A. Chandra. Theory of database queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1-9. ACM Press, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....all nite structures, as they incorporate recursion and iteration mechanisms in the form of xpoint operators. For this reason, they have been studied extensively in database theory and have become a standard for comparing and calibrating the expressive power of other database query languages (cf. [Cha88]) A subsequent turning point in the study of the connections between logic and complexity was the paper by Abiteboul and Vianu [AV91] which established that the problem of separating xpoint logic LFP from partial xpoint logic PFP on the class of all nite structures is equivalent to the ....

A. Chandra. Theory of database queries. In Proc. 7th ACM Symp. on Principles of Database Systems, pages 1-9, 1988.

....the field towards algorithmic questions. Each of these directions has remained important for database theory. I will not discuss database theory in this paper. The interested reader is referred to textbooks by Ullman [Ull89] and Maier [Mai83] and survey papers by Kanellakis [Kan90] Chandra [Cha88], and by Vardi and myself [FV86] Perhaps the actual reason for the current interest in finite model theory is that critical mass is starting to be achieved. I hope that this paper can help add to the critical mass. Definitions are given in Section 2. Some differences between the model theory of ....

A. Chandra. Theory of database queries. In Proc. 7th ACM Symp. on Principles of Database Systems, pages 1--9, 1988.

....horizontal coordinate. To choose a flight from Rome to Toronto based on the elapsed time from departure to arrival, the data display of Figure 6 (iii) conveys more information at a glance than the original graph display of the data of Figure 6 (ii) There is a rich theory of the expressive power [Cha88] of database languages, developed initially for pm 7am Rome (i) ff(t 0 Gamma t) t 0 t Y X Y X t t t t t 0 t t 0 t t t 0 TempChart TempChart TempChart TempChart TempChart FlightGraph Toronto Toronto 2pm 12pm 9am Rome Rome (ii) iii) am 7 9 am 2 12 pm ....

Ashok K. Chandra. Theory of database queries. In ACM Symposium on Principles of Database Systems, pages 1--9, 1988.

....that we always deal with a single intensional predicate in our queries. It is worth emphasizing here that semi Horn formulas are strictly more expressive than Horn clauses. For instance, semi Horn formulas express the complement of a relation which is not expressible by Horn clauses (see e.g. [2]) Also existential quantifiers in the scope of universal quantifiers are not, in general, reducible to Horn clauses, but are allowed in semi Horn formulas. Let us now introduce the definition of declarative queries and declarative query language. As we shall see in Theorem 4.3 all the queries of ....

....language defined in Definition 4.1 provided that the domain of B is linearly ordered. Proof The first part of the theorem can be proved by noticing that semi Horn formulas reduce to fixpoint formulas and using the well known fact that fixpoint queries are computable in polynomial time (see e.g. [2, 7]) If Theta(Q) is an Ackermann reducible formula, then both Q and the coherence condition are expressed in classical first order logic and therefore are computable in logarithmic space. To prove the second part of the theorem we use the following known facts: ffl if the domain of the database ....

[Article contains additional citation context not shown here]

Chandra, A. K. (1988) Theory of Database Queries, Proc. 7th ACM Symp. on Principles of Database Systems, 1-9.

....in case the information is only partly uncertain. We also discuss approximations of the semantics making it tractable in real world applications. It has been argued that the design of a knowledge representation language is a trade off between expressiveness and computational tractability [2, 5, 23]. Similarly, we think that the design of a calculus to deal with uncertainty is also a compromise between precision and computational complexity. We present here new techniques which seem to be well suited for many applications requesting the handling of uncertain information. Our framework is ....

A. K. Chandra. Theory of Database Queries. In Proc. Symp. on Principles of Database Systems, pages 1--9, 1988.

....extensively investigated (cf. 26, 11] Query languages for retrieving information from disjunctive databases are an open area of research. In the framework of relational databases, many alternative query languages have been proposed; they have been extensively studied in the literature (cf. [38, 20, 6, 7, 2] for fundamentals and overviews) and, in particular, they have been compared to each other by characterizing their expressiveness, i.e. the class of queries that they can express. These relationships are quite well understood [2, 7] The study of query languages for disjunctive databases is much ....

