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General issues of the data integration problem are discussed, including ontology-based data integration in the semantic web. The importance of establishing mappings between ontologies and relational databases is shown, and a brief analytical review of studies in this field is given. The binary relational data model is defined and the mapping of the description logic ALC and its extensions to the binary relational data model is described.

Despite the huge amount of work devoted to the treatment of time within the relational context, few relevant temporal phenomena still remain to be addressed. One of them is the treatment of “ nearly periodic events ”, i.e., events/facts that occur in intervals of time which repeat periodically (e.g., a meeting occurring twice each Monday , possibly not at regular times ). Nearly periodic events are quite frequent in everyday life, and thus in many applicative contexts. Their treatment within the relational model is quite challenging, since it involves the integrated treatment of three aspects: (i) the number of repetitions, (ii) their periodicity , and (iii) temporal indeterminacy . Coping with this problem requires an in-depth extension of current temporal relational database techniques. In this paper, we introduce a new data model, and new definitions of relational algebraic operators coping with the above issues. We ascertain the properties of the new model and algebra, with emphasis on the expressiveness of our representation model, on the reducibility property, and on the correctness of the algebraic operators.

Compound approximation spaces for relational data are proposed.They are viewed as expansions of tolerance approximation spaces to a relational case.Properties of compound approximation spaces are investigated.Compound approximation spaces enable to derive new knowledge from relational data. Rough set theory provides a powerful tool for dealing with uncertainty in data. Application of variety of rough set models to mining data stored in a single table has been widely studied. However, analysis of data stored in a relational structure using rough sets is still an extensive research area. This paper proposes compound approximation spaces and their constrained versions that are intended for handling uncertainty in relational data. The proposed spaces are expansions of tolerance approximation ones to a relational case. Compared with compound approximation spaces, the constrained version enables to derive new knowledge from relational data. The proposed approach can improve mining relational data that is uncertain, incomplete, or inconsistent.

Graphical abstractDisplay Omitted HighlightsFormula-based relations defined in a granular computing framework are proposed.The relations are used to construct more informative granules.The granules are used to represent relational data and patterns.Thanks to this approach, the generation of patterns can be speeded up.The approach makes it possible to discover richer knowledge from relational data. The complex structure of relational data makes the process of knowledge discovery from data a more challenging task compared with the single table data structure. The usefulness of granular computing based approaches to mining data stored in a single table is a driving force for adapting this method to relational data. This paper proposes relation-based granules that are defined in a granular computing based approach to mining relational data. The relations are used to represent relational data and patterns to be discovered. Thanks to this representation, the generation of patterns can be speeded up. The representation also makes it possible to discover richer knowledge from relational data.

In 1970, an article by Edgar F. Codd determined the primary direction of high-level database languages for the next 40 years. The authors give an overview of the relational model for database systems, then highlight three of the masterminds who created and developed it: Codd, Michael Stonebraker, and Larry Ellison.

We present a new approach lo learn from relational data based on re-representation of the examples. This approach, called property-based re-representation is based on a new analysis of the structure of refinement graphs used in ILP and relational learning in general. This analysis allows the characterization of relational examples by a set of multi-relational patterns called properties. Using them, we perform a property-based re-representation of relational examples that facilitates the development of relational learning techniques. Additionally, we show the usefulness of re-representation with a collection of experiments in the context of nearest neighbor classification. © 2015 - IOS Press and the authors., Research partially supported by Projects Next-CBR (TIN2009-13692-C03-01) and Cognitio (TIN2012-38450- C03-03) and by the Generalitat de Catalunya under the grants 2009-SGR-1434.

Information granulation is a powerful tool for data analysis and processing. However, not much attention has been devoted to application of this tool to data stored in a relational structure. This paper extends the notion of information granules to a relational case. Two information systems intended to store relational data are proposed. This study also extends a granule description language to express information granules derived from relational data. The proposed approach enables to analyze a given problem at different levels of granularity of relational data. This can find application in searching for patterns in data mining.

