G.M. Kuper and M.Y. Vardi. A new approach to database logic. In Proc. 3rd ACM Symp. on Principles of Database Systems, 86-97, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of data, databases are collections of relations, i.e. sets of tuples. The data items, the tuples, are unordered, and the relations contain no duplicates, and cannot be nested. Relaxing these assumptions leads to numerous distinct data types, such as the complex objects (nested sets) Jac82, AB87, KV84, KRS85, AG91] the bags (sets with duplicates) BK90, Mum90, Alb91, BS91, GM93, LW94] the lists (internal order) the ordered sets, and the pomsets (partially ordered multisets) Pra84] 2.1 Partially Ordered Multisets Pomsets The pomset type generalizes sets, bags, lists, trees, and other ....

G.M. Kuper and M.Y. Vardi. A new approach to database logic. In Proc. 3rd ACM Symp. on Principles of Database Systems, 86-97, 1984.

....The trees of possibilities they explore have different roots and are rapidly evolving into a forest as diverse as the implementations of OO databases that exist now. One important concept that has arisen from the forest of formalization efforts is the concept of an object identifier [4, 17, 29, 31, 34, 45], itself stemming from the concept of a surrogate [14, 27] In this paper, I try to develop a theory of objects, using the concept of object identifier (oid) as root from which to develop and formalize other concepts. The language defined in this process is called CMSL (Conceptual Model ....

G.M. Kuper and M.Y. Vardi. A new approach to database logic. In 3rd ACM SIGACT-SIGMOD symposium on the principles of database systems, pages 8696, Waterloo, Ontario, March 1984. ACM.

....Value schemes comprise a set of attributes which can be either atomic or multi valued and nesting of attributes is possible. An object over a value scheme is a pair i,v , where i is the unique object identifier (object id) and v is the object value. Our representation of objects subsumes that of [11, 12] in which all objects are constrained to have object ids regardless of the level of nesting. In contrast, in GROOVY the S component of an object schema indicates all the sub object schemas and only objects and sub objects must have an object id. In other words, we argue that object ids should only ....

....the information currently stored for this object. For example, if PERSON = NAME, CHILDREN is a value scheme representing the fact that PERSON objects have a NAME and a set of CHILDREN, we may have an object O = i 1 , John, Jack, Jill . Our representation of objects subsumes that of [11, 12] in which all objects are constrained to have object ids regardless of their level of nesting. For example, with these models, the set Jack, Jill would also have to possess an object id, and the resulting object would be of the form i 1 , John, i 2 , Jack, Jill . Conversely, in GROOVY, ....

KUPER G. M., AND VARDI M. Y. 1984. A new approach to database logic. Proceedings of ACM Symposium on Principles of Database Systems, pp. 86-96.

....of data, databases are collections of relations, i.e. sets of tuples. The data items, the tuples, are unordered, and the relations contain no duplicates, and cannot be nested. Relaxing these assumptions leads to numerous distinct data types, such as the complex objects (nested sets) Jac82, AB87, KV84, KRS85, AG91] the bags (sets with duplicates) BK90, Mum90, Alb91, BS91, GM93, LW94] the lists (internal order) the ordered sets, and the pomsets (partially ordered multisets) Pra84] 2.1 Partially Ordered Multisets Pomsets The pomset type generalizes sets, bags, lists, trees, and other ....

G.M. Kuper and M.Y. Vardi. A new approach to database logic. In Proc. 3rd ACM Symp. on Principles of Database Systems, 86-97, 1984.

....and semantic models, languages that allow one to access such structures are important and worthy of study. We consider a calculus based language (similar to the one proposed by Jacobs [37] and those in [34, 41] an algebra, and a logic programming language (similar to those presented in [15, 3, 16, 44, 42]) 1 In the original report [2] we used the term complex object instead of complex value. Since then, this term has been more and more associated to the object oriented paradigm and we decided not to use it. Note that in particular, our complex values have no identity. 2 Our main results ....

....can easily be extended if heterogeneous sets are allowed. The expressive power of languages for a model that allows heterogeneous sets is considered in [35] 2 One of these, the powerset, was added for a different reason, as explained above. 5 Our types can be described by trees. Unlike in [44], cycles are not allowed in type definitions; equivalently, we disallow recursive type definitions, so that one cannot, for example, define lists in terms of pair and variant constructions. However, note that even in a model with objects and object identity, hence models where cycles are allowed, ....

