Relational calculus

The design of several database query languages has been influenced by Codd's relational algebra. This paper discusses the difficulty of optimizing queries based on the relational algebra operations select, project, and join. A matrix, called a tableau, is proposed as a useful device for representing the value of a query, and optimization of queries is couched in terms of finding a minimal tableau equivalent to a given one. Functional dependencies can be used to imply additional equivalences among tableaux. Although the optimization problem is NP-complete, a polynomial time algorithm exists to optimize tableaux that correspond to an important subclass of queries.

The integration of Logic Programming and Relational Databases has many advantages: 'on one hand, a better flexibility is obtained in the use of relational databases by allowing deductive inference and unification; on the other hand, techniques developed within a rich body of literature on databases can be exploited to speed up the execution of logic programs. The main point of this chapter is to allow Horn clauses to be expressed and computed in terms of the Relational Algebra operators, even in the case of recursive clauses. Our work builds on and completes the results of Zaniolo who has extended Relational Algebra to deal with unification in non-recursive Horn clauses. Recursive Horn clauses are considered as set transformations, hence the set of tuples satisfying a predicate defined by a system of (mutually) recursive Horn clauses is an inductively defined set, namely the smallest set closed under these transformations. Closure sets can be computed by an iterative algorithm traversing a cyclic graph whose nodes are labelled by extended relational algebra operators.

Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators such as set difference, projection, coprojection, and residuation. For each considered fragment, a characterization is obtained for when two given binary relational structures are indistinguishable by expressions in that fragment. The characterizations are based on appropriately adapted notions of simulation and bisimulation.

Literature suggests that trust can take a number of forms, two notable ones being calculus-based and relational trust. Researchers have also argued that it is important to understand how these forms can be blended in different situations. However, there is limited empirical work that has explored how this blending can be managed in construction settings, where calculus-based forms of trust have often been overemphasized. In these situations, parties often depend excessively on contracts, incentives, and deterrents in ways that are counterproductive, perhaps even leading to distrust. Existing models of trust provide limited guidelines on how to achieve an optimal mix. We use qualitative case studies and actor-network approaches to explore these forms of trust, along with the movements between them, in two settings. Based on our findings, we argue that trust can initially emerge not just as calculus-based but also as dominantly relational and that trajectories of trust reflect complex...

Database applications often require to evaluate queries containing quantifiers or disjunctions, e.g., for handling general integrity constraints. Existing efficient methods for processing quantifiers depart from the relational model as they rely on non-algebraic procedures. Looking at quantified query evaluation from a new angle, we propose an approach to process quantifiers that makes use of relational algebra operators only. Our approach performs in two phases. The first phase normalizes the queries producing a canonical form. This form permits to improve the translation into relational algebra performed during the second phase. The improved translation relies on a new operator - the complement-join - that generalizes the set difference, on algebraic expressions of universal quantifiers that avoid the expensive division operator in many cases, and on a special processing of disjunctions by means of constrained outer-joins. Our method achieves an efficiency at least comparable with...

Reiter has proposed extended relational theory to formulate relational databases with null values and presented a query evaluation algorithm for such databases. However, due to indefinite information brought in by null values, Reiter's algorithm is sound but not complete. In this paper, we first propose an extended relation to represent indefinite information in relational databases. Then, we define an extended relational algebra for extended relations. Based on Reiter's extended relational theory, and our extended relations and the extended relational algebra, we present a sound and complete query evaluation algorithm for relational databases with null values

Functional completeness of a relational language is the ability to express linear recursive queries. We present such a language that also has the property of relational completeness (relational algebra is, in fact, embedded in it). The transitive closure of a binary relation is carried out by means of the projection function and its inverse.

This paper, the first step to connect relational databases with systems consequence (Kent [5]), is concerned with the semantics of relational databases. It aims to to study system consequence in the logical/semantic system of relational databases. The paper, which was inspired by and which extends a recent set of papers on the theory of relational database systems (Spivak [6] [7]), is linked with work on the Information Flow Framework (IFF [9]) connected with the ontology standards effort (SUO), since relational databases naturally embed into first order logic. The database semantics discussed here is concerned with the conceptual level of database architecture. We offer both an intuitive and technical discussion. Corresponding to the notions of primary and foreign keys, relational database semantics takes two forms: a distinguished form where entities are distinguished from relations, and a unified form where relations and entities coincide. The distinguished form corresponds to the theory presented in (Spivak [6]). The unified form, a special case of the distinguished form, corresponds to the theory presented in (Spivak [7]). A later paper will discuss various formalisms of relational databases, such as relational algebra and first order logic, and will complete the description of the relational database logical environment.