Analogy is an important cognitive process that has been researched extensively. Functional accounts of it typically involve at least four stages of processing (access, mapping, transfer, and evaluation); however, these accounts take the way in which the base analogue is understood, along with its relational structure, for granted. The goal of this paper is to open up a discussion about how this process (which we will call “relational recognition”) may occur. To this end, this paper describes two experiments that vary the level of relational complexity across exemplars. It was found that relational recognition tasks benefit from increased complexity, while mapping tasks suffer from it.

Event relations are used in many temporal relational database approaches to represent facts occurring at time instants. However, to the best of our knowledge, none of such approaches fully copes with the definition of events as provided, e.g., by the “consensus” temporal database glossary. We propose a new approach which overcomes such a limitation, allowing one to cope with multiple events occurring in the same temporal granule. This move involves major extensions to current approaches, since indeterminacy about the time and number of occurrences of events need to be faced. Specifically, we have introduced a new data model, and new definitions of relational algebraic operators coping with the above issues, and we have studied their reducibility. Last, but not least, we have shown that our approach can be easily extended in order to cope with a general form of temporal indeterminacy. Such an extension further increases the applicability of our approach.

The traditional relational database model RDM is not effective for dealing with imprecise and uncertain data as it deals with precise and unambiguous data. Hence, Beaubouef et al. proposed the rough relational database model RRDM for the management of uncertainty in relational databases. Beaubouef et al. defined the corresponding rough relational operators in rough relational databases as in ordinary relational databases. And to give an effective measure of uncertainty in rough relational databases, they defined the rough relation entropy. In this paper, we further discuss the issues of relational operations and uncertainty measure in rough relational databases. We give some new definitions for rough relational operators and rough relation entropy in rough relational databases. Furthermore, we discuss the basic properties of rough relational operators and rough relation entropy, as well as the connections between rough relational operators and rough relation entropy.

In many languages, compounding is a fundamental process for the generation of novel words. When this process is productive (as, e.g., in English), native speakers can juxtapose two words to create novel compounds that can be readily understood by other speakers. The present paper proposes a large-scale, data-driven computational system for compound semantic processing based on distributional semantics, the CAOSS model (Compounding as Abstract Operation in Semantic Space). In CAOSS, word meanings are represented as vectors encoding their lexical co-occurrences in a reference corpus. Given two constituent words, their composed representation (the compound) is computed by using matrices representing the abstract properties of constituent roles (modifier vs. head). The matrices are also induced through examples of language usage. The model is then validated against behavioral results concerning the processing of novel compounds, and in particular relational effects on response latencies. The effects of relational priming and relational dominance are considered. CAOSS predictions are shown to pattern with previous results, in terms of both the impact of relational information and the dissociations related to the different constituent roles. The simulations indicate that relational information is implicitly reflected in language usage, suggesting that human speakers can learn these aspects from language experience and automatically apply them to the processing of new word combinations. The present model is flexible enough to emulate this procedure, suggesting that relational effects might emerge as a by-product of nuanced operations across distributional patterns.

Serving as an informal technical introduction to this Annals special issue on relational database management systems, this article gives an introductory overview of the relational model and discusses the value of Edgar F. (Ted) Codd's model. Then, after providing an account of Chris Date's contributions, the author assesses the relational model's effect on the industry and how it might affect future developments.

E.F. Codd developed his relational database concept within a community that was attempting to create a general-purpose machine for retrieving and reasoning with data. Rather than just making progress toward that goal, this article argues that Codd's accomplishment marked the end of that effort and traces the heritage of the relational database system as it relates to the concept of an information system.

