Top-Down Query Processing in First-Order Deductive Databases under the DWFS

A top-down query-processing method for first-order deductive databases under the disjunctive well-founded semantics (DWFS) is presented. The method is based on a characterization of the DWFS in terms of the Gelfond–Lifschitz transformation and employs a hyperresolution-like operator and quasi-cyclic trees to handle minimal model processing. The method is correct and complete and can be guaranteed to terminate given certain mild constraints on the format of database rules. The efficiency of the method is enhanced by the fact that large parts of the search tree are naturally grounded, even for first-order queries and databases. In the case of a grounded yes/no answer, the search tree becomes nongrounded only if processing enters the definite part of the database. For finite propositional databases the method runs in polynomial space. Efficiency may be enhanced by the application of partial compilation.     

COMPUTING PERFECT AND STABLE MODELS USING ORDERED MODEL TREES

Ordered model trees were introduced as a normal form for disjunctive deductive databases. They were also used to facilitate the computation of minimal models for disjunctive theories by exploiting the order imposed on the Herbrand base of the theory. In this work we show how the order on the Herbrand base can be used to compute perfect models of a disjunctive stratified finite theory. We are able to compute the stable models of a general finite theory by combining the order on the elements of the Herbrand base with previous results that had shown that the stable models of a theory T can be computed as the perfect models of a corresponding disjunctive theory ɛ T resulting from applying the so called evidential transformation to T. While other methods consider many models that are rejected at the end, the use of atom ordering allows us to guarantee that every model generated belongs to the class of models being computed. As for negation-free databases, the ordered tree serves as the canonical representation of the database.     

Dynamic maintenance of the transitive closure in disjunctive graphs

We propose an approach with feasible space requirement to maintain the transitive closure of a class of hypergraphs called OR-graphs. OR-graphs are equivalent to disjunctive deductive databases where disjunctions are limited to one attribute in each OR-table. It has been shown that query processing in disjunctive deductive databases grows into CoNP with very simple examples, but few attempts have been made, as is done in this paper, to obtain classes of disjunctive databases and queries for which efficient algorithms exist. Polynomial time algorithms are presented to compute the transitive closure of OR-graphs and to handle dynamic insertions and deletions. With algorithms for insertions and deletions, we provide a simple but efficient technique to solve the failure set problem in reliability models, which is equivalent to finding the closure of an arbitrary non-empty set of simple nodes. We also show that a minimal extension to OR-graphs makes the computational complexity of the transitive closure CoNP-complete.Research supported in part by NSF under IRI-9210220 and IRI-9111988, Omron Corporation and Omron Management Center of America.     

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.     

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.     

Model theoretic approach to view updates in deductive databases

The view update problem for deductive databases has been defined as the problem of accomplishing the update of an intensional predicate by modifying appropriately the extensional database. A previous paper by Grant, Horty, Lobo, and Minker developed algorithms for the insertion and the deletion of an intensional predicate in certain important classes of stratified disjunctive deductive databases. This paper introduces a model theoretic approach which encompasses a wide class of Herbrand semantics, including the perfect model and stable model semantics, for disjunctive databases including negation. This generalizes the earlier results: now the intensional database may contain disjunctive and denial rules, and the database may be required to satisfy integrity constraints. As in the previous paper, the algorithms are proved to be correct and best according to the criterion of causing minimal change to the database, where the first priority is to minimize deletions.     

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.     

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.     

Computing Only Minimal Answers in Disjunctive Deductive Databases

A method is presented for computing minimal answers of the form in disjunctive deductive databases under the disjunctive stable model semantics. Such answers are constructed by repeatedly extending partial answers. Our method is complete (in that every minimal answer can be computed) and does not admit redundancy (in the sense that every partial answer generated can be extended to a minimal answer), thus no non-minimal answer is generated. The method does not (necessarily) require the computation of models of the database in their entirety. A partitioning of the database into extensional and intensional components is employed in order to overcome the problems caused by the possible non-existence of disjunctive stable models, and a form of compilation is presented as a means of simplifying and improving the efficiency of the run-time computation, which then reduces to relatively trivial processing within the extensional database. In addition, the output from this compilation process has the significant advantage of being immune to updates to the extensional database. Other forms of database pre-processing are also considered, and three transformations are presented mapping a database onto an equivalent positive database, non-disjunctive database, and set of conditional facts.     

Duality for Goal-Driven Query Processing in Disjunctive Deductive Databases

Bottom-up query-answering procedures tend to explore a much larger search space than what is strictly needed. Top-down processing methods use the query to perform a more focused search that can result in more efficient query answering. Given a disjunctive deductive database, DB, and a query, Q, we establish a strong connection between model generation and clause derivability in two different representations of DB and Q. This allows us to use a bottom-up procedure for evaluating Q against DB in a top-down fashion. The approach requires no extensive rewriting of the input theory and introduces no new predicates. Rather, it is based on a certain duality principle for interpreting logical connectives. The duality transformation is achieved by reversing the direction of implication arrows in the clauses representing both the theory and the negation of the query. The application of a generic bottom-up procedure to the transformed clause set results in top-down query answering. Under favorable conditions efficiency gains are substantial, as shown by our preliminary testing. We give the logical meaning of the duality transformation and point to the conditions and sources of improved efficiency. We show how the duality approach can be used for refined query answering by specifying the minimal conditions (weakest updates) to DB under which Q becomes derivable. This is shown to be useful for view updates in disjunctive deductive databases as well as for other interesting applications.     

