Deductive Databases Research Articles

Space‐efficient data structures for the inference of subsumption and disjointness relations

AbstractConventional database systems function as static data repositories, storing vast amounts of facts and offering efficient query processing capabilities. The sheer volume of data these systems store has a direct impact on their scalability, both in terms of storage space and query processing time. Deductive database systems, on the other hand, require far less storage space since they derive new knowledge by applying inference rules. The challenge is how to efficiently obtain the required derivations, compared to having them in explicit form. In this study, we concentrate on a set of predefined inference rules for subsumption and disjointness relations, including their negations. We use compact data structures to store the facts and provide algorithms to support each type of relation, minimizing even further the storage space requirements. Our experimental findings demonstrate the feasibility of this approach, which not only saves space but is often faster than a baseline that uses well‐known graph traversal algorithms implemented on top of a traditional adjacency list representation to derive the relations.

Trilattice-Based Access Control Models: How to Secure Current Computer Network Mikhail

Designing security, from the hardware level, is essential to ensure the integrity of the intelligent cyberphysical infrastructure that is the Industrial Internet of Things (IIoT). If intelligent cyber-physical infrastructure fails to do the right things because it is insecure and vulnerable, then there will be negative social consequences [1]. Security is, in a sense, the access control to IIoT systems, which increasingly relies on the ability to compose different policies. Therefore, the advantage in any framework for compiling policies is that it is intuitive, formal, expressive, application-independent, as well as expandable to create domain-specific instances. Recently, such a scheme was proposed based on Belnap logic FOUR2 [2]. Four values of the Belnap bilattice have been interpreted as grant, deny, conflict, or unspecified with respect to access-control policy. Belnap's four-valued logic has found a variety of applications in various fields, such as deductive database theory, distributed logic programming, and other areas. However, it turns out that the truth order in FOUR2 is a truth-and-falsity order at the same time [3]. The smallest lattice, where the orders of truth and falsity are independent of each other, which is especially important for security policy, is that of Shramko-Wansing’s SIXTEEN3. This generalization is well-motivated and leads from the bilattice FOUR2 with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN3 with an information ordering together with a truth ordering and a (distinct) falsity ordering. Based on SIXTEEN3 and new Boolean predicates to control access [4], we define an expressive access-control policy language, having composition statements based on the statements of Schramko-Wansing’s logic. Natural orderings on politics are obtained by independent lifting the orders of truth and falsity of trilattice, which results in a query language in which conflict freedom analysis can be developed. The reduction of formal verification of queries to that on predicates over access requests enables to carry out policy analysis. We evaluate our approach through examples of control access model policy.

A neuro-symbolic system over knowledge graphs for link prediction

Neuro-Symbolic Artificial Intelligence (AI) focuses on integrating symbolic and sub-symbolic systems to enhance the performance and explainability of predictive models. Symbolic and sub-symbolic approaches differ fundamentally in how they represent data and make use of data features to reach conclusions. Neuro-symbolic systems have recently received significant attention in the scientific community. However, despite efforts in neural-symbolic integration, symbolic processing can still be better exploited, mainly when these hybrid approaches are defined on top of knowledge graphs. This work is built on the statement that knowledge graphs can naturally represent the convergence between data and their contextual meaning (i.e., knowledge). We propose a hybrid system that resorts to symbolic reasoning, expressed as a deductive database, to augment the contextual meaning of entities in a knowledge graph, thus, improving the performance of link prediction implemented using knowledge graph embedding (KGE) models. An entity context is defined as the ego network of the entity in a knowledge graph. Given a link prediction task, the proposed approach deduces new RDF triples in the ego networks of the entities corresponding to the heads and tails of the prediction task on the knowledge graph (KG). Since knowledge graphs may be incomplete and sparse, the facts deduced by the symbolic system not only reduce sparsity but also make explicit meaningful relations among the entities that compose an entity ego network. As a proof of concept, our approach is applied over a KG for lung cancer to predict treatment effectiveness. The empirical results put the deduction power of deductive databases into perspective. They indicate that making explicit deduced relationships in the ego networks empowers all the studied KGE models to generate more accurate links.