Latent relational search is a novel entity retrieval paradigm based on the proportional analogy between two entity pairs. Given a latent relational search query {(Japan, Tokyo), (France, ?)}, a latent relational search engine is expected to retrieve and rank the entity “Paris” as the first answer in the result list. A latent relational search engine extracts entities and relations between those entities from a corpus, such as the Web. Moreover, from some supporting sentences in the corpus, (e.g., “Tokyo is the capital of Japan” and “Paris is the capital and biggest city of France”), the search engine must recognize the relational similarity between the two entity pairs. In cross-language latent relational search, the entity pairs as well as the supporting sentences of the first entity pair and of the second entity pair are in different languages. Therefore, the search engine must recognize similar semantic relations across languages. In this article, we study the problem of cross-language latent relational search between Japanese and English using Web data. To perform cross-language latent relational search in high speed, we propose a multi-lingual indexing method for storing entities and lexical patterns that represent the semantic relations extracted from Web corpora. We then propose a hybrid lexical pattern clustering algorithm to capture the semantic similarity between lexical patterns across languages. Using this algorithm, we can precisely measure the relational similarity between entity pairs across languages, thereby achieving high precision in the task of cross-language latent relational search. Experiments show that the proposed method achieves an MRR of 0.605 on Japanese-English cross-language latent relational search query sets and it also achieves a reasonable performance on the INEX Entity Ranking task.

Relational similarity can be defined as the similarity between two semantic relations R and R' that exist respectively in two word pairs (A,B) and (C,D). Relational search, a novel search paradigm that is based on the relational similarity between word pairs, attempts to find a word D for the slot ? in the query {(A,B), (C,?)} such that the relational similarity between the two word pairs (A, B) and (C, D) is a maximum. However, one problem frequently encountered by a Web-based relational search engine is that the inherent noise in Web text leads to incorrect measurement of relational similarity. To overcome this problem, we propose a method for verifying a relational search result that exploits the symmetric properties in proportional analogies. To verify a candidate result D for a query {(A, B), (C, ?)}, we replace the original question mark by D to create a new query {(A,B),(?,D)} and verify that we can retrieve C as a candidate for the new query. The score of C in the new query can be seen as a complementary score of D because it reflects the reliability of D in the original query. Moreover, transformations of words in proportional analogies lead to relational symmetries that can be utilized to accurately measure the relational similarity between two semantic relations. For example, if the two word pairs (A,B) and (C, D) show a high degree of relational similarity then the two word pairs (B,A) and (D,C) also have a high degree of relational similarity. We apply this idea in relational search by using symmetric queries such as {(B, A), (D, ?)} to create six queries for verifying a candidate answer D to improve the reliability of the verification process. Our experimental results on the Scholastic Aptitude Test (SAT) analogy benchmark show that the proposed method improves the accuracy of a relational search engine by a wide margin.

The theory of nominal sets is a theory for names, freshness and binders. It has recently been suggested as a framework for modelling local store because it allows for a more elementary development than the traditional presheaf models. However, when modelling the important principle of relational reasoning for local store all these models use families of relations indexed by relations on store, and thus essentially return to presheaf models on the relational level. In this paper we show how relational reasoning can also be modelled using nominal sets. Building on a model suggested by Pitts and Shinwell we construct a relational model for local store in nominal sets in which types are interpreted as relations. These relational interpretations of types capture, in a single relation for each type, the relational reasoning principle for local store which in previous models was captured using a family of relations for each type. The relational model also demonstrates how the relations constitute a model in their own right, which hopefully means that they can be used to construct better models. Using the relational model we construct a relational parametricity principle for the operation allocating local store, and we show how this implies the relational reasoning principle.

Integrating and querying data from heterogeneous sources is a hot research topic in database research field. The emergence of the Semantic Web brings new paradigm shift of computing in data integration research where data is heterogeneous and distributed. To solve the problem this paper proposes a semantic-based approach. A Semantic-based Heterogeneous Relational Data Integration System, called SHRDIS, is presented. In this system, ontology is used as the mediated schema for the representation of the data source semantics. SPARQL queries over global schema are rewritten into local SQL queries that can be executed on heterogeneous relational databases. The architecture and implementation of SHRDIS is illustrated in detail. The experiment results show that the SHRDIS system has nice performance and scalability.