....have been extensively studied in the literature (cf. 38, 20, 6, 7, 2] for fundamentals and overviews) and, in particular, they have been compared to each other by characterizing their expressiveness, i.e. the class of queries that they can express. These relationships are quite well understood [2, 7]. The study of query languages for disjunctive databases is much less established. Work on querying incomplete databases is related; cf. 14, 1] for relations with null values, and [39] for the similar proviso of missing unique names axioms in logical databases. In these works, disjunctive ....

A. K. Chandra. Theory of Database Queries. In Proceedings PODS-88, 1988.

....precisely those which are recognizable in C. For example, Fagin s celebrated theorem is that class of SO 9 queries captures the class NP [30] Figure 2 describes well known relations between the expressive powers of several query languages and correspondences to complexity classes, cf. 31] [32], 2] Each edge denotes inclusion, i.e. less expressive power, which assuming that complexity classes do not collapse is always strict. As well known, DATALOG does not express all queries computable in polynomial time, and is incomparable to rst order logic. Strati ed DATALOG and in ationary ....

Ashok K. Chandra, \Theory of Database Queries", in Proceedings PODS-88, 1988.

....commands with navigation in diagrams. The main problem was to prove the equivalence of such navigations to (at least) the relational algebra, and this is what we initially did [20] Still working on expressive power, we concentrated on expressing non relational queries, such as transitive closure [24]. Extending the expressive power of query languages was very fashionable at that time, especially because of Datalog growth [57] and graphical query languages with high expressive power were mainly proposed by Alberto Mendelzon s group at the University of Toronto (they were then working on the ....

....They are people having a general knowledge about computer science but no experience on databases. For the purpose of our experiments we needed to identify prototypical classes of queries. One could argue that several query classifications have already been proposed in the literature (see, e.g. [24, 34, 10]) However, those classifications are all based on the so called expressive power of the query language. These kinds of classifications, while extremely valuable in general, were inadequate for our purposes. Indeed, they are mainly based on the idea of grouping queries depending on the constructs ....

A.K. Chandra. Theory of database queries. In Proceedings of the Seventh ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS-88), Austin, USA, pp. 1--9, ACM Press (1988).

....an explicit domain. Structures are always assumed to be nite in this paper. We denote the domain of a structure A by A, and the interpretation of the relation symbol R in A by R A . 1 The analogous result for BQL (which is weaker than FO(FOR) was stated by Chandra in the early eighties [Cha81, Cha88], but no proof has been published. 3 A k ary query Q is a computable function that maps each structure A to a subset of A k , such that if A and B are isomorphic via then (Q(A) Q(B) We also call a nullary query a Boolean query. The query language of rst order logic (the relational ....

....between in ationary xpoint logic with modular counting and partial xpoint logic with (proper) counting. For the last separation, we showed that FO(FOR) cannot check whether two sets have the same cardinality. This result is a generalization of the same result for BQL announced by Chandra [Cha81, Cha88]. The in ationary variant of FO(FOR) lies strictly between in ationary xed point logic and full FO(FOR) This separation should be contrasted with the corresponding issue in the case of while loops. Recall that with while loops, a separation of in ationary from full partial xed point logic would ....

A. Chandra. Theory of database queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1-9. ACM Press, 1988.

....s is within one course of a degree in discipline d. Note that the premise of the first rule is a hypothetical query similar to the query in Example 2.2. 2.2. Rulebase Queries A database query is often treated as a mapping that takes a relational database as input and returns a relation as output [20, 19]. The expressibility of a query language is therefore the set of mappings that the language represents. Many expressibility results based on this idea have appeared in the literature [3, 21, 22, 40, 2, 1, 39] and we have established numerous results of this kind using Hypothetical Datalog as a ....

A.K. Chandra. Theory of Database Queries. In Proceedings of the ACM Symposium on the Principles of Database Systems (PODS), pages 1--9, Austin, Texas, March 1988.

....the context of evolving information systems or not, should not only provide language facilities on a conceptual level, but should also provide enough expressive power and be suitable. Expressive power is a purely theoretical matter. An expressiveness hierarchy for query languages exists (see e.g. [8]) Suitability is a notion which is more difficult to capture formally. Suitability addresses the match between concepts offered by the language involved and concepts occurring in the application domain (Universe of Discourse) involved. A language can have sufficient expressive power for a certain ....

A.K. Chandra. Theory of Database Queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1--9, Austin, Texas, March 1988.