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Kuper, G.M., M.Y. Vardi. A new approach to database logic. Proc. 3rd PODS (1984)

....[BS91] However, while the expressive power of database languages is of major interest in database research, the expressive power of languages for manipulating bags constitutes a new topic of research. On the other hand, there has been a wide interest in languages for hierarchical data structures [KV84, TF86]. The complexity and the expressive power of languages for nested relations have been extensively studied [KV88, HS91, PG92, GG92, AFS89, HS89, GV90, GV95] Collection types have been investigated in [BBN91, BTBW92] in connection with structural recursion. Nested bags, on the other hand had never ....

G.M. Kuper and M.Y. Vardi. A new approach to database logic. In Proc. 3rd ACM Symp. on Principles of Database Systems, 1984.

.... the integration of efficient techniques and methods for mass storing with advanced linguistic paradigms and data models (logic programming, complex objects, functional models, semantic models) In particular, much work has been devoted, on one hand, to the formalization of novel data models (e.g. [4, 20, 22]) and on the other hand to the design of advanced database query languages (e.g. 3, 5, 14, 16, 26] and to the development of efficient query answering techniques (e.g. 11, 12, 27] Less attention has been deserved to the problem of defining update languages for advanced database environments, ....

G.M. Kuper and M.Y. Vardi. A new approach to database logic. In Third ACM SIGACT SIGMOD Symp. on Principles of Database Systems, pages 86-- 96, 1984.

....applications. On the other hand, it should be rather simple to be understandable by nonsophisticated users. We use here the model of [5] i.e. a simple model with sets, tuples, object identity and structural inheritance. This model can be viewed as a least generalization of the models of [1, 31]. We make two additions to it. First, we introduce a list constructor. Such constructor was avoided in [5] for safety reasons, but is certainly useful for many applications. Also, we consider methods . The various features that can be found in the data structure are standard in database models. ....

G.M. Kuper and M.Y. Vardi. A New Approach to Database Logic. In Proc. ACM PODS, 86--96, 1984.

....well established. The relational approach has initiated such a focus on formal aspects: its definitions of the relational algebra and calculus have been extremely beneficial to the development of different manipulation languages. An equivalent concern for a sound theoretical framework [Jacob 82] Kuper 84] has influenced the work on modern data modelling approaches, such as, in particular, non first normal form (NF 2 ) relations [Roth 85] and object oriented models [Abiteboul 87] Hull 87] Both are provided with an algebra and a calculus, as well as with the equivalence in between. However, ....

G.M. Kuper, M.Y. Vardi: "A new approach to data base logic", Proc. ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, 1984

....defined, essentially corresponding to hereditarely finite sets. The connection between hereditarely finite set construction and value invention was shown by Van den Bussche et al. 37] which reconciled the two approaches. The idea of value invention originates from a proposal by Kuper and Vardi [31, 32] to choose arbitrary symbolic object names to manage new complex object values defined in their logical queries. The concept of object name is a refinement of Codd s notion of surrogate [15] nowadays, we use the term object identity. The mechanism of value invention has been recasted into an ....

G.M. Kuper and M.Y. Vardi. A new approach to database logic. In Third ACM SIGACT SIGMOD Symp. on Principles of Database Systems, 1984.

....it possible to change connections between objects, insert objects into types or classes, create an object and delete an object. These operations can require changes to the schema as discussed below, and the creation of object identifiers. The creation of object identifiers has been addressed in [3, 6, 66, 71]. Integrity constraints ensure that the database is consistent CHAPTER 7 : CONCLUSION 114 after a transaction. As in deductive databases, integrity constraints in deductive objectoriented databases can be represented as clauses. However, the efficient checking of integrity constraints in deductive ....

G. Kuper and M. Vardi. A new approach to database logic. In Proc. 3rd ACM SIGACTSIGMOD -SIGART Symposium on Principles of Database Systems, 1984.

....and semantic models, languages that allow one to access such structures are important and worthy of study. We consider a calculus based language (similar to the one proposed by Jacobs [31] and those in [28, 35] an algebra, and a logic programming language (similar to those presented in [13, 14, 37, 36, 4]) 1 Note that the word object as used in complex object , and in this paper, does not refer to the notion of object as known in object oriented database models. In particular, our objects have no identity that is distinct from their values. They are essentially composite values. Our main ....