Formal concept analysis (FCA) is a mathematical description and theory of concepts implied in formal contexts. And the current formal contexts of FCA aim to model the binary relations between individuals (objects) and attributes in the real world. In the real world we usually describe each individual by some attributes, which induces the relations between individuals and attributes. But there also exist many relations between individuals, for instance, the parent-children relation in a family. In this paper, to model the relations between individuals in the real world, we propose a new context - relational context for FCA, which contains a set U of objects and a binary relation r on U. Corresponding to the formal concepts in formal contexts, we present different kinds of relational concepts in relational contexts, which are the pairs of sets of objects. First we define the standard relational concepts in relational contexts. Moreover, we discuss the indirect relational concepts and negative relational concepts in relational contexts, which aim to concern the indirection and negativity of the relations in relational contexts, respectively. Finally, we define the hybrid relational concepts in relational contexts, which are the combinations of any two different kinds of relational concepts. In addition, we also discuss the application of relational contexts and relational concepts in the supply chain management field.

Properties of a relational framework synthesized over a set of semantically atomic predicates are analyzed. A relational framework is shown to be stable with respect to a modification in the basic predicate set. The stability, uniqueness, and completeness allow one to consider a relational framework as a universal "carrier" for object domains with arbitrary semantics.

Data refinement in a state-based language such as Z is defined using a relational model in terms of the behaviour of abstract programs. Downward and upward simulation conditions form a sound and jointly complete methodology to verify relational data refinements. On the other hand, refinement in a process algebra takes a number of different forms depending on the exact notion of observation chosen, which can include the events a system is prepared to accept or refuse.In this paper we continue our program of deriving relational simulation conditions for process algebraic refinement by defining further embeddings into our relational model: traces, completed traces, failure traces and extension.

Relational thinking plays a central role in human cognition. However, it is not known how children and adults acquire relational concepts and come to represent them in a form that is useful for the purposes of relational thinking (i.e., as structures that can be dynamically bound to arguments). The authors present a theory of how a psychologically and neurally plausible cognitive architecture can discover relational concepts from examples and represent them as explicit structures (predicates) that can take arguments (i.e., predicate them). The theory is instantiated as a computer program called DORA (Discovery Of Relations by Analogy). DORA is used to simulate the discovery of novel properties and relations, as well as a body of empirical phenomena from the domain of relational learning and the development of relational representations in children and adults.

This chapter examines each of Codd’s rules for a “fully relational” database design. The discussion presents practical reasons for adhering to the rules. It also looks at why, in some cases, the rules have to be extended to include developments in database technology since the rules were first published.

In the real world, many phenomena are time related and in the last three decades the database community has devoted much work in dealing with "time of facts" in databases. While many approaches incorporating time in the relational model have been already devised, most of them assume that the exact time of facts is known. However, this assumption does not hold in many practical domains, in which temporal indeterminacy of facts occurs. The treatment of valid-time indeterminacy requires in-depth extensions to the current relational approaches. In this paper, we propose a theoretically grounded approach to cope with this issue, overcoming the limitations of related approaches in the literature. In particular, we present a 1NF temporal relational model and propose a new temporal relational algebra to query it. We also formally study the properties of the new data model and algebra, thus granting that our approach is interoperable with pre-existent temporal and non-temporal relational approaches, and is implementable on top of them. Finally, we consider computational complexity, showing that only a limited overhead is added when moving from determinate to indeterminate time.