Towards a geometry deductive database prover

The Geometry Automated-Theorem-Provers (GATP) based on the deductive database method use a data-based search strategy to improve the efficiency of forward chaining. An implementation of such a method is expected to be able to efficiently prove a large set of geometric conjectures, producing readable proofs. The number of conjectures a given implementation can prove will depend on the set of inference rules chosen, the deductive database method is not a decision procedure. Using an approach based in an SQL database library and using an in-memory database, the implementation described in this paper tries to achieve the following goals. Efficiency in the management of the inference rules, the set of already known facts and the new facts discovered, by the use of the efficient data manipulation techniques of the SQL library. Flexibility, by transforming the inference rules in SQL data manipulation language queries, will open the possibility of meta-development of GATP based on a provided set of rules. Natural language and visual renderings, possible by the use of a synthetic forward chaining method. Implemented as an open source library, that will open its use by third-party programs, e.g. the dynamic geometry systems.

Special issue for the 36th Italian Conference on Computational Logic (CILC 2021)

This volume contains a selection of the papers presented at the |$36^{\textrm {th}}$|Italian Conference on Computational Logic (CILC 2021), held on September |$7^{\textrm {th}}$|–|$9^{\textrm {th}}$|⁠, |$2021$| in Parma, Italy. The Italian Conference on Computational Logic is the annual conference organized by the Group of researchers and Users of Logic Programming (GULP, www.programmazionelogica.it). Since the first event of the series, which took place in Genoa in |$1986$|⁠, the annual GULP conference represents a major opportunity for researchers and practitioners interested in computational logic to meet and exchange ideas. Furthermore, over the years, the conference broadened its horizons from logic programming to include related topics, such as declarative programming, formal verification of systems, knowledge representation, deductive databases and a wide range of applications in the broader area of Artificial Intelligence. The annual GULP conference is a traditional event of the Italian community of researchers and practitioners interested in logic programming, but its scope has become more and more international over the years. Despite the very peculiar situation caused by the COVID-19 pandemic, the community significantly responded to the call, thus allowing the technical program of CILC |$2021$| to feature |$23$| presentations of high-quality papers, of which |$19$| were original papers. This volume of the Journal of Logic and Computation contains extended and revised versions of a selection of the papers presented at CILC |$2021$|⁠. As a result of an additional review process, during which each submission was reviewed by three referees, |$8$| papers were accepted to be included in this volume. Accepted contributions range from foundations and theoretical results to practical experiences, case studies and applications. They cover a wide range of relevant topics related to computational logic in the broad sense, including agents and multi-agent systems, logic programming, runtime verification and healthcare. In the following, the featured papers are briefly summarized.

A Rule Based Theorem Prover: an Introduction to Proofs in Secondary Schools

The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers and the normal practice of conjecturing and proving in schools is a major barrier to a wider use of such tools in an educational environment. Since the early implementations of geometry automated theorem provers, applications of artificial intelligence methods, synthetic provers based on inference rules and using forward chaining reasoning are considered to be more suited for education proposes. Choosing an appropriate set of rules and an automated method that can use those rules is a major challenge. We discuss one such rule set and its implementation using the geometry deductive databases method (GDDM). The approach is tested using some chosen geometric conjectures that could be the goal of a 7th year class (approx. 12-year-old students). A lesson plan is presented, its goal is the introduction of formal demonstration of proving geometric theorems, trying to motivate students to that goal

Deductive databases in four-valued logic: rule semantics and models

Abstract In this paper, we investigate rule semantics for deductive databases in the context of four-valued logic. In our approach, a database is a pair $\varDelta =(E,R)$, where $E$ is a set of pairs, each pair associating a ground fact with a truth value (thus, allowing to store true, false or inconsistent facts) and $R$ is a set of rules generalizing standard Datalog rules in the following sense: (i) the head of a rule can be a positive or a negative atom and (ii) the body can involve any among the connectors of four-valued logic. We define the database semantics as the least fixed point of a monotonic operator and we compare this semantics with that of k-existential programs defined by Fitting and paraconsistent extended logic programs defined by Arieli. Our main contribution is to show that, if we consider rules as implications (i.e. if we view the database as a set of formulas) then the semantics of the database is the unique minimal model of the set of database formulas. Here, minimality is understood with respect to the knowledge ordering of four-valued logic satisfying a monotonicity property whereby the truth value of the head of an instantiated rule is greater than that of the body. Moreover, we characterize databases having finite semantics and then, we address the issue of database updating. We argue that our approach allows for a new kind of updates, in which the update result depends not only on the fact involved in the update but also on its current truth value in the database.