....considered. In that respect, the data structure that we study is strictly weaker than those considered in [5, 6, 30] but we believe that our results can easily be extended if heterogeneous sets are allowed. Our types can be described by trees, that is, our objects are actually values. Unlike in [37], cycles are not allowed in type definitions. However, note that even in a model where objects have identities, hence cycles are allowed, a query result is defined by an expression that is applied to each object in a set, and contains conditions that the object and other objects and values that ....

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Kuper, G.M., M.Y. Vardi. A new approach to database logic. Proc. 3rd PODS (1984)

....model theory (cf. Section 13) 1 General Introduction Computability over sets (of tuples of sets of tuples of sets, etc. or over complex objects is at present rather popular subject, especially in connection with nested data bases. There may be distinguished two directions: typed (e.g. [1, 13, 19, 22]) and untyped (cf. 6, 7, 8, 26, 30, 32, 34] ones. The first is based on the direct product and powerset type constructs and presupposes, at least at the beginning, the hyperexponential (i.e. Kalmar elementary) computational complexity. Some additional special efforts are necessary to find ....

Kuper, G.M., Vardi, M.Y.: A new approach to database logic. Proc. 3rd ACM Symp. on Principles of Database Systems 1984

....object algebra, query languages, complex objects, conceptual schema. 1 Introduction The characteristics of a database algebra have to reflect the properties of the algebraic structures for which algebraic operations are intended. From this perspective, the differences between an object algebra [55, 2, 47, 53, 32, 29, 33, 51] and an algebraic language defined for the manipulation of relations [16, 41, 1] for instance, can be regarded as the consequences of differences in the underlying data models. The features that have to be included in the object algebra are operations for handling the modelling constructs which ....

G.M. Kuper, M.Y. Vardi, A New Approach to Database Logic, Proc. of the ACM Conf. on Management of Data, 1984, pp. 86-96.

....to syntactic items by applying the function I which returns for the parameter the corresponding interpretation. The convention throughout the paper is that I denotes the interpretation of a syntactic item. 2 Object identities have appeared under the name surrogates in [Cod79] l values in [KV84] and object identifiers in [AH87] the freedom and flexibility offered by the above interpretation for object sorts and, in consequence of this, from the freedom for the interpretation of attributes. The following situation can occur: There may be objects which have different identities, say ....

G.M. Kuper and M.Y. Vardi. A New Approach to Database Logic. In Proc. 3th ACM Symp. Principles of Database Systems (PODS), pages 86-- 96, 1984.

....On the other hand, deductive databases rely on a flat data model and do not support data abstraction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g. [1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra logical features; or they would omit important aspects of object oriented systems, such as typing and ....

G. Kuper and M.Y. Vardi. A new approach to database logic. In ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS), 1984.

....tractable query languages. Work supported in part by an INRIA NSF cooperation grant, and the National Science Foundation under grants IRI 8816078 and INT 8817874. Languages for complex objects which have been proposed are roughly of three types: extensions of relational calculus [Jac82, AB87, KV84, KRS85] extensions of relational algebra [AB87, AB86, FT83, KV84, SS86] and deductive languages [AG88, BNR 87, Kup87, Kup88] They all use higher order types. Previous investigations of their expressive power have focused on the gain in expressivity resulting from the use of higher order ....

....cooperation grant, and the National Science Foundation under grants IRI 8816078 and INT 8817874. Languages for complex objects which have been proposed are roughly of three types: extensions of relational calculus [Jac82, AB87, KV84, KRS85] extensions of relational algebra [AB87, AB86, FT83, KV84, SS86] and deductive languages [AG88, BNR 87, Kup87, Kup88] They all use higher order types. Previous investigations of their expressive power have focused on the gain in expressivity resulting from the use of higher order types, when queries are applied to flat databases [HS88, KV88] In ....

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G.M. Kuper and M.Y. Vardi. A new approach to database logic. In Proc. 3rd ACM Symp. on Principles of Database Systems, 1984.

....with structured values [LR89] However we are not aware of a complete formal description of this language. The presented query formalism is essentially useful for the ad hoc manipulation of structured values. With that it stands in tradition of the query calculi proposed for complex object models [KV84, BK86, RKS88, ABGG89] Most of these calculi turn out to be direct extensions of relational domain and tuple calculus, thereby showing the same deficiencies in explaining some important facets of concrete SQL: 1. Missing simple characterization of safe queries: Standard SQL queries are always ....

