An alternative approach to the semantics of disjunctive logic programs and deductive databases

In this paper, we study a new semantics of logic programming and deductive databases. Thepossible model semantics is introduced as a declarative semantics of disjunctive logic programs. The possible model semantics is an alternative theoretical framework to the classical minimal model semantics and provides a flexible inference mechanism for inferring negation in disjunctive logic programs. We also present a proof procedure for the possible model semantics and show that the possible model semantics has an advantage from the computational complexity point of view.This is a revised and extended version of the paper [36] which was presented at the Tenth International Conference on Logic Programming, Budapest, 21–25 June 1993.     

Ordered model trees: A normal form for disjunctive deductive databases

Model trees were conceived as a structure-sharing approach to represent information in disjunctive deductive databases. In this paper we introduce the concept ofordered minimal model trees as a normal form for disjunctive deductive databases. These are model trees in which an order is imposed on the elements of the Herbrand base. The properties of ordered minimal model trees are investigated as well as their possible utilization for efficient manipulation of disjunctive deductive databases. Algorithms are presented for constructing and performing operations on ordered model trees. The complexity of ordered model tree processing is addressed. Model forests are presented as an approach to reduce the complexity of ordered model tree construction and processing.This research was supported by the National Science Foundation, under the grant Nr. IRI-89-16059, the Air Force Office of Scientific Research, under the grant Nr. AFOSR-91-0350, and the Fulbright Scholar Program.This work was done while visiting at the University of Maryland Institute for Advanced Computer Studies.     

Coping with indefinite and negative data in deductive databases: A survey

A problem with current database systems is the limitation placed on the type of data which may be represented and manipulated within such systems. In an attempt to broaden this to a wider class of data (i.e. rules as well as facts) and a more powerful set of manipulations, the concept of a deductive database was introduced. However, for the sake of efficiency the type of rule which is allowed in a deductive database is restricted in form. This paper surveys a number of attempts to move towards less restrictive forms of rules in deductive databases which allow indefinite and negative data to be handled.     

Closed world assumption for disjunctive reasoning

In this paper,the relationship between argumentation and closed world reasoning for disjunctive information is studied.In particular,the authors propose a simple and intuitive generalization of the closed world assumption(CWA) for general disjunctive deductive databases(with default negation).This semantics,called DCWA,allows a natural argumentation-based interpretation and can be used to represent reasoning for disjunctive information.We compare DCWA with GCWA and prove that DCWA extends Minker‘s GCWA to the class of disjunctive databases with defacult negation.Also we compare our semantics with some related approaches.In addition,the computational complexity of DCWA is investigated.     

析取封闭世界假设的一种过程语义

析取信息的表示是一个重要的研究问题.DCWA(析取封闭假设)为一般演绎数据库提供了一种谨慎语义,并且扩充了标准的良基语义.同时DCWA支持争论推理,为广义封闭世界假设提供了一种逼近.基于此,提出了DCWA的过程语义,并证明了它的可靠性和完备性.     

Deduction in non-Horn databases

The class of non-Horn, function-free databases is investigated and several aspects of the problem of using theorem proving techniques for such databases are considered. This includes exploring the treatment of negative information and extending the existing method, suggested by Minker, to accept non-unit negative clauses. It is shown that the algorithms based on the existing methods for the treatment of negative information can be highly inefficient. An alternative approach is suggested and a simpler algorithm based on it is given. The problems associated with query answering in non-Horn databases are addressed and compared with those for the Horn case. It is shown that the query evaluation process can be computationaly difficult in the general case. Conditions under which the process is simplified are discussed. The topic of non-Horn general laws is considered and some guidelines are suggested to divide such laws into derivation rules and integrity constraints. The effect of such a division on the query evaluation process is discussed.     

View updates in stratified disjunctive databases

The view update problem is considered in the context of deductive databases where the update of an intensional predicate is accomplished by modifying appropriately the underlying relations in the extensional database. Two classes of disjunctive databases are considered. The first class contains those disjunctive databases which allow only definite rules in the intensional database and disjunctive facts in the extensional database. The second class contains stratified disjunctive databases so that in addition to the first class, negation is allowed in the bodies of the rules, but the database must be stratified. Algorithms are given both for the insertion of an intensional predicate into and the deletion of an intensional predicate from the database. The algorithms use SLD resolution and the concept of minimal models of the extensional database. The algorithms are proved to be correct and best according to the criterion of causing minimal change to the database, where we give first priority to minimizing deletions.Research supported by the National Science Foundation under grant numbers IRI-8916059, IRI-8921591, IRI-9200898, and IRI-9210220.     

Protecting databases from inference attacks

This paper presents a model of database inference and a taxonomy of inference detection approaches. The Merlin inference detection system is presented as an example of an automated inference analysis tool that can assess inference vulnerabilities using the schema of a relational database. A manual inference penetration approach is then offered as a means of detecting inferences that involve instances of data or characteristics of groups of instances. These two approaches are offered as practical approaches that can be applied today to address the database inference problem. The final section discusses future directions in database inference research.     

An Extension to GCWA and Query Evaluation for Disjunctive Deductive Databases

We present a simple and intuitive extension GCWA^G of the generalized closed world assumption (GCWA) from positive disjunctive deductive databases to general disjunctive deductive databases (with default negation). This semantics is defined in terms of unfounded sets and possesses an argumentation-theoretic characterization. We also provide a top-down procedure for GCWA^G, which is sound and complete with respect to GCWA^G. We investigate two query evaluation methods for GCWA^G: database partition, and database splitting. The basic idea of these methods is to divide the original deductive database into several smaller sub-databases and the query evaluation in the original database is transformed into the problem of query evaluation in smaller or simplified components. We prove that these two methods of query evaluation are all sound with respect to GCWA^G.     