....of positions in a 2 person game (see figure 7) In this domain the relationship type describes how positions can be reached from one another. The unary relationship type gives all winning positions for the first player. The question now is to yield all positions from which the first player can win [17]. This is captured by the following macro: Exploiting Fact Verbalisation in Conceptual Information Modelling may lead to is a direct win Position Fig. 7: Schema of a simple game The above query is an example of a query that cannot be expressed as a so called stratified query (see figure 8, ....

....captured by the following macro: Exploiting Fact Verbalisation in Conceptual Information Modelling may lead to is a direct win Position Fig. 7: Schema of a simple game The above query is an example of a query that cannot be expressed as a so called stratified query (see figure 8, taken from [17]) Stratified queries can express all the first order queries and negation is allowed between the so called strata. It has been shown however that stratified queries do not express all fixpoint queries, in particular, they have difficulty taking fixpoints over universal quantifiers, as needed in ....

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A.K. Chandra. Theory of Database Queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pp. 1--9, Austin, Texas (1988).

....schema for a 2 person game as illustrated in figure 23. In this domain the fact type describes how positions can be reached from one another. The unary fact type gives all winning positions for the first player. The question now is to yield all positions from which the first player can win ( Cha88] This is captured by the following macro: The above query is an example of a query that cannot be expressed as a so called stratified query (see figure 24, taken from [Cha88] Stratified queries can express all the first order queries and negation is allowed between the so called strata. It ....

....winning positions for the first player. The question now is to yield all positions from which the first player can win ( Cha88] This is captured by the following macro: The above query is an example of a query that cannot be expressed as a so called stratified query (see figure 24, taken from [Cha88] Stratified queries can express all the first order queries and negation is allowed between the so called strata. It has been shown however that stratified queries do not express all fixpoint queries, in particular, they have difficulty taking fixpoints over universal quantifiers, such as is ....

[Article contains additional citation context not shown here]

A.K. Chandra. Theory of Database Queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1--9, Austin, Texas, March 1988.

....an explicit domain. Structures are always assumed to be nite in this paper. We denote the domain of a structure A by A, and the interpretation of the relation symbol R in A by R A . 1 The analogous result for BQL (which is weaker than FO(FOR) was stated by Chandra in the early eighties [Cha81, Cha88], but no proof has been published. 3 A k ary query Q is a computable function that maps each structure A to a subset of A k , such that if A and B are isomorphic via then (Q(A) Q(B) We also call a nullary query a Boolean query. The query language of rst order logic (the relational ....

A. Chandra. Theory of database queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1-9. ACM Press, 1988.

....The different forms of visualisation that a query could use are textual, form, graph diagrammatic, iconic and multi paradigm. ffl Expressive Power this defines the types of queries that can be created with the interface. Catarci et al. [8] used and extended a previous classification by Chandra [10] known as Chandra s hierarchy. This hierarchy can be seen in Figure 22 with the extended classes of Catarci et al. [8] shown as gray hatched boxes. It was noted by Catarci et al. [8] that most visual query systems are less expressive than relation algebra, and very few are placed in the upper ....

A. K. Chandra. Theory of Database Queries. In Proceedings of the ACM Symposium on Principles of Database Systems, pages 1--9, 1988.

....system to extract meaningful information from the database, is a basic aspect in query languages. Unfortunately, traditional query languages, based on relational algebra and calculus [12] have a limited expressive power, i.e. they can compute the class of firstorder queries, while, as shown in [8] other more general classes of queries exist. In particular, an important extension of the class of first order queries is obtained by adding to a relational query language some operators allowing for expressing some kind of recursion. A notable example of recursion is the transitive closure, but ....

....by adding to a relational query language some operators allowing for expressing some kind of recursion. A notable example of recursion is the transitive closure, but it has been proved that there exist several recursive queries which cannot be expressed using the transitive closure operator [8]. As a consequence, researches in the area of database querying are devoted to find query languages able to express notable classes of recursive queries. Relevant proposals in this sense are based on the logical paradigm, introducing the query languages known as Datalog and stratified Datalog ....

Chandra A.K. Theory of Database Queries. In: Proc. Symp. Principles of Database Systems, 1988.

....in terms of the SMH query system. 7.2. Expressive Power The expressive power of a query system, i.e. the ability of the system to extract information from the database, is also a basic aspect in VQSs, as stressed by Aho and Ullman in [82] Meaningful classes of queries have been investigated in [102], giving rise to the so called Chandra s hierarchy. Among the different VQSs referred to in the literature, only a few have been formally characterized in terms of the expressive power of their query languages. In this subsection we briefly discuss an enlarged Chandra s hierarchy and show the ....