60 років базам даних (частина третя)

The article provides an overview of research and development of databases since their appearance in the 60s of the last century to the present time. The following stages are distinguished: the emergence formation and rapid development, the era of relational databases, extended relational databases, post-relational databases and big data. At the stage of formation, the systems IDS, IMS, Total and Adabas are described. At the stage of rapid development, issues of ANSI/X3/SPARC database architecture, CODASYL proposals, concepts and languages of conceptual modeling are highlighted. At the stage of the era of relational databases, the results of E. Codd’s scientific activities, the theory of dependencies and normal forms, query languages, experimental research and development, optimization and standardization, and transaction management are revealed. The extended relational databases phase is devoted to describing temporal, spatial, deductive, active, object, distributed and statistical databases, array databases, and database machines and data warehouses. At the next stage, the problems of post-relational databases are disclosed, namely, NOSQL-, NewSQL- and ontological databases. The sixth stage is devoted to the disclosure of the causes of occurrence, characteristic properties, classification, principles of work, methods and technologies of big data. Finally, the last section provides a brief overview of database research and development in the Soviet Union.

Aggregate Semantics for Propositional Answer Set Programs

AbstractAnswer set programming (ASP) emerged in the late 1990s as a paradigm for knowledge representation and reasoning. The attractiveness of ASP builds on an expressive high-level modeling language along with the availability of powerful off-the-shelf solving systems. While the utility of incorporating aggregate expressions in the modeling language has been realized almost simultaneously with the inception of the first ASP solving systems, a general semantics of aggregates and its efficient implementation have been long-standing challenges. Aggregates have been proposed and widely used in database systems, and also in the deductive database language Datalog, which is one of the main precursors of ASP. The use of aggregates was, however, still restricted in Datalog (by either disallowing recursion or only allowing monotone aggregates), while several ways to integrate unrestricted aggregates evolved in the context of ASP. In this survey, we pick up at this point of development by presenting and comparing the main aggregate semantics that have been proposed for propositional ASP programs. We highlight crucial properties such as computational complexity and expressive power, and outline the capabilities and limitations of different approaches by illustrative examples.

A Survey of the Proof-Theoretic Foundations of Logic Programming

AbstractSeveral formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this article, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract data types. Term-level bindings are another kind of abstraction, and these are given an elegant and direct treatment within both proof theory and these extended logic programming languages. Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs. These recent results provide a high-level means for presenting the differences between forward-chaining and backward-chaining style inferences. Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking.

Design and Implementation of EFSC Algorithm for Hybrid Representation of Distributed Databases

In distributed database management systems, fragmenting base connections increases concurrency and hence system throughput for query processing. User queries use hybrid fragmentation methods focused on vector bindings, and deductive database implementations lack query-access-rule dependence. As a result, for hierarchical deductive information implementations, a hybrid fragmentation solution is used. The method considers the horizontal partition of base relations based on the bindings placed on user requests, then produces vertical fragments of the horizontally partitioned relations, and finally clusters rules based on attribute affinity and query and rule access frequency. The suggested fragmentation approach makes distributed deductive database structures easier to develop.

Application of first-order logic to identify organizers and perpetrators of illegal actions in teams of a limited circle of people

There are three main families of inference algorithms in first-order logic: direct inference and its application to deductive databases and production systems; backward inference procedures and logic programming systems; theorem proving systems based on the resolution method. When solving specific problems, the most effective algorithms are those that allow you to cover all the facts and axioms and must be taken into account in the process of inference. An example is considered in which it is necessary to prove the guilt of a person in murder. On the basis of statements, a knowledge base is formed from expressions, with the help of which an expression of first-order logic is compiled and proved using direct logical inference. The proof of the reasoning obtained in direct inference using the proof tree is given. However, direct inference provides for the implementation of all admissible stages of logical inference based on all known facts. The article also considers a method based on the resolution when implementing the reverse inference, taking into account the expression obtained in the direct inference. This expression is converted into a conjunctive normal formula using the laws of Boolean algebra and is proved by the elimination of events using the conjunction operation.