In this paper, we propose a design of fuzzy relational database to deal with a conditional probability relation using fuzzy relational calculus. In the previous, there are several researches about equivalence class in fuzzy database using similarity or approximate relation. It is an interesting topic to investigate the fuzzy dependency using equivalence classes. Our goal is to introduce a formulation of a fuzzy relational database model using the relational calculus on the category of fuzzy relations. We also introduce general formulas of the relational calculus for the notion of database operations such as 'projection', 'selection', 'injection' and 'natural join'. Using the fuzzy relational calculus and conditional probabilities, we introduce notions of equivalence class, redundant, and dependency in the theory fuzzy relational database.

Background Once multi-relational approach has emerged as an alternative for analyzing structured data such as relational databases, since they allow applying data mining in multiple tables directly, thus avoiding expensive joining operations and semantic losses, this work proposes an algorithm with multi-relational approach. Methods Aiming to compare traditional approach performance and multi-relational for mining association rules, this paper discusses an empirical study between PatriciaMine - an traditional algorithm - and its corresponding multi-relational proposed, MR-Radix. Results This work showed advantages of the multi-relational approach in performance over several tables, which avoids the high cost for joining operations from multiple tables and semantic losses. The performance provided by the algorithm MR-Radix shows faster than PatriciaMine, despite handling complex multi-relational patterns. The utilized memory indicates a more conservative growth curve for MR-Radix tha...

Se incluyen los antecedentes del grupo, una reseña histórica, la organización, los logros alcanzados en su línea de investigación y las oportunidades de crecimiento y continuación a futuro. Palabras clave: bases de datos; lógica difusa; computación y tecnología; USB; grupo de investigación.

In the past decade, Statistical Relational Learning (SRL) has emerged as a new branch of machine learning for representing and learning a joint probability distribution over relational data. Relational representations have the necessary expressive power for important real-world problems, but until recently have not supported uncertainty. Statistical relational models fill this gap. Among the languages recently developed for statistical relational representations is Multi-Entity Bayesian Networks (MEBN). MEBN is the logical basis for Probabilistic OWL (PR-OWL), a language for uncertainty reasoning in the Semantic Web. However, until now there has been no implementation of MEBN learning. This paper describes the first implementation of MEBN learning. The algorithm learns a MEBN theory for a domain from data stored in a relational Database. Several issues are addressed such as aggregating influences, optimization problem, and so on. In this paper, as our contributions, we will provide a MEBN-RM (Relational Model) Model which is a bridge between MEBN and RM, and suggest a basic structure learning algorithm for MEBN. And the method was applied to a test case of a maritime domain in order to prove our basic method.

This paper presents a probabilistic relational modelling (implementation) of the major probabilistic retrieval models. Such a high-level implementation is useful since it supports the ranking of any object, it allows for the reasoning across structured and unstructured data, and it gives the software (knowledge) engineer control over ranking and thus supports customisation. The contributions of this paper include the specification of probabilistic SQL (PSQL) and probabilistic relational algebra (PRA), a new relational operator for probability estimation (the relational Bayes), the probabilistic relational modelling of retrieval models, a comparison of modelling retrieval with traditional SQL versus modelling retrieval with PSQL, and a comparison of the performance of probability estimation with traditional SQL versus PSQL. The main findings are that the PSQL/PRA paradigm allows for the description of advanced retrieval models, is suitable for solving large-scale retrieval tasks, and outperforms traditional SQL in terms of abstraction and performance regarding probability estimation.

Intelligent databases are a developing field since the early nineties. Using fuzzy numbers to model imprecise information is a well-known concept. In this paper, we will show how to implement FSQL queries that can also handle priority. FSQL is actually a superset of SQL, thus queries that deal with fuzzy values need to be pre and post processed. We will only sketch some technical aspects of the ongoing implementation process.

In this paper, we study the (positive) graph relational calculus. The basis for this calculus was introduced by Curtis and Lowe in 1996 and some variants, motivated by their applications to semantics of programs and foundations of mathematics, appear scattered in the literature. No proper treatment of these ideas as a logical system seems to have been presented. Here, we give a formal presentation of the system, with precise formulation of syntax, semantics, and derivation rules. We show that the set of rules is sound and complete for the valid inclusions, and prove a finite model result as well as decidability. We also prove that the graph relational language has the same expressive power as a first-order positive fragment (both languages define the same binary relations), so our calculus may be regarded as a notational variant of the positive existential first-order logic of binary relations. The graph calculus, however, has a playful aspect, with rules easy to grasp and use. This opens a wide range of applications which we illustrate by applying our calculus to the positive relational calculus (whose set of valid inclusions is not finitely axiomatizable), obtaining an algorithm for deciding the valid inclusions and equalities of the latter.