....SQL, for instance the possibility to obtain duplicates in query results or grouping cannot be adequately mirrored in tuple calculus. The calculus of Abiteboul Beeri. In query calculi for extended relational models the requirement that answers to queries must result in new relations is obsolete [KV84, BK86, RKS88, ABGG89] In order to allow for answers of any structure, in an approach to a query calculus for Complex Object models proposed by Abiteboul and Beeri called CALC [AB88] the restriction forcing variables to be of atomic data sorts (or tuple expressions built over these sorts) is ....

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G.M. Kuper and M.Y. Vardi, A New Approach to Database Logic, Proc. 3th ACM Symp. Principles of Database Systems (PODS), 1984, pp. 86-- 96.

....of data, databases are collections of relations, i.e. sets of tuples. The data items, the tuples, are unordered, and the relations contain no duplicates, and cannot be nested. Relaxing these assumptions leads to numerous distinct data types, such as the complex objects (nested sets) Jac82, AB87, KV84, KRS85, AG91] the bags (sets with duplicates) BK90, Mum90, Alb91, BS91, GM93, LW94] the lists (internal order) the ordered sets, and the pomsets (partially ordered multisets) Pra84] 2.1 Partially Ordered Multisets Pomsets The pomset type generalizes sets, bags, lists, trees, and other ....

G.M. Kuper and M.Y. Vardi. A new approach to database logic. In Proc. 3rd ACM Symp. on Principles of Database Systems, 86-97, 1984.

.... not always have [SS77,Co79] This has motivated a great deal of research during the past decade on structured data models: the so called semantic data models (cf. AH87, HM81, Sh81] nested relations (cf. FT83,JS82] and complex objects (cf. BK86] Continuing in this spirit, we introduced in [KV84,Ku85] the Logical Data Model (LDM) which combines and extends Jacobs database logic [Ja82] and Hull and Yap s format model [HY82] This model uses three basic operations to structure data: product, union, and power set. 1 These operations can be combined not only hierarchically but also in a ....

....j ) for 1 j n, 3. if v is a union node with successors v 1 ; v n , then data(l) has to be a member of [ n j=1 I(v j ) and 4. if v is a power node with successor w, then data(l) has to be a subset of I(w) For more formal definitions and several examples the reader is referred to [KV84,Ku85]. 2.2 LDM Logic Let S be a schema. We define a many sorted logic L(S) over S. Each variable in L(S) has a sort, where the sorts are the nodes of S. The sorts restrict the possible values that the variables can take. For example, if x is a variable of type v, then x can assume values only from ....

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Kuper, G.M., Vardi, M.Y.: A new approach to database logic. Proc. ACM Symp. on Principles of Database Systems, 1984.

....Programming With Sets Gabriel M. Kuper IBM T. J. Watson Research Laboratory Yorktown Heights, New York 1 Introduction In recent years there has been a large amount of interest in extending the relational model of a database to capture more of the structure of the data, e.g. HY82] JS82] [KV84] [OY85] RR83] SP82] SS77] Most of this work has focussed on two issues: How to model the physical structure of the data, and how to define query languages on structures that are more general than flat relations. One popular model has been non first normal form (non 1NF) or nested, relations. ....

G. M. Kuper and M. Y. Vardi. A new approach to database logic. In Proc. Third Annual ACM Symposium on Principles of Database Systems, pages 86--96, ACM, Waterloo, Ontario, 1984.

.... of our query language is studied in [KV85, 41 Our work unifies and generalizes a long sequence of previous works on semantic data models [AB84, DB82, FK77, GDB82, Gra79, Har78, Kob80, Mak77, MP82, OY85, RR83, SP82, SS77, Tsi76] The preliminary publication of our results in [KV84], stimulated later work, such [ All these models can be viewed as special cases of LDM, designed to make certain classes of queries easier to express, or more efficient to implement. Our model incorporates two important object oriented features: object identity, captured by the ....

G. M. Kuper and M. Y. Vardi. A new approach to database logic. In Proc. Third Annual ACM Symposium on Principles of Database Systems, pages 86--96, Waterloo, Ontario, 1984. ACM.

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G. Kuper and M.Y. Vardi. A new approach to database logic. In Proc. ACM Symp. on Principles of Database Systems, pages 86--96, 1984.

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G. Kuper and M. Y. Vardi. A new approach to database logic. In Proc. ACM Symp. on Principles of Database Systems, pages 86--96, 1984.

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G. M. Kuper, and M. Y. Verdi. A new approach to database logic. Proc. of ACM PODS Symposium, 1984.

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