Now-related temporal data play an important role in many applications. Clifford et al.’s approach is a milestone to model the semantics of ‘now’ in temporal relational databases. Several relational representation models for now-related data have been presented; however, the semantics of such representations has not been explicitly studied. Additionally, the definition of a relational algebra to query now-related data is an open problem. We propose the first integrated approach that provides both a neat semantics for now-related data and a compact 1NF representation (data model and relational algebra) for them. Additionally, our approach also extends current approaches to consider (i) domains where it is not always possible to know when changes in the world are recorded in the database and (ii) now-related data with a bound on their persistency in the future. To do so, we explicitly model the notion of temporal indeterminacy in the future for now-related data. The properties of our approach are also analyzed both from a theoretical (semantic correctness and reducibility of the algebra) and from an experimental point of view. Experiments show that, despite the fact that our approach is a major extension to current temporal relational approaches, no significant overhead is added to deal with ‘now’.

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 the monotonic relational expressions of Sagiv and Yannakakis.

Relational algebra serves as the theoretical basis for database design and queries. This paper extends our efforts on fuzzy relational algebraic operations under a fuzzy relational data model, namely, extended-possibility-based model. With a more general setting of fuzzy relational algebraic operators, some properties of the operators are investigated including equivalent definitions and transformation rules of the operators. These properties are important and desirable for processing queries in an effective and efficient manner.

In recent years various proposals have been offered for increasing the richness of the relational data model by addressing specific user requirements, particularly with regard to structural and behavioral expressiveness. Although there have been some criticisms of the semantic limitations of the model, few proposals have emerged to address them. In this paper we propose an extension of the model to address some of the semantic limitations around the use of multi-face attributes in everyday activity. We present a formal discussion of multi-face attributes and suggest how they can be accommodated in the relational model and relational database software systems. The resulting model offers a higher-level expressiveness and will provide the user with increased flexibility in the input, output and storage of data, and the specification of queries. Finally we outline some of the implications for database design methods that emerge for the extension.

Calendars and periodicity play a fundamental role in many applications. Recently, some commercial databases started to support user-defined periodicity in the queries in order to provide "a human-friendly way of handling time" (see, e.g., TimeSeries in Oracle 8). On the other hand, only few relational data models support user-defined periodicity in the data, mostly using "mathematical" expressions to represent periodicity. In this paper, we propose a high-level "symbolic" language for representing user-defined periodicity which seems to us more human-oriented than mathematical ones, and we use the domain of Gadia's temporal elements in order to define its properties and its extensional semantics. We then propose a temporal relational model which supports user-defined "symbolic" periodicity (e.g., to express "on the second Monday of each month") in the validity time of tuples and also copes with frame times (e.g., "from 1/1/98 to 28/2/98"). We define the temporal counterpart of the standard operators of the relational algebra, and we introduce new temporal operators and functions. We also prove that our temporal algebra is a consistent extension of the classical (atemporal) one. Moreover, we define both a fully symbolic evaluation method for the operators on the periodicities in the validity times of tuples, which is correct but not complete, and semisymbolic one, which is correct and complete, and study their computational complexity.

According to relational database theory, solid foundation, and mature technology, various products have made it the first consideration for studying and storing massive data. But how to build an effective knowledge base which is based on the powerful storage and processing capability of relational database is not only one of the key issue for the research and application relating to knowledge engineering and intelligent system, but also is the technological bottleneck of how to turn knowledge management into application. In developing the query text data and content management application, there are some issues discovered with using the traditional method to retrieve content based on the contents of the title, author, and time to search. For instance, concerning a large amount of construction work on resources preparing, low query efficiency, and being unable to search out interrelated content and so on. In this paper, a relational model of semantic networks is given and a two-dimensional storage structure of relational data table based on the semantic network knowledge with practical examples is discussed. At the same time, this paper designs the stored procedure based on SQL language description; moreover its key searching skill lies in keywords and the connections among the keywords. The semantic network relational models, storage structure and query algorithm can solve the foregoing problems related to the knowledge or content management. That is to say it is used to inquire the contents of query system of laws and regulations, which gained excellent result. This technique is easy to require without specialized knowledge processing tool. Only a simple training can help people get hold on it.