A.K. Chandra (1988) Theory of Database Queries. In: Proc. of the ACM Symp. on Principles of Database Systems, pp. 1-9.

....are persons having a general knowledge about computer science but no experience on databases 3.3 Query Classes For the purpose of our experiment we need to identify prototypical classes of queries. One could argue that several query classifications have been proposed in the literature (see, e.g. (Chandra 1988; Kanellakis, 1990; Catarci, 1991) However, those classifications are all based on considering the so called expressive power of the query language, i.e. the ability of the language to extract meaningful information from the database, and or the complexity of computing the query answer. These ....

Chandra, A.K. (1988) "Theory of Database Queries", in M. Yannakakis (ed.), Proceedings of the ACM Symp. on Principles of Database Systems, pp. 1-9.

....and manipulation languages, etc. and often like to acquire a deep understanding of the system they are using. 3.2 The Query Classes For the purpose of our experiment we need to identify meaningful classes of queries. Several query classifications have been proposed in the literature (see, e.g. [35, 36, 37]) However, those classifications are all based on considering the so called expressive power of the query language, i.e. the ability of the language to extract meaningful information from the database, and or the complexity of computing the 10 query answer. While extremely valuable in general, ....

Chandra A.K. Theory of Database Queries. In: Proc. of the ACM Symp. on Principles of Database Systems, 1988, pp 1-9.

....that we always deal with a single intensional predicate in our queries. It is worth emphasizing here that semi Horn formulas are strictly more expressive than Horn clauses. For instance, semi Horn formulas express the complement of a relation which is not expressible by Horn clauses (see e.g. [3]) The semi Horn (w.r.t. Q) formula 8 x(Q( x)R( x) 8 x( Q( x) R( x) expresses the complement of a relation, R. In addition, existential quantifiers in the scope of universal quantifiers are not, in general, reducible to Horn clauses, but are allowed in semi Horn formulas. Let us now introduce ....

....language defined in Definition 10 provided that the domain of B is linearly ordered. Proof The first part of the theorem can be proved by noticing that semi Horn formulas reduce to fixpoint formulas and using the well known fact that fixpoint queries are computable in polynomial time (see e.g. [3, 10]) If Theta(Q) is an Ackermann reducible formula, then both Q and the coherence condition are expressed in classical first order logic and therefore are computable in logarithmic space. To prove the second part of the theorem we use the following known facts: ffl if the domain of the database is ....

[Article contains additional citation context not shown here]

A. K. Chandra. Theory of database queries. In Proceedings of the 7th ACM Symposium on Principles of Database Systems, pages 1--9, 1988.

....been extensively investigated (cf. 26, 11] Query languages for retrieving information from disjunctive databases are an open area of research. In the framework of relational databases, many alternative query languages have been proposed; they have been extensively studied in the literature (cf. [38, 20, 6, 7, 2] for fundamentals and overviews) and, in particular, they have been compared to each other by characterizing their expressiveness, i.e. the class of queries that they can express. These relationships are quite well understood [2, 7] The study of query languages for disjunctive databases is much ....

....have been extensively studied in the literature (cf. 38, 20, 6, 7, 2] for fundamentals and overviews) and, in particular, they have been compared to each other by characterizing their expressiveness, i.e. the class of queries that they can express. These relationships are quite well understood [2, 7]. The study of query languages for disjunctive databases is much less established. Work on querying incomplete databases is related; cf. 14, 1] for relations with null values, and [39] for the similar proviso of missing unique names axioms in logical databases. In these works, disjunctive ....

A. K. Chandra. Theory of Database Queries. In Proceedings PODS-88, 1988.

....independence and finiteness. Finally, we give a simple procedure for translating safe firstorder queries into relational algebra expressions as a basis for evaluating safe queries in all of the above query classes. 1 Introduction There is now a rich theory of queries for relational databases [3, 4, 6, 14]. This theory encompasses dependencies and database design [14] the relative expressive power of different query languages [3] the complexity of query evaluation [3] the domain independence and finiteness of queries [6] sufficient conditions for domain independence and finiteness [12, 16] and ....

....as a basis for evaluating safe queries in all of the above query classes. 1 Introduction There is now a rich theory of queries for relational databases [3, 4, 6, 14] This theory encompasses dependencies and database design [14] the relative expressive power of different query languages [3], the complexity of query evaluation [3] the domain independence and finiteness of queries [6] sufficient conditions for domain independence and finiteness [12, 16] and efficient query evaluation [14, 15] Almost all of this work, however, has been for relations over a domain of uninterpreted ....

