery. ....

....be learned for semantic query optimization. We then show the correspondence between basic transformation rules and patterns in the data distribution, which forms the basis of the datadriven rule discovery algorithm. 3.1. Representation Language We follow a logic based representation proposed in [1, 14, 15] for queries, integrity constraints and query transformation rules in this paper. For relations P, the atomic formula will be written as P(a 1 op t 1 , a n op t n ) where a 1 , a n are some attributes of P. The operation op is a comparison operator which will include = and . ....

J. M. Nicolas, Logic for Improving Integrity Checking in Relational Databases, Acta Informatica 18 pp. 227253 Springer Verlag, (1982).

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J.-M. Nicolas. Logic for improving integrity checking in relational databases. Acta Informatica, 18(3):227-253, 1982.

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Nicolas, J.-M. (1992) Logic for Improving Integrity Checking in Relational Databases. Acta Informatica, 18, 227--253.

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J.M. Nicolas. Logic for improving integrity checking in relational databases. Acta Informatica 18, pp 227-253, 1982.

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