Making data to be more connected is one of the goals of Semantic Technology. Therefore, relational data model as one of important data resource type, is needed to be mapped and converted to graph model. In this paper we focus in mapping and converting without semantically loss, by considering semantic abstraction of the real world, which has been ignored in some previous researches. As a graph schema model, it can be implemented in graph database or linked data in RDF/OWL format. This approach studies that relationship should be paid more attention in mapping and converting because, often be found a gap semantic abstraction during those processes. In our small experiment shows that our idea can map and convert relational model to graph model without semantically loss.

We propose an approach for designing an object-relational database. We inspect each case of semantic relationships (one-to-one, one-to-many, many-to-many and n -ary). For each of these cases we list the different solutions for implementation and propose some solutions. We also make a comparison with the relational data model. Our results can be applied to current RDBMS including object extensions (Oracle8, DB2-IBM, Informix…).

Many problems encountered when building applications of database systems involve the manipulation of models. By "model," we mean a complex structure that represents a design artifact, such as a relational schema, object-oriented interface, UML model, XML DTD, web-site schema, semantic network, complex document, or software configuration. Many uses of models involve managing changes in models and transformations of data from one model into another. These uses require an explicit representation of "mappings" between models. We propose to make database systems easier to use for these applications by making "model" and "model mapping" first-class objects with special operations that simplify their use. We call this capability model management.In addition to making the case for model management, our main contribution is a sketch of a proposed data model. The data model consists of formal, object-oriented structures for representing models and model mappings, and of high-level algebraic operations on those structures, such as matching, differencing, merging, selection, inversion and instantiation. We focus on structure and semantics, not implementation.

In this paper, we present the concept of relational patterns and our approach to extract them from multiple relational tables. Relational patterns are analogous to frequent itemsets extracted by the Apriori algorithm [R. Agrawal, H. Mannila, R. Srikant, H. Toivonen, A.I. Verkamo, Advances in Knowledge Discovery and Data Mining, AAAI Press, 1995.] in the case of a single table. However, for the multiple relational tables, relational patterns capture co-occurrences of attributes as well as the relationships between these attributes, which are essential to avoid information loss. We describe our experiences from a test-bed implementation of our approach on a real hospital's discharge abstract database. This process raised issues, which were then implemented in order to enhance an analyst's ability to explore patterns while preventing high diversity and abundance of available data from blurring subtle patterns of interest. Finally, we evaluate the usefulness of relational patterns in the context of the discharge abstract data as well in other possible domains.

An extended relational model without semantic ambiguity, called a semantic-ambiguity-free relational model, is proposed using fuzzy sets and the theory of possibility. The model features every attribute having a membership attribute whose value consists of a pair of values based on necessity and possibility measures. The membership attribute value of an attribute in a base relation is the degree to which the attribute value is compatible with integrity constraints imposed on the base relation. This clarifies the source of the membership attribute value. The model has no semantic ambiguity for interpreting membership attribute values, unlike models consisting of relations with membership attribute values attached to tuple values. We show the formulation of 8 operations - union, intersection, difference, Cartesian product, projection, join, selection, and quotient - consisting of relational algebra proposed by Codd for query processing. This approach shows how to prevent users from misinterpreting tuples in databases allowing imperfect information.

Software specifications often involve data structures with huge numbers of value, and consequently they cannot be checked using standard state exploration or model-checking techniques. Data structures can be expressed with binary relations, and operations over such structures can be expressed as formulae involving relational variables. Checking properties such as preservation of an invariant thus reduces to determining the validity of a formula or, equivalently, finding a model (of the formula's negation). A new method for finding relational models is presented. It exploits the permutation invariance of models—if two interpretations are isomorphic, then neither is a model, or both are—by partitioning the space into equivalence classes of symmetrical interpretations. Representatives of these classes are constructed incrementally by using the symmetry of the partial interpretation to limit the enumeration of new relation values. The notion of symmetry depends on the type structure of the formula; by picking the weakest typing, larger equivalence classes (and thus fewer representatives) are obtained. A more refined notion of symmetry that exploits the meaning of the relational operators is also described. The method typically leads to exponential reductions; in combination with other, simpler, reductions it makes automatic analysis of relational specifications possible for the first time.