Relational lattices are obtained by interpreting lattice connectives as natural join and inner union between database relations. Our study of their equational theory reveals that the variety generated by relational lattices has not been discussed in the existing literature. Furthermore, we show that addition of just the header constant to the lattice signature leads to undecidability of the quasiequational theory. Nevertheless, we also demonstrate that relational lattices are not as intangible as one may fear: for example, they do form a pseudoelementary class. We also apply the tools of Formal Concept Analysis and investigate the structure of relational lattices via their standard contexts. Furthermore, we show that the addition of typing rules and singleton constants allows a direct comparison with monotonic relational expressions of Sagiv and Yannakakis.

Relational lattices are obtained by interpreting lattice connectives as natural join and inner union between database relations. Our study of their equational theory reveals that the variety generated by relational lattices has not been discussed in the existing literature. Furthermore, we show that addition of just the header constant to the lattice signature leads to undecidability of the quasiequational theory. Nevertheless, we also demonstrate that relational lattices are not as intangible as one may fear: for example, they do form a pseudoelementary class. We also apply the tools of Formal Concept Analysis and investigate the structure of relational lattices via their standard contexts. Furthermore, we show that the addition of typing rules and singleton constants allows a direct comparison with monotonic relational expressions of Sagiv and Yannakakis.

In this paper, we study the (positive) graph relational calculus. The basis for this calculus was introduced by Curtis and Lowe in 1996 and some variants, motivated by their applications to semantics of programs and foundations of mathematics, appear scattered in the literature. No proper treatment of these ideas as a logical system seems to have been presented. Here, we give a formal presentation of the system, with precise formulation of syntax, semantics, and derivation rules. We show that the set of rules is sound and complete for the valid inclusions, and prove a finite model result as well as decidability. We also prove that the graph relational language has the same expressive power as a first-order positive fragment (both languages define the same binary relations), so our calculus may be regarded as a notational variant of the positive existential first-order logic of binary relations. The graph calculus, however, has a playful aspect, with rules easy to grasp and use. This opens a wide range of applications which we illustrate by applying our calculus to the positive relational calculus (whose set of valid inclusions is not finitely axiomatizable), obtaining an algorithm for deciding the valid inclusions and equalities of the latter.

We consider the problem of, given a probabilistic model on a set of random variables, how to add a new variable that depends on the other variables, without changing the original distribution. In particular, we consider relational models (such as Markov logic networks (MLNs)), where we cannot directly define conditional probabilities. In relational models, there may be an unbounded number of parents in the grounding, and conditional distributions need to be defined in terms of aggregators. The question we ask is whether and when it is possible to represent conditional probabilities at all in various relational models. Some aggregators have been shown to be representable by MLNs, by adding auxiliary variables; however it was unknown whether they could be defined without auxiliary variables. For other aggregators, it was not known whether they can be represented by MLNs at all. We obtained surprisingly strong negative results on the capability of flexible undirected relational models ...

The fuzzy relational database model as defined by Buckles and Petry employs sets in place of atomic values for components of tuples in database relations. This technique for dealing with imprecision in relational databases is intuitively appealing. Moreover, the model preserves several im~rtant properties of classical relational databases. In recent works we have demonstrated that the existence of partitions on scalar domains is the key to ensuring conformity with the classical relational model. Specifically, by restricting the components of fuzzy tuples to be nonempty subsets of equivalence classes from domain partitions, it is possible to define the notions of redundant tuples and consistent database relations, and to specify a well-defined fuzzy relational algebra. Since these properties are obtained by working only with equivalence classes, the fuzzy relational model of Buckles and Petty is generalized to an equivalence classes model of relational databases. In this work, additional properties of the fuzzy relational database model are presented. By employing equivalence classes from domain partitions, we define functional dependencies and normal forms for the fuzzy relational model. These definitions extend the corresponding classical definitions. Moreover, our definitions of functional dependencies and normal forms provide valuable guidelines for designing fuzzy relational databases.