Introduction to Logic Programming

Logic Programming is a style of programming in which programs take the form of sets of sentences in the language of Symbolic Logic. Over the years, there has been growing interest in Logic Programming due to applications in deductive databases, automated worksheets, Enterprise Management (business rules), Computational Law, and General Game Playing. book introduces Logic Programming theory, current technology, and popular applications. this volume, we take an innovative, model-theoretic approach to logic programming. We begin with the fundamental notion of datasets, i.e., sets of ground atoms. Given this fundamental notion, we introduce views, i.e., virtual relations; and we define classical logic programs as sets of view definitions, written using traditional Prolog-like notation but with semantics given in terms of datasets rather than implementation. We then introduce actions, i.e., additions and deletions of ground atoms; and we define dynamic logic programs as sets of action definitions. addition to the printed book, there is an online version of the text with an interpreter and a compiler for the language used in the text and an integrated development environment for use in developing and deploying practical logic programs. This is a book for the 21st century: presenting an elegant and innovative perspective on logic programming. Unlike other texts, it takes datasets as a fundamental notion, thereby bridging the gap between programming languages and knowledge representation languages; and it treats updates on an equal footing with datasets, leading to a sound and practical treatment of action and change. – Bob Kowalski, Professor Emeritus, Imperial College London In a world where Deep Learning and Python are the talk of the day, this book is a remarkable development. It introduces the reader to the fundamentals of traditional Logic Programming and makes clear the benefits of using the technology to create runnable specifications for complex systems. – Son Cao Tran, Professor in Computer Science, New Mexico State University Excellent introduction to the fundamentals of Logic Programming. The book is well-written and well-structured. Concepts are explained clearly and the gradually increasing complexity of exercises makes it so that one can understand easy notions quickly before moving on to more difficult ideas. – George Younger, student, Stanford University

Proving semantic properties as first-order satisfiability

The semantics of computational systems (e.g., relational and knowledge data bases, query-answering systems, programming languages, etc.) can often be expressed as (the specification of) a logical theory Th. Queries, goals, and claims about the behavior or features of the system can be expressed as formulas φ which should be checked with respect to the intended model of Th, which is often huge or even incomputable. In this paper we show how to prove such semantic properties φ of Th by just finding a modelA of Th∪{φ}∪Zφ, where Zφ is an appropriate (possibly empty) theory depending on φ only. Applications to relational and deductive databases, rewriting-based systems, logic programming, and answer set programming are discussed.

BigData Applications from Graph Analytics to Machine Learning by Aggregates in Recursion

In the past, the semantic issues raised by the non-monotonic nature of aggregates often prevented their use in the recursive statements of logic programs and deductive databases. However, the recently introduced notion of Pre-mappability (PreM) has shown that, in key applications of interest, aggregates can be used in recursion to optimize the perfect-model semantics of aggregate-stratified programs. Therefore we can preserve the declarative formal semantics of such programs while achieving a highly efficient operational semantics that is conducive to scalable implementations on parallel and distributed platforms. In this paper, we show that with PreM, a wide spectrum of classical algorithms of practical interest, ranging from graph analytics and dynamic programming based optimization problems to data mining and machine learning applications can be concisely expressed in declarative languages by using aggregates in recursion. Our examples are also used to show that PreM can be checked using simple techniques and templatized verification strategies. A wide range of advanced BigData applications can now be expressed declaratively in logic-based languages, including Datalog, Prolog, and even SQL, while enabling their execution with superior performance and scalability.

Information and Education Systems in the Context of Digitalization of Education

The article describes the changes in the modern socio-economic environment, which affect the digitalization of society, including the socio-educational sphere. On the basis of the authors’ proposals for the development of the concept of “information-educational systems”, mathematical models for their description and mechanisms for analysing their essential characteristics determined by modern processes of development and digitalization of society are indicated. Through the example of using elements of the theory of dynamic deductive databases and the theory of neural networks, the article describes mathematical models that adequately reflect strategies for the development of people and stable small groups, as well as large dynamic human communities, on the basis of which recommendations are proposed for developing such strategies. The results can be used in the pedagogical design of various models of educational activities and information and educational systems for various purposes, including education management and direct training. It also seems that the mechanisms and features of information and educational systems described in the article will allow us to establish an evidence-based educational policy at various levels in the context of digitalization

Partial Compilation of ASP Programs

AbstractAnswer Set Programming (ASP) is a well-known declarative formalism in logic programming. Efficient implementations made it possible to apply ASP in many scenarios, ranging from deductive databases applications to the solution of hard combinatorial problems. State-of-the-art ASP systems are based on the traditional ground&solve approach and are general-purpose implementations, i.e., they are essentially built once for any kind of input program. In this paper, we propose an extended architecture for ASP systems, in which parts of the input program are compiled into an ad-hoc evaluation algorithm (i.e., we obtain a specific binary for a given program), and might not be subject to the grounding step. To this end, we identify a condition that allows the compilation of a sub-program, and present the related partial compilation technique. Importantly, we have implemented the new approach on top of a well-known ASP solver and conducted an experimental analysis on publicly-available benchmarks. Results show that our compilation-based approach improves on the state of the art in various scenarios, including cases in which the input program is stratified or the grounding blow-up makes the evaluation unpractical with traditional ASP systems.