Currently, most database management systems (DBMS) are based on the relational data model. Design methods that target relational models as the end product of logical design are generally based on the entity relationship model (ER) or semantic object model. Such methods entail developing an ER or semantic object representation followed by translation to the relational representation by the designer or by a CASE tool. However, there is no popular method that uses the relational concepts directly, that is, without an intermediate representation such as ER. Mathematically rigorous approaches using decomposition or synthesis do not seem to have been adopted by designers. When user views are complex, designers may encounter difficulty in the absence of an understandable method. This paper suggests a practical method for arriving at a normalized solution of user views.

We present a query language for similarity-based relational model of data with support of ordinal ranking and imperfect matches. The model utilized in this paper results from Codd's model of data by considering general residuated partially ordered scales of degrees of satisfaction in place of the two-element Boolean scale implicitly used in the Codd model. As a result, we look at the traditional relational model of data from the perspective of general scales allowing us to represent partial matches of relational queries. From the data representation point of view, the basic structures representing both the stored data and results of queries are so-called ranked data tables, generalizing the ordinary data tables (relations). Compared to other approaches dealing with ranking and imperfect matches, ours has several benefits: (i) it is based on solid logical foundations-we do not introduce an additional ranking module on top of the Codd model but have all the necessary concepts as an integral part of the model, (ii) the model is very general and several ranking procedures introduced in the past can be shown to be particular cases of our model, (iii) the model is not oriented just to query answering, it allows to handle similarity-based data dependencies, approximate constraints and other issues that cannot be properly formalized in the classic Codd model, (iv) despite of its generality, query execution in the model is tractable. In this paper, we present logical foundations of the query language and show how it implements the underlying similarity-based model of data.

Relational structure is important for various cognitive tasks, such as analogical transfer, but its role in learning of new relational concepts is poorly understood. This article reports two experiments testing people’s ability to learn new relational categories as a function of their relational structure. In Experiment 1, each stimulus consisted of 4 objects varying on 2 dimensions. Each category was defined by two binary relations between pairs of objects. The manner in which the relations were linked (i.e., by operating on shared objects) varied between subjects, producing 3 logically different conditions. In Experiment 2, each stimulus consisted of 4 objects varying on 3 dimensions. Categories were defined by three binary relations, leading to six logically different conditions. Various learning models were compared to the behavioral data, based on the theory of schema refinement. The results highlight several shortcomings of schema refinement as a model of relational learning: (1) it can make unreasonable demands on working memory, (2) it does not allow schemas to grow in complexity, and (3) it incorrectly predicts learning is insensitive to relational structure. We propose schema elaboration as an additional mechanism that provides a more complete account, and we relate this mechanism to previous proposals regarding interactions between analogy and representation construction. The current findings may advance understanding of the cognitive mechanisms involved in learning and representing relational concepts.

Although the relational model for databases provides a great range of advantages over other data models, it lacks a comprehensive way to handle incomplete and uncertain data. Uncertainty in data values, however, is pervasive in all real-world environments and has received much attention in the literature. Several methods have been proposed for incorporating uncertain data into relational databases. However, the current approaches have many shortcomings and have not established an acceptable extension of the relational model. In this paper, we propose a consistent extension of the relational model. We present a revised relational structure and extend the relational algebra. The extended algebra is shown to be closed, a consistent extension of the conventional relational algebra, and reducible to the latter.