This book series provides a forum to systematically summarize recent developments, discoveries and progress on multi-sensor, multi-source/multi-level data and information fusion along with its connection to data-enabled science. Emphasis is also placed on fundamental theories, algorithms and real-world applications of massive data as well as information processing, analysis, fusion and knowledge generation. The aim of this book series is to provide the most up-to-date research results and tutorial materials on current topics in this growing field as well as to stimulate further research interest by transmitting the knowledge to the next generation of scientists and engineers in the corresponding fields. The target audiences are graduate students, academic scientists as well as researchers in industry and government, related to computational sciences and engineering, complex systems and artificial intelligence. Formats suitable for the series are contributed volumes, monographs and lecture notes.

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Program traces are often used for explaining the dynamic behavior of programs. Unfortunately, program traces can grow quite big very quickly, even for small programs, which compromises their usefulness. In this paper we present a visual notation for program traces that supports their succinct representation, as well as their dynamic transformation through a structured query language. An evaluation on a set of standard examples shows that our representation can reduce the overall size of traces by at least 79%, which suggests that our notation is an effective improvement over the use of plain traces in the explanation of dynamic program behavior.

Our aim is to design a pattern classifier using fuzzy relational calculus (FRC) which was initially proposed by W. Pedrycz. In the course of doing this we introduce a new interpretation of multidimensional fuzzy implication (MFI) to represent our knowledge about the training data set. The new interpretation is basically a set of one-dimensional fuzzy implications. The consequences of all one-dimensional fuzzy implications are finally collected through one intersection operator '5'. Subsequently, we consider the notion of a fuzzy pattern vector, which is formed by the cylindrical extension of the antecedent part of each one-dimensional fuzzy implication. Thus, we get a set of fuzzy pattern vectors for the new interpretation of MFI and represent the population of training patterns in the pattern space. We also introduce a new approach to the computation of the derivative of the fuzzy max and min functions using the concept of a generalized function. During the construction of the classifier, based on FRC, we use fuzzy linguistic statements (or fuzzy membership function to represent the linguistic statement) to represent the ranges of features (e.g. feature F G is small/medium/big, etc. ∀i) for a population of patterns. Note that the construction of the classifier essential depends on the estimate of a fuzzy relation R G between the antecedent part and consequent part of each one-dimensional fuzzy implication. Thus, a set of fuzzy relations is formed from the new interpretation of MFI. This set of fuzzy relations is termed as a core of the classifier. Once the classifier is constructed the non-fuzzy features of a pattern can be classified. At the time of classification of the test patterns, we use the concept of fuzzy singleton to fuzzify the non-fuzzy feature values of the test patterns. The performance of the proposed scheme is tested on synthetic data. Finally, we use the proposed scheme for the vowel classification problem of Indian languages.

Many natural intensional properties in arti cial and natural languages are hard to compute. We show that randomized algorithms are often necessary to have good estimators of natural properties and to verify some speci c relations. We concentrate on the reliability of queries to show the advantage of randomized algorithms in uncertain cognitive worlds.

Abstract— This paper introduces U-relations, a succinct and purely relational representation system for uncertain databases. U-relations support attribute-level uncertainty using vertical partitioning. If we consider positive relational algebra e xtended by an operation for computing possible answers, a query on the logical level can be translated into, and evaluated as, a sin gle relational algebra query on the U-relational representation.

This paper introduces U-relations, a succinct and purely relational representation system for uncertain databases. U-relations support attribute-level uncertainty using vertical partitioning. If we consider positive relational algebra extended by an operation for computing possible answers, a query on the logical level can be translated into, and evaluated as, a single relational algebra query on the Urelation representation. The translation scheme essentially preserves the size of the query in terms of number of operations and, in particular, number of joins. Standard techniques employed in off-the-shelf relational database management systems are effective for optimizing and processing queries on U-relations. In our experiments we show that query evaluation on U-relations scales to large amounts of data with high degrees of uncertainty.

We present a sound and complete graph calculus for modalities. This calculus is a general framework for expressing modal formulas and frame properties, with a rich repertoire of relations, and reasoning about them in a uniform manner. The calculus employs graphical interpretations of logical operators and builds graphical objects that represent conditions on Kripke structures.

The relationship between belief networks and relational databases is examined. Based on this analysis, a method to construct belief networks automatically from statistical rela tional data is proposed. A comparison be tween our method and other methods shows that our method has several advantages when generalization or prediction is deeded.

