A Fixpoint Semantics for Stratified Databases

Przmusinski extended the notion of stratified logic programs,developed by Apt,Blair and Walker,and by van Gelder,to stratified databases that allow both negative premises and disjunctive consequents.However,he did not provide a fixpoint theory for such class of databases.On the other hand,although a fixpoint semantics has been developed by Minker and Rajasekar for non-Horn logic programs,it is tantamount to traditional minimal model semantics which is not sufficient to capture the intended meaning of negation in the premises of clauses in stratified databases.In this paper,a fixpoint approach to stratified databases is developed,which corresponds with the perfect model semantics.Moreover,algorithms are proposed for computing the set of perfect models of a stratified database.     

The Least Fixpoint Transformation for Disjunctive Logic Programs

The paradigm of disjunctive logic programming(DLP)enhances greatly the expressive power of normal logic programming(NLP)and many(declarative)semantics have been defined for DLP to cope with various problems of knowledge representation in artificial intelligence.However,the expressive ability of the semantics and the soundness of program transformations for DLP have been rarely explored.This paper defines an immediate consequence operatro T^GP for each disjunctive program and shows that T^GP has the least and computable fixpoint Lft(P),Lft is,in fact,a program transformation for DLP,which transforms all disjunctive programs into negative programs.It is shown that Lft preserves many key semantics,including the disjunctive stable models,well-founded model,disjunctive argunent semantics DAS,three-valued models,ect.Thic means that every disjunctive program P has a unique canonical form Lft(P)with respect to these semantics.As a result,the work in this paper provides a unifying framework for studying the expressive ability of various semantics for DLP On the other hand,the computing of the above semantics for negative programs is ust a trivial task,therefore,Lft(P)is also an optimization method for DLP.Another application of Lft is to derive some interesting semantic results for DLP.     

A Comparison of Closed World Assumptions

In this paper, we introduce a notion of the family of closed world assumptions and compare severalwell-known closed world approaches in the family to the extent to which an incomplete database is com-pleted.     

Fuzzy functional dependencies and Bayesian networks

Bayesian networks have become a popular technique for representing and reasoning with probabilistic information.The fuzzy functional dependency is an important kind of data dependencies in relational databases with fuzzy values,The purpose of this paper is to set up a connection between these data dependencies and Bayesian networks.The connection is done through a set of methods that enable pepople to obtain the most information of independent conditions from fuzzy functional dependencies.     

A Comparison of Closed World Assumptions

In this Paper.we introduce a notion of the family of closed world assumptions and compare several well-known closed world approaches in the family to the extent to whic an incomplete database is com pleted.     

Extending the relational model to deal with probabilistic data

According to the soundness and completeness of information in databases,the expressive form and the semantics of incomplete information are discussed in this paper.On the basis of the discussion,the current studies on incomplete data in relational databases are reviewed.In order to represent stochastic uncertainty in most general sense in the real world,probabilistic data are introduced into relational databases.An extended relational data model is presented to express and manipulate probabilistic data and the operations in relational algebra based on the extended model are defined in this paper.     

多媒体推理的概念框架

Up to now, AI technology is dominated by the Physical Symbolic System(PSS), in which symbolic information is used as the medium for reasoning, In these approaches, information other than symbols, such as image, graphics, and even video should first be represented by symbols, and after reasoning, the symbolic result is again changed into its original media form. In this paper, we will propose a new form of reasoning method called multimedia reasoning (MR), a kind of reasoning that is based on the different media such as text, image, video, audio and so on. By introducing the concept of multimedia transformation theory (MTT), it presents a conceptual framework for multimedia reasoning, In the end, it discusses the importance and potentials in applications.     

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.     

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.     