Various temporal extensions to the relational model have been proposed. All of these, however, deviate significantly from the original relational model. This paper presents a temporal extension of the relational algebra that is not significantly different from the original relational model, yet is at least as expressive as any of the previous approaches. This algebra employs multidimensional tuple time-stamping to capture the complete temporal behavior of data. The basic relational operations are redefined as consistent extensions of the existing operations in a manner that preserves the basic algebraic equivalences of the snapshot (i.e., conventional static) algebra. A new operation, namely temporal projection, is introduced. The complete update semantics are formally specified and aggregate functions are defined. The algebra is closed, and reduces to the snapshot algebra. It is also shown to be at least as expressive as the calculus-based temporal query language TQuel. In order to assess the algebra, it is evaluated using a set of twenty-six criteria proposed in the literature, and compared to existing temporal relational algebras. The proposed algebra appears to satisfy more criteria than any other existing algebra.

We apply the established relational theory of stored data to the management of propositions in two-valued logic. Since the truth table for a propositional formula is a virtual relation, we can establish a correspondence between the relational algebra, as applied to the management of stored data, and the same algebra, as applied to the management of logical formulas. In doing so, we present a single comprehensive framework for the management of these two types of information.

Queries with vague qualifications are taking growing interests in various applications such as decision supporting systems and advice giving systems. To accomodate the vagueness handling capabilities into the widely used relational framework, Level-1 Fuzzy Relational Data Model(FRDM-1) has been proposed in [3]. In this paper, we generalize the model to acquire more practical usefulness. We also describe how non-fundamental relational operators such as join and division can have extended semantics in the proposed model.

Expression and processing of vagueness, which has many real world applications, are not handled effectively in the conventional relational data model. In this paper we investigate a fuzzy extension to the relational data model and propose three fuzzy relational query languages. Two of them are the Level-1 Fuzzy Relational Algebra and Level-1 Fuzzy Relational Calculus . They are fundamental query languages and serve as a theoretical framework for the fuzzy relational database. Finally, the Fuzzy Selective Relational Algebra is presented to express fuzzy constants and fuzzy comparators, which are more effective to represent vagueness in user queries. We show that the three proposed query languages have the same expressive powers. We also present various aspects of the proposed model and its functional advantages over the conventional relational data model.

This paper presents logical foundations for an extension of Codd's relational model of data which aims at utilizing various aspects of similarity in data processing. A need for development of solid foundations for such extensions, sometimes called similarity-based relational databases, has repeatedly been emphasized by leading database experts. This paper argues that, contrary to what may be perceived from the literature, solid foundations for similarity-based databases can be developed in a conceptually sound way. In this paper, we outline the foundations and propose two query systems for similarity-based databases: a domain relational calculus (DRC) and a relational algebra (RA). We compare the expressive power of DRC and RA in our model and prove relational completeness of RA over DRC. A major implication of the paper is that similarity-based data querying can be made an integral part of an extended, similarity-based, relational model of data which is based on first-order predicate logics using residuated structures of truth values in much the same way as the querying in the Codd's model is based on the classic first-order predicate logic.

In this paper we introduce the notion of a Temporal Relational Semantic System (TRSS) as a relational extension of a Temporal Conceptual Semantic System (TCSS) as defined by the author in 2007. TCSSs allow to represent states of distributed objects in concept lattices of specified views, the TRSSs enable the user to work in a conceptually simple way with arbitrary relational structures changing temporally. The flexible tools of conceptual scaling can now be applied also to relational structures. That yields for example a clear theoretical notion of the state of a temporal relation at some time granule. The main notions in TRSSs are visualized in some diagrams constructed from an example of a TRSS.

Relational search is a novel paradigm of search which focuses on the similarity between semantic relations. Given three words (A, B, C) as the query, a relational search engine retrieves a ranked list of words D, where a word D ∈ D is assigned a high rank if the relation between A and B is highly similar to that between C and D. However, if C and D has numerous co-occurrences, then D is retrieved by existing relational search engines irrespective of the relation between A and B. To overcome this problem, we exploit the symmetry in relational similarity to rank the result set D. To evaluate the proposed ranking method, we use a benchmark dataset of Scholastic Aptitude Test (SAT) word analogy questions. Our experiments show that the proposed ranking method improves the accuracy in answering SAT word analogy questions, thereby demonstrating its usefulness in practical applications.