Binary relational algebra provides semantic foundations for major areas of computing, such as database design, state-based modeling and functional programming. Remarkably, static checking support in these areas fails to exploit the full semantic content of relations. In particular, properties such as the simplicity or injectivity of relations are not statically enforced in operations such as database queries, state transitions, or composition of functional components. When data models, their constraints and operations are represented by point-free binary relational expressions, proof obligations can be expressed as inclusions between relational expressions. We developed a type-directed, strategic term rewriting system that can be used to simplify relational proof obligations and ultimately reduce them to tautologies. Such reductions can be used to provide extended static checking for design contraints commonly found in software modeling and development. .

Binary relational algebra provides semantic foundations for major areas of computing, such as database design, state-based modeling and functional programming. Remarkably, static checking support in these areas fails to exploit the full semantic content of relations. In particular, properties such as the simplicity or injectivity of relations are not statically enforced in operations such as database queries, state transitions, or composition of functional components. When data models, their constraints and operations are represented by point-free binary relational expressions, proof obligations can be expressed as inclusions between relational expressions. We developed a typedirected, strategic term rewriting system that can be used to simplify relational proof obligations and ultimately reduce them to tautologies. Such reductions can be used to provide extended static checking for design contraints commonly found in software modeling and development.

In commercial network database management systems, set-valued fields and aggregate functions are commonly supported. However, the relational database model, as defined by Codd, does not include set-valued attributes or aggregate functions. Recently, Klug extended the relational model by incorporating aggregate functions and by defining relational algebra and calculus languages. In this paper, relational algebra and relational calculus database query languages (as defined by Klug) are extended to manipulate set-valued attributes and to utilize aggregate functions. The expressive power of the extended languages is shown to be equivalent. We extend the relational algebra with three new operators, namely, pack, unpack, and aggregation-by-template. The extended languages form a theoretical framework for statistical database query languages.

We prove that the complexity of Lamping's optimal graph reduction technique for the A-calculus can be exponential in the number of L6vy 's family reductions. Starting from this consideration, we propose a new measure for what could be considered as "the intrinsic complexity" of A-terms.

In this paper I review the Neo-Davidsonian semantics of prepositional phrases and secondary predication. I argue that certain types of examples pose challenge to this semantics. I present an alternative to the Neo-Davidsonian analysis which successfully deals with the problematic examples. The core idea lies in representing thetaroles not as functions from events to their participants, but rather as argument-labels encoding the role of each argument in a given verb. As a result, natural-language predicates can now be treated in the manner in which relations are treated in the relational model of data, that is, as naming sets of tuples in which every object is given together with its role named by a corresponding attribute (a theta-role). Such a representation allows the employment of relational algebra operators to calculate the extensions of complex predicates (predicates built out of atomic predicates and/ or atomic predicates and prepositions). I lay out the foundations of a relational FOL appropriate for the representation of natural-language predicates and present solutions to the problematic examples. From a practical perspective, the expressions of a relational FOL can be translated to a relational algebra or SQL, which makes it possible to operate with these three languages on the same relational model of data. From a philosophical perspective, a relational FOL permits a return to 'propertybased' semantics, one in which properties named by predicates are those of individuals, and not of events.

In this work, formulas are inclusions t 1 ⊆ t 2 and non-inclusions t 1 ⊆ t 2 between Boolean terms t 1 and t 2. We present a set of rules through which one can transform a term t in a diagram ∆t and, consequently, each inclusion t 1 ⊆ t 2 (non-inclusion t 1 ⊆ t 2) in an inclusion ∆t 1 ⊆ ∆t 2 (noninclusion ∆t 1 ⊆ ∆t 2) between diagrams. Also, by applying the rules just to the diagrams we are able to solve the problem of verifying if a formula ϕ is consequence of a, possibly empty, set Σ of formulas taken as hypotheses. Our system has a diagrammatic language based on Venn diagrams that are read as sets, and not as statements about sets, as usual. We present syntax and semantics of the diagrammatic language, define a set of rules for proving consequence, and prove that our set of rules is strongly sound and complete in the following sense: given a set Σ ∪ ϕ of formulas, ϕ is a consequence of Σ iff there is a proof of this fact that is based only on the rules of the system and involves only diagrams associated to ϕ and to the members of Σ.

In service-oriented computing, correlations are used to determine links between service providers and users. A correlation contains values for some variables received in a communication. Subsequent messages will only be received when they match the values of the correlation. Correlations allow for the implementation of sessions, local shared memory, gradually provided input, or input provided in arbitrary order-thus presenting a challenge to static analysis. In this work, we present a static analysis in relational form of correlations. It is defined in terms of a fragment of the process calculus COWS that itself builds on the Fusion Calculus. The analysis is implemented and practical experiments allow us to automatically establish properties of the flow of information between services.