A possible world semantics for disjunctive databases

The fundamental problem that arises when a ground atom in a disjunctive database is assumed false is discussed. There are basically two different approaches for inferring negative information for disjunctive databases: J. Minker's (1982) generalized closed world assumption (GCWA) and K.A. Ross and R.W. Topor's (1988) disjunctive database rule (DDR). It is argued that neither approach is satisfactory. A database semantics called PWS is proposed. It is shown that for propositional databases with no negative clauses, the problem of determining if a negative ground literal is inferred under the GCWA is co-NP-hard, while the same problem can be solved efficiently under the DDR and PWS. However, in the general case, the problem becomes co-NP-complete for the DDR and PWS. Relationships among GCWA, DDR, and PWS are highlighted. In general, disjunctive clauses are interpreted inclusively under the DDR and unpredictably under the GCWA     

Inferring negative information from disjunctive databases

We propose criteria that any rule for inferring negative information from disjunctive databases should satisfy, and examine existing rules from this viewpoint. We then present a new inference rule, the ‘disjunctive database rule’ (DDR), and compare it to the existing rules with respect to the criteria. In particular, the DDR is equivalent to the CWA for definite databases, it infers no more negative information than the GCWA, and it interprets disjunction inclusively rather than exclusively. We generalize the DDR to a class of layered databases, describe an implementation of the DDR, ‘negation as positive failure’, and study its soundness and completeness properties.     

Weak Generalized Closed World Assumption

Explicit representation of negative information in logic programs is not feasible in many applications such as deductive databases and artificial intelligence. Defining default rules which allow implicit inference of negated facts from positive information encoded in a logic program has been an attractive alternative to the explicit representation approach. There is, however, a difficulty associated with implicit default rules. Default rules such as the CWA and the GCWA, which closely model logical negation, are in general computationally intractable. This has led to the development of weaker definitions of negation such as the Negation-As-Failure (NF) and the Support-For-Negation (SN) rules which are computationally simpler. These are sound implementations of the CWA and the GCWA, respectively. In this paper, we define an alternative rule of negation based upon the fixpoint definition of the GCWA. This rule, called the Weak Generalized Closed World Assumption (WGCWA), is a weaker definition of the GCWA that allows us to implement a sound negation rule, called the Negation-As-Finite-Failure (NAFF), similar to the NF-rule and less cumbersome than the SN-rule. We present three definitions of the NAFF. Two declarative definitions similar to those for the NF-rule and one procedural definition based on SLI-resolution.     

Classical negation in logic programs and disjunctive databases

An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter.     

Logic programming and reasoning with incomplete information

The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and negation by failure is further expanded by new modal operators K and M (where for the set of rulesT and formulaF, KF stands for F is known to be true by a reasoner with a set of premisesT and MF means F may be believed to be true by the same reasoner). Sets of rules in the extended language will be called epistemic specifications. We will define the semantics of epistemic specifications (which expands the semantics of disjunctive databases from) and demonstrate their applicability to formalization of various forms of commonsense reasoning. In particular, we suggest a new formalization of the closed world assumption which seems to better correspond to the assumption's intuitive meaning.     

Overview of disjunctive logic programming

The field of disjunctive programming started approximately in 1982 and has reached its first decade. The first result in the field was the development of the Generalized Closed World Assumption (GCWA). Major results have been made in this field since 1986. An overview is presented of the developments that have taken place, which include model theoretic, proof theoretic and fixpoint semantics for disjunctive, and extended normal disjunctive theories including alternative forms of negation.Dedicated to Chitta Baral, José Alberto Fernández, Jorge Lobo and Arcot Rajasekar.     

Default logic as a query language

Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI formalisms as relational database query languages has been investigated to a much smaller extent. In this work, we propose a novel application of Reiter's default logic by introducing a default query language (DQL) for finite relational databases, which is based on default rules. The main result of this paper is that DQL is as expressive as SO_∃∀ the existential-universal fragment of second-order logic. This result is not only of theoretical importance: We exhibit queries-which are useful in practice-that can be expressed with DQL and cannot with other query languages based on nonmonotonic logics such as DATALOG with negation under the stable model semantics. In particular, we show that DQL is well-suited for diagnostic reasoning