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.     

Extending Datalog with Declarative Updates

The semantics of static deductive databases is well understood based on the work in logic programming. In the past decade, various methods to incorporate update constructs into logic programming and deductive databases have been proposed. However, there is still no consensus about the appropriate treatment of dynamic behavior in deductive databases. In this paper, we propose a language called DatalogU, which is a minimal but powerful extension of Datalog with updates to base relations. DatalogU allows the user to program set-oriented complex database transactions with concurrent, disjunctive and sequential update operations in a simple and direct way. It has a simple and intuitive declarative semantics that naturally accounts for set-oriented updates in deductive databases.     

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.     

On the Computation of the Disjunctive Well-Founded Semantics

A characterization of the disjunctive well-founded semantics (DWFS) is given in terms of the Gelfond–Lifschitz transformation. This characterization is used to develop a top-down method of testing DWFS membership, employing a hyperresolution-like operator and quasi-cyclic trees to handle minimal model processing. A flexible bottom-up method of computing the DWFS is also given that admits the use of a powerful reduction operator. For finite propositional databases, all of our methods run in polynomial space.     

Sturmian Trees

We consider Sturmian trees as a natural generalization of Sturmian words. A Sturmian tree is a tree having n+1 distinct subtrees of height n for each n. As for the case of words, Sturmian trees are irrational trees of minimal complexity.     

On the partial semantics for disjunctive deductive databases

Partial stable models for deductive databases, i.e., normal function-free logic programs (also called datalog programs), have two equivalent definitions: one based on 3-valued logics and another based on the notion of unfounded set. The notion of partial stable model has been extended to disjunctive deductive databases using 3-valued logics. In this paper, a characterization of partial stable models for disjunctive datalog programs is given using a suitable extension of the notion of unfounded set. Two interesting sub-classes of partial stable models, M-stable (Maximal-stable) (also called regular models, preferred extension,and maximal stable classes) and L-stable (Least undefined-stable) models, are then extended from normal to disjunctive datalog programs. On the one hand, L-stable models are shown to be the natural relaxation of the notion of total stable model; on the other hand the less strict M-stable models, endowed with a nice modularity property, may be appealing from the programming and computational point of view. M-stable and L-stable models are also compared with the regular models for disjunctive datalog programs recently proposed in the literature.     

基于满十六叉有序树的程序行为建模搜索方法

程序行为建模及搜索是异常检测研究中的关键问题。本文提出利用系统调用发生时的程序计数器值对应的段号和段内偏移作为事件,将滑动窗口在有序事件上滑动得到事件序列集合,利用满十六叉有序树算法建立正常行为模型库。满十六叉有序树是为提高规则库的存储及搜索的效率而设计的,其存储的字节顺序隐含着结点间关系信息。在规则库中搜索某条规则的时间复杂度仅与树的深度有关,树的深度固定时的时间复杂度为O（1）。文中给出了满十六叉有序树的定义,分析了它的特点,并给出生成算法和搜索算法。     

Static semantics for normal and disjunctive logic programs

In this paper, we propose a newsemantic framework for disjunctive logic programming by introducingstatic expansions of disjunctive programs. The class of static expansions extends both the classes of stable, well-founded and stationary models of normal programs and the class of minimal models of positive disjunctive programs. Any static expansion of a programP provides the corresponding semantics forP consisting of the set of all sentences logically implied by the expansion. We show that among all static expansions of a disjunctive programP there is always theleast static expansion, which we call thestatic completion ¯P ofP. The static completion¯P can be defined as the least fixed point of a naturalminimal model operator and can be constructed by means of a simpleiterative procedure. The semantics defined by the static completion¯P is called thestatic semantics ofP. It coincides with the set of sentences that are true inall static expansions ofP. For normal programs, it coincides with the well-founded semantics. The class of static expansions represents a semantic framework which differs significantly from the other semantics proposed recently for disjunctive programs and databases. It is also defined for a much broader class of programs.Dedicated to Jack MinkerPartially supported by the National Science Foundation grant # IRI-9313061.     

Incremental Construction of Minimal Tree Automata

We describe an algorithm that allows the incremental addition or removal of unranked ordered trees to a minimal frontier-to-root deterministic finite-state tree automaton (DTA). The algorithm takes a tree t and a minimal DTA A as input; it outputs a minimal DTA A′ which accepts the language L(A) accepted by A incremented (or decremented) with the tree t. The algorithm can be used to efficiently maintain dictionaries which store large collections of trees or tree fragments.     

Theoretical and practical considerations of uncertainty andcomplexity in automated knowledge acquisition

Inductive machine learning has become an important approach to automated knowledge acquisition from databases. The disjunctive normal form (DNF), as the common analytic representation of decision trees and decision tables (rules), provides a basis for formal analysis of uncertainty and complexity in inductive learning. A theory for general decision trees is developed based on C. Shannon's (1949) expansion of the discrete DNF, and a probabilistic induction system PIK is further developed for extracting knowledge from real world data. Then we combine formal and practical approaches to study how data characteristics affect the uncertainty and complexity in inductive learning. Three important data characteristics, namely, disjunctiveness, noise and incompleteness, are studied. The combination of leveled pruning, leveled condensing and resampling estimation turns out to be a very powerful method for dealing with highly disjunctive and inadequate data. Finally the PIK system is compared with other recent inductive learning systems on a number of real world domains