[Article contains additional citation context not shown here]

A. K. Chandra. Theory of database queries. In Proc. Seventh ACM Symp. on Principles of Database Systems, pages 1--9, Austin, 1988.

....independence and finiteness. Finally, we give a simple procedure for translating safe first order queries into relational algebra expressions as a basis for evaluating safe queries in all of the above query classes. 1 Introduction There is now a rich theory of queries for relational databases [3, 4, 6, 14]. This theory encompasses dependencies and database design [14] the relative expressive power of different query languages [3] the complexity of query evaluation [3] the domain independence and finiteness of queries [6] sufficient conditions for domain independence and finiteness [11, 16] and ....

....as a basis for evaluating safe queries in all of the above query classes. 1 Introduction There is now a rich theory of queries for relational databases [3, 4, 6, 14] This theory encompasses dependencies and database design [14] the relative expressive power of different query languages [3], the complexity of query evaluation [3] the domain independence and finiteness of queries [6] sufficient conditions for domain independence and finiteness [11, 16] and efficient query evaluation [14, 15] Almost all of this work, however, has been for relations over a domain of uninterpreted ....

[Article contains additional citation context not shown here]

A. K. Chandra. Theory of database queries. In Proc. Seventh ACM Symp. on Principles of Database Systems, pages 1--9, Austin, 1988.

....moves beyond NF 2 models and systems, the implementation status and examples will largely be omitted. We will not discuss the relative power of the underlying data models, exhaustive sets of algebraic equivalence rules, or other theoretical language issues. Many of these issues are covered in [Pare88, VanG87, VanG86, Hull87, Hull89a, Chan88]. The purpose of this survey is to convey some idea of the general nature of database algebras in 9 the hope of gaining some insight into why certain operations exist and of identifying common themes among these algebras. It is inevitable that some algebras have been either omitted or described ....

....question of expressive equivalence for this algebra is not whether it can express exactly the queries of some formal calculus but whether it can express exactly the queries of EXCESS. Furthermore, we do not address here the issues of computable queries and complexity classes, as is discussed in [Chan88]. It is, of course, crucial that any EXCESS query be expressible in the algebra. This direction of the proof is constructive, and thus it also provides a complete semantics for the EXCESS query language. The tortuousness of the EXCESS to algebra reduction is a result of EXCESS s derivation from ....

A. Chandra, "Theory of Database Queries", Proc. ACM PODS Conf., 1988.

....no constant symbols. Theorem 7.3 is particularly interesting because it establishes a strong link between an important complexity class, polynomial space, and a well known logic, intuitionistic logic. Other database query languages have been developed that are expressively complete for PSPACE [16, 18, 2, 3], but the language of stratified embedded implications is the only one based on a model theoretic semantics, and the only one to have an Prolog style proof procedure, one based on resolution and unification in the logic programming tradition [39] Furthermore, unlike other languages, our results ....

A.K. Chandra. Theory of Database Queries. In Proceedings of the ACM Symposium on the Principles of Database Systems (PODS), pages 1--9, Austin, Texas, March 1988.

....can be viewed as computing on an ordered database obtained by replacing each equivalence class produced in the analysis phase by its corresponding integer. By applying the normal form to the while queries, we show that fixpoint = while iff ptime = pspace. We thereby answer an open question of [Cha88] Surprisingly, the result also applies to the ptime fragment of while (i.e. whilej PT IME ) we prove that ptime = pspace iff fixpoint = whilej PT IME . Note that this reduces the separation of ptime and pspace to the separation of two classes of queries within ptime. The while queries are ....

.... [Gur88, Fag90] The study of computable queries originated in the work of Chandra and Harel [CH80, Cha81, CH82] Since then, the complexity and expressiveness of query languages, and the relationship with logic, have been widely investigated, e.g. Var82, CH85, GS86, Imm86, Imm87a, Imm87b, Cha88, Gur88, KV90, Lei89a, Lei89b, AV91a] Below NP, expressiveness results usually assume an ordered input. Without order, languages typically express queries complete within a class, but are unable to express simple queries. It remains open whether there is a language expressing exactly ptime. The ....

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A. K. Chandra. Theory of database queries. In Proc. ACM Symp. on Principles of Database Systems, pages 1--9, 1988.