A Logic Framework for P2P Deductive Databases

AbstractThis paper presents a logic framework for modeling the interaction among deductive databases in a peer-to-peer (P2P) environment. Each peer joining a P2P systemprovides or imports datafrom its neighbors by using a set ofmapping rules, that is, a set of semantic correspondences to a set of peers belonging to the same environment. By using mapping rules, as soon as it enters the system, a peer can participate and access all data available in its neighborhood, and through its neighborhood it becomes accessible to all the other peers in the system. A query can be posed to any peer in the system and the answer is computed by using locally stored data and all the information that can be consistently imported from the neighborhood. Two different types of mapping rules are defined: mapping rules allowing to import a maximal set of atoms not leading to inconsistency (calledmaximal mapping rules) and mapping rules allowing to import a minimal set of atoms needed to restore consistency (calledminimal mapping rules). Implicitly, the use of maximal mapping rules statesit is preferable to import as long as no inconsistencies arise; whereas the use of minimal mapping rules states thatit is preferable not to import unless a inconsistency exists. The paper presents three different declarative semantics of a P2P system: (i) theMax Weak Model Semantics, in which mapping rules are used to importas much knowledge as possiblefrom a peer’s neighborhood without violating local integrity constraints; (ii) theMin Weak Model Semantics, in which the P2P system can be locally inconsistent and the information provided by the neighbors is used to restore consistency, that is, to only integrate the missing portion of a correct, but incomplete database; (iii) theMax-Min Weak Model Semanticsthat unifies the previous two different perspectives captured by the Max Weak Model Semantics and Min Weak Model Semantics. This last semantics allows to characterize each peer in the neighborhood as a resource used either to enrich (integrate) or to fix (repair) the knowledge, so as to define a kind ofintegrate–repairstrategy for each peer. For each semantics, the paper also introduces an equivalent and alternative characterization, obtained by rewriting each mapping rule into prioritized rules so as to model a P2P system as a prioritized logic program. Finally, results about the computational complexity of P2P logic queries are investigated by consideringbraveandcautiousreasoning.

Incorporating Stratified Negation into Query-Subquery Nets for Evaluating Queries to Stratified Deductive Databases

Most of the previously known evaluation methods for deductive databases are either breadth-first or depth-first (and recursive). There are cases when these strategies are not the best ones. It is desirable to have an evaluation framework for stratified DatalogN that is goal-driven, set-at-a-time (as opposed to tuple-at-a-time) and adjustable w.r.t. flow-of-control strategies. These properties are important for efficient query evaluation on large and complex deductive databases. In this paper, by incorporating stratified negation into so-called query-subquery nets, we develop an evaluation framework, called QSQNSTR, with such properties for evaluating queries to stratified DatalogN databases. A variety of flow-of-control strategies can be used for QSQNSTR. The generic evaluation method QSQNSTR for stratified DatalogN is sound, complete and has a PTIME data complexity.

A Fuzzy Datalog Deductive Database System

This paper describes a proposal for a deductive database system with fuzzy Datalog as its query language. Concepts supporting the fuzzy logic programming system Bousi~Prolog are tailored to the needs of the deductive database system DES. We develop a version of fuzzy Datalog where programs and queries are compiled to the DES core Datalog language. Weak unification and weak SLD resolution are adapted for this setting, and extended to allow rules with truth degree annotations. We provide a public implementation in Prolog, which is open source, multiplatform, portable, and in-memory, featuring a graphical user interface. A distinctive feature of this system is that, unlike others, we have formally demonstrated that our implementation techniques fit the proposed operational semantics. We also study the efficiency of these implementation techniques through a series of detailed experiments. Moreover, a database example for a recommender system is used to illustrate some of the features of the system and its usefulness.