We consider the problem of learning Boltzmann machine classifiers from relational data. Our goal is to extend the deep belief framework of RBMs to statistical relational models. This allows one to exploit the feature hierarchies and the non-linearity inherent in RBMs over the rich representations used in statistical relational learning (SRL). Specifically, we use lifted random walks to generate features for predicates that are then used to construct the observed features in the RBM in a manner similar to Markov Logic Networks. We show empirically that this method of constructing an RBM is comparable or better than the state-of-the-art probabilistic relational learning algorithms on six relational domains.

In this paper, we propose a new probabilistic relational database model, denote by PRDB, as an extension of the classical relational database model where the uncertainty of relational attribute values and tuples are respectively represented by finite sets and probability intervals. A probabilistic interpretation of binary relations on finite sets is proposed for the computation of their probability measures. The combination strategies on probability intervals are employed to combine attribute values and compute uncertain membership degrees of tuples in a relation. The fundamental concepts of the classical relational database model are extended and generalized for PRDB. Then, the probabilistic relational algebraic operations are formally defined accordingly in PRDB. In addition, a set of the properties of the algebraic operations in this new model also are formulated and proven.

Analyzing time to event data arises in a number of fields such as Biology and Engineering. A common feature of this data is that, the exact failure time for all units may not be observable. Accordingly, several types of censoring were presented. Progressive censoring allows units to be randomly removed before the terminal point of the experiment. Marshall-Olkin bivariate lifetime distribution was first introduced in 1967 using the exponential distribution. Recently, bivariate Marshall-Olkin Kumaraswamy lifetime distribution was derived. This paper derives the likelihood function under progressive type-I censoring for the bivariate Marshall-Olkin family in general and applies it on the bivariate Kumaraswamy lifetime distribution. Maximum likelihood estimators of model parameters were derived. Simulation study and a real data set are presented to illustrate the proposed procedure. Absolute bias, mean square error, asymptotic confidence intervals, confidence width and coverage probability are obtained. Simulation results indicate that the mean square error is smaller and confidence width is narrower and more precise when number of removals gets smaller. Also, increasing the terminal point of the experiment results in reducing the mean square error and confidence width.

Abstract: Alloy is an increasingly popular lightweight specification language based on relational logic. Alloy models can be automatically verified within a bounded scope using off-the-shelf SAT solvers. Since false assertions can usually be disproved using small counter-examples, this approach suffices for most applications. Unfortunately, it can sometimes lead to a false sense of security, and in critical applications a more traditional unbounded proof may be required. The automatic theorem prover Prover9 has been shown to be ...

Algebraic optimisation is both theoretically and practically important for query processing in complex value databases. In this paper, we consider this issue and investigate some algebraic properties concerning the nested relational operators. The join operation is one of the most time-consuming operations in nested relational query processing. We introduce a new join operator, called P-join, which combines the advantages of Roth's extended natural join and Colby's recursive join for efficient data access. We also investigate some algebraic properties concerning the P-join operator and extended relational operators, which can be used for query optimisation in nested relational databases. We then examine the role of the restructuring operators nest and unnest in their interactions with the extended relational operators proposed by Roth et al. Under certain functional and mutual data dependencies, the six nested relational equations will hold. Finally, we outline the steps of a heuristic optimisation algorithm that utilises algebraic transformation rules developed in this paper and previous related work to transform an initial query to an optimised one that is more efficient to execute.

*-Existing database security mechanisms are not sufficient for detecting malicious activities targeted at corrupting data. With the increase of attacks toward database-centered applications, an effective intrusion detection system is essential for application security. Although someresearches havebeen done on the database intrusion detection, methods for detecting anomalous activitiesin databases haveonly recently been explored in detail. In this paper, we present an approach employing inter-transaction data dependency mining fordetecting well-crafted attacks thatconsists a group of seemingly harmless database transactions. Our experiments illustrated the advantage of this new approach and validated the effectiveness of the model proposed.

MatBase is a prototype data and knowledge base management expert intelligent system based on the Relational, Entity-Relationship, and (Elementary) Mathematical Data Models. Dyadic relationships are quite common in data modeling. Besides their relational-type constraints, they often exhibit mathematical properties that are not covered by the Relational Data Model. This paper presents and discusses the MatBase algorithm that assists database designers in discovering all non-relational constraints associated to them, as well as its algorithm for enforcing them, thus providing a significantly higher degree of data quality.