....with operations for data manipulation (e.g. update, delete, aggregate manipulation) Relational languages have also been extended with the ability to apply transitive closure, but we shall not consider such languages here. For a survey of the power of such extensions to the relational algebra see [26]. The requirement that relations be normalized (i.e. tuple field values be primitive) is eased in the non first normal form relational model [47, 63, 100, 114, 124] This model provides more natural modelling of one to many relationships by allowing fields of tuples to be relations. Algebras for ....

....should be considered when posing database queries. When restricted to the relational model, the EQUAL operations can simulate the relational algebra and thus would support relational systems embedded in an object oriented database. As a relational simulation, EQUAL is a complete database language [26]. With the full expression of EQUAL on an object oriented model, we can express first order queries and we chose to limit the algebra to not express recursive queries. 3.3 Query Transformation In order to manipulate queries in an optimizer it is necessary to define transformations which preserve ....

Ashok K. Chandra. Theory of database queries. In Proceedings of the Symposium on Principles of Database Systems, pages 1--9. ACM, March 1988.

....the context of evolving information systems or not, should not only provide language facilities on a conceptual level, but should also provide enough expressive power and be suitable. Expressive power is a purely theoretical matter. An expressiveness hierarchy for query languages exists (see e.g. [8]) Suitability is a notion which is more difficult to capture formally. Suitability addresses the match between concepts offered by the language involved and concepts occurring in the application domain (Universe of Discourse) involved. A language can have sufficient expressive power for a certain ....

A.K. Chandra. Theory of Database Queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1--9, Austin, Texas, March 1988.

....constructs and the efficiency of verification. Previous work in database programming language design has focused on two areas; one is extending general purpose programming languages to database applications[7] and another is the expressiveness characterization of various language constructs[4]. Mathematical logics have been used in databases as specification and verification tools. As specification languages, first order logic has been the dominant choice for the expression of static semantics, while temporal logic is most widely used for the expression of dynamic semantics[3] Program ....

Chandra, A., "Theory of Database Queries"; Proceedings of the Seventh ACM Symposium on Principles of Database Systems , 1988, 1-9.

....query. In this section, for simplicity, we have assumed that C = the more general case, where C , is investigated in Section 4. There has been much interest in generic computable queries since the seminal work of [AHO79] and [CHAN80] a summary of the research in this area was presented in [CHAN88]. In order to motivate generic queries we give four quotes, which stipulate the principles that queries ought to satisfy. The first two are from [CHAN80, p.158] and the last two are from [AHO79, p.111] 1.1) the result of a query should be independent of the representation of the data in a data ....

A.K. Chandra, Theory of database queries, Proceedings of the 7th ACM Symposium on Principles of Database Systems (Austin, Texas), 1988, pp. 1-9.

....semantics in case the information is only partly uncertain. We also discuss approximations of the semantics making it tractable in real world applications. It has been argued that the design of a knowledge representation language is a trade off between expressiveness and computational tractability [9, 17, 82]. Similarly, we think that the design of a calculus to deal with uncertainty is also a compromise between precision and computational complexity. CHAPTER 3. UNCERTAINTY 43 We present here new techniques which seem to be well suited for many applications requesting the handling of uncertain ....

A. K. Chandra. Theory of Database Queries. In Proc. Symp. on Principles of Database Systems, pages 1--9, 1988.

....following SQL query: SELECT FROM emp, dept WHERE emp:D = dept:D AND emp:S dept:MS If a tuple emp(e; d1; 50) is inserted into relation emp, the local test is evaluated by the following SQL query: SELECT FROM emp WHERE emp:D = d1 AND emp:S 50 2 5. 3 Datalog Conjunctive queries in Datalog [C88] extended with arithmetic inequalities and safe negation map to our language for integrity constraint assertions directly. An integrity constraint is expressed as a safe Datalog query that defines a 0 ary derived predicate panic. Panic becomes true when the violation condition for the constraint ....

A. K. Chandra. Theory of Database Queries. In Proceedings of ACM SIGMOD 1988, pages 1--9. ACM, 1988.

....whose abstract equivalents are of different types, for example queries defined over relations representing interval data with those defined over relations representing point data. The notion of query expressiveness has been very important in the theory of query languages for relational databases [17, 3, 2]. Data complexity of query evaluation was defined in [19, 125] to mean the computational complexity of the set of finite databases for which a given, fixed query evaluates to true. One can also study combined complexity where the query is also a part of the input. However, data complexity seems ....