Minimal model generation for refined answering of generalized queries in disjunctive deductive databases

Generalized queries are defined as sets of clauses in implication form. They cover several tasks of practical importance for database maintenance such as answering positive queries, computing database completions and integrity constraints checking. We address the issue of answering generalized queries under the minimal model semantics for the class of disjunctive deductive databases (DDDBs). The advanced approach is based on having the query induce an order on the models returned by a sound and complete minimal model generating procedure. We consider answers that are true in all and those that are true in some minimal models of the theory. We address the issue of answering positive queries through the construction of the minimal model state of the DDDB, using a minimal model generating procedure. The refinements allowed by the procedure include isolating a minimal component of a disjunctive answer, the specification of possible updates to the theory to enable the derivability of certain queries and deciding the monotonicity properties of answers to different classes of queries.     

Interpreting disjunctive logic programs based on a strong sense of disjunction

This paper studies a strong form of disjunctive information in deductive databases. The basic idea is that a disjunctionA B should be considered true only in the case when neitherA norB can be inferred, but the disjunctionA B is true. Under this interpretation, databases may be inconsistent. For those databases that are consistent, it is shown that a unique minimal model exists. We study a fixpoint theory and present a sound and complete proof procedure for query processing in consistent databases. For a class of inconsistent databases, we obtain a declarative semantics by selecting an interpretation that maximizes satisfaction, and minimizes indefiniteness. Two notions of negation are introduced.     

Bottom-up Evaluation of Datalog with Negation

Declarative semantics gives the meaning of a logic program in terms of properties,while the procedural semantics gives the meaning in terms of the execution or evaluation of the program.From the database point of view,the procedural semantics of the program is equally important.This paper focuses on the study of the bottom-up evaluation of the WFM semantics of datalog‘ programs.To compute the WFM,first,the stability transformation is revisited,and a new operator Op and its fixpoint are defined. Based on this,a fixpoint semantics,called oscillating fixpoint model semantics,is defined.Then,it is shown that for any datalog‘ program the oscillating fixpoint model is identical to its WFM.So,the oscillating fixpoint model can be viewed as an alternative (constructive) definition of WFM.The underlying operation (or transformation) for reaching the oscillating fixpoint provides a potential of bottom-up evaluation.For the sake of computational feasibility,the strongly range-restricted program is considered,and an algorithm used to compute the oscillating fixpoint is described.     

On computing minimal and perfect model membership

The computational complexity of a number of problems relating to minimal models of non-Horn deductive databases is considered. In particular, the problem of determining minimal model membership is shown to be NP-complete for non recursive propositional databases. The structure of minimal models is also examined using the notion of a cyclic tree, and methods of determining minimal model membership, minimality of models and compiling the GCWA are presented. The handling of negative premises is also considered using perfect model semantics, and methods for computing perfect model membership are presented.     

Protecting deductive databases from unauthorized retrieval and update requests

We show how deductive databases may be protected against unauthorized retrieval and update requests issued by authenticated users. To achieve this protection, a deductive database is expressed in a form that guarantees that only authorized access requests are permitted. Authorized retrieval and update requests are specified by using an access control theory that is expressed in normal clause logic. The approach has a number of attractive technical results associated with it, can be efficiently implemented, and can be used to protect the information in any normal deductive database.     

Inference by generating in deductive databases

A method, APEX, for query evaluation in deductive databases presented in this work is based on discovering of axioms and facts relevant to a given query. The notion of relevancy and migration of facts is derived from an analysis of data flow in the system. APEX is complete, and incorporates efficient query evaluation heuristics. Operation of APEX is illustrated by sample databases involving non-linear recursive axioms and cyclic relations. Main virtues of the method are its generality and adaptivity: it imposes no restrictions on the structure of axioms or the contents of relations, and it employs the knowledge of the actual data acquired at each step of a query evaluation.     

Selection propagation in deductive databases from pushing selections to magic sets

This paper discusses the relationship between two optimization methods in deductive databases: the distribution of selections and the magic sets method. The former is a direct generalization of pushing selections in relational databases, and the latter realizes a more general view of selection propagation. The characteristics of the generalized form of the distribution of selections are discussed and compared to other methods. It is shown that the distribution of selections corresponds to one of the least effective variations of the magic sets method. It is also shown that both methods have essentially the same power for non-recursive queries. Hence, the magic sets method can be regarded as a natural generalization of pushing selections in relational databases.     

从合取范式到析取范式的转换研究

为了解决粗糙集分辨函数的计算、概念格中内涵缩减的计算、逻辑程序设计的规则简化等问题,抽象出了从合取范式到析取范式转换这一核心问题。提出了利用极小覆盖来实现从合取范式到析取范式的转换,给出了一个增量式的算法。为了扩大范式转换的使用范围,定义了伪合取范式,并给出伪合取范式到析取范式的转换方法。     

逻辑数据库中参数化CWAs问题研究

闭世界假设（ＣＷＡｓ）是逻辑数据库中一类主要的隐含完备．本文给出了一种参数化ＣＷＡ的一般定义,使用这种参数化定义,已知的以及新的ＣＷＡｓ可作为特殊情况推导出,并可对数据库完备的概念进行更有效的描述．