....to true. One can also study combined complexity where the query is also a part of the input. However, data complexity seems to measure better the computational effort necessary for evaluating queries formulated in a given language. This notion has also been extensively used in database theory [17, 2]. 4 Abstract query languages 4.1 Relational calculus The first order language L 0 D of an abstract temporal database (assuming the model theoretic view) can be used as a query language, as suggested in [64, 115] It is commonly known as the domain relational calculus . Its semantics is the ....

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A.K Chandra. Theory of Database Queries. In ACM Symposium on Principles of Database Systems, pages 1--9, 1988.

....from sets of nodes to sets of nodes. Chapter 4 Filtering Languages and Hygraph Patterns In this chapter we develop the formal basis for assigning semantics to Hy patterns. The material presented here contributes to the theory of database languages. The following statement from Chandra [Cha88] provides an excellent description of our objectives. One goal of the theory of database queries is to provide an understanding of query language constructs so that query languages could be designed that are natural to use, expressive, and efficient in practice. The other, as always, is elegance. ....

Ashok K. Chandra. Theory of database queries. In Proceedings of the ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, pages 1--9, 1988.

....is mutually coherent. In particular, we concentrate on the class of conjunctive (select project join) queries, which abstract a set of requests commonly made by casual users, so being utilized in most cases by the majority of users [Chandra and Merlin, 1977; Jarke and Vassiliou, 1985; Chandra, 1988] . To formulate such queries, the user focuses on one or more classes of objects, selects a subset of their instances and properties, and reaches other classes through shared properties. Every query representation provided in our multiparadigmatic interface allows one to express at least the ....

Chandra, A.K.(1988). Theory of Database Queries. Proc. Symp. Principles of Database Systems.

....semantics in case the information is only partly uncertain. We also discuss approximations of the semantics making it tractable in real world applications. It has been argued that the design of a knowledge representation language is a trade off between expressiveness and computational tractability [3, 11, 63]. Similarly, we think that the design of a calculus to deal with uncertainty is also a compromise between precision and computational complexity. We present here new techniques which seem to be well suited for many applications requesting the handling of uncertain information. Our framework is the ....

A. K. Chandra. Theory of Database Queries. In Proc. Symp. on Principles of Database Systems, pages 1--9, 1988.

....describes how positions can be reached from one another. The unary fact type is a direct win gives all winning positions for the first player. The question now may lead to is a direct win Position Figure 23: Schema of a simple game is to yield all positions from which the first player can win ( Cha88] This is captured by the following macro: Winning Positions IS is direct win UNION may lead to Position ALL IN Position may lead to Winning Positions The above query is an example of a query that cannot be expressed as a so called stratified query (see figure 24, taken from [Cha88] ....

.... can win ( Cha88] This is captured by the following macro: Winning Positions IS is direct win UNION may lead to Position ALL IN Position may lead to Winning Positions The above query is an example of a query that cannot be expressed as a so called stratified query (see figure 24, taken from [Cha88] Stratified queries can express all the first order queries and negation is allowed between the so called strata. It has been shown however that stratified queries do not express all fixpoint queries, in particular, they have difficulty taking fixpoints over universal quantifiers, such as is ....

[Article contains additional citation context not shown here]

A.K. Chandra. Theory of Database Queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1--9, Austin, Texas, March 1988.

....constructs is a natural way to increase the limited expressive power of FO. Such extensions have been the subject of extensive study focusing on their expressive power, their relationship to complexity classes, in particular to PTIME and PSPACE, and their asymptotic probability properties (cf. [AV89, AV95, Cha88, CH82, Imm86, KV87, Var82]) Of particular importance among these extensions is least fixpoint logic (LFP) which is obtained from FO by adding least fixpoints of positive first order formulas. It is by now widely recognized that it is extremely useful to view fixpoint logics as effective fragments of L 1 , ....

A. Chandra. Theory of database queries. In Proc. 7th ACM Symp. on Principles of Database Systems, pages 1--9, 1988.

....logic from an assertional logic to a computational logic. Such extensions of first order logic have been the subject of extensive study focusing on their expressive power, their relationship to complexity classes, in particular to P and PSPACE, and their asymptotic probability properties (cf. [AV91a, Cha88, CH82, Imm86, KV87, Var82]) Of particular importance among these extensions are inflationary fixpoint logic, which is obtained from first order logic by adding fixpoints of inflationary first order formulas, and noninflationary fixpoint logic, which is obtained from first order logic by adding fixpoints of general ....

A. Chandra. Theory of database queries. In Proc. 7th ACM Symp. on Principles of Database Systems, pages 1--9, 1988.

.... n Owns Car 100,000 . Query Area Car Plate, String Owns Owns, 1, Employee Salary, Integ. Name,String Person Age, Integ. 1,1) Name, String Age,Integ. 100,000 Fig. 2. 1: A sample display It is worth noting that these queries, although at a low level in the query hierarchies (see [15, 11]) are generally considered as fundamental components of more complex queries. This is true both from the data model and the usermodel point of view. Indeed, in recent works on deductive and object oriented databases, conjunctive queries are considered the basic step to achieve a well founded ....

A.K. Chandra, "Theory of Database Queries," in Proc. of the ACM Symp. on Principles of Database Systems, pp. 1-9, 1988.

....by a transaction language. Database programs differ from other types of computer programs in the sense that they are dominated by data retrieval and manipulation tasks rather than by complex computations. Just like the design of query languages has been focused on what sets of data can be retrieved[5], the design of transaction languages should be focused on what updates can be performed. Another requirement of database programming is the ability to reason about the effect of program executions on the database semantics expressed as integrity constraints. To design programming languages for ....

.... basis for other aspects of database programming, such as transaction verification, optimization, and synthesis[1, 11, 13] The above concern for balance is reflected in the continuous effort in searching for natural language constructs that express efficient classes of queries and updates (see [5] for a survey) in particular the class of PTIME computable queries and updates. The popularity of constructs such as bounded iteration foreach x in Rjp do t od over constructs like recursion in database programming also indicates the importance of the above mentioned balance. Almost all database ....

[Article contains additional citation context not shown here]

Chandra, A., "Theory of Database Queries"; Proceedings of the Seventh ACM Symposium on Principles of Database Systems, 1988, 1-9.

....5. An example of an if statement. ####################################################### ###################################################### We next define two types of loop: for loops, which give us a bounded looping construct, and while loops, which give us an unbounded looping construct [CHAN88]. The syntax of a for loop is defined as follows: for all for predicate do TB compound statement TE where for predicate is one of the following five membership testing predicates: X nodes(G) X1, X2) arcs(G) X db( X node to graphs(v) and X arc to graphs(v 1 , v 2 ) The semantics ....

....nondeterminism, since the choice of p in assumption (a) can be made, for example, by using the physical layout of the database. Since this layout changes over time the result of a query or an update will appear to the user to be non deterministic. For more discussion on computable updates see [ABIT89, ABIT90, CHAN80, CHAN88, HULL90, HULL91, NAQV89]. VI. BRIDGING THE GAP BETWEEN GRAPH BASED AND SET BASED DATA MODELS In this section we endeavour to bridge the gap between graph based and set based data models by considering a transformation from one to the other. We first define the important notions of copy and copy elimination. Two ....

A.K. Chandra, "Theory of database queries", in Proceedings of ACM Symposium on Principles of Database Systems, Austin, Texas, pp. 1-10, 1988.

....of the data in a database and should treat the elements of the database as uninterpreted objects. Excluding queries expressing undecidable problems, computable queries can be seen as the more general class of reasonable queries. Other meaningful classes of queries have been investigated in [8], giving rise to the so called Chandra s hierarchy. A significant class of queries inside the hierarchy (i.e. the class of first order queries) was due to Codd [11] who examined two basic ways of querying a relational database, one using first order logic, the other using relational algebra. Codd ....

CHANDRA, A.K. 1988. Theory of Database Queries. Proc. of the ACM Symp. on Principles of Database Systems, 1-9.

No context found.

A. Chandra. Theory of database queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1-9. ACM Press, 1988.

No context found.

A.K. Chandra. Theory of Database Queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1--9, Austin, Texas, March 1988.

No context found.

A.K. Chandra. Theory of Database Queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1--9, Austin, Texas, March 1988.

No context found.

A. Chandra. Theory of database queries. In Proc. 7th ACM Symp. on Principles of Database Systems, pages 1-9, 1988.

No context found.

Chandra, A. (1988), Theory of database queries. In Proceedings of the Seventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Austin, pages 1--9, 1988.

No context found.

A. Chandra. Theory of database queries. In Proc. Conf. on Principles of

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