CWA formalizations in multi-valued logics

This paper extends Reiter’s closed world assumption to cases where the assumption is applied in a precedence order between predicates. The extended assumptions are: thepartial closed world assumption, thehierarchical closed world assumption and thestepwise closed world assumption. The paper also defines an extension of Horn formulas and shows several consistency results about the theory obtained from the extended Horn formulas by applying the proposed assumptions. In particular, the paper shows that both the hierarchical closed world assumption and the stepwise closed world assumption characterize the perfect model of stratified programs.

Checkpoint-Restart is the ability to save a set of running processes to a checkpoint image on disk, and to later restart them from the disk. In addition to its traditional use in fault tolerance, recovering from a system failure, it has numerous other uses, such as for application debugging and save/restore of the workspace of an interactive problem-solving environment. Transparent checkpointing operates without modifying the underlying application program, but it implicitly relies on a "Closed World Assumption" --- the world (including file system, network, etc.) will look the same upon restart as it did at the time of checkpoint. This is not valid for more complex programs. Until now, checkpoint-restart packages have adopted ad~hoc solutions for each case where the environment changes upon restart.

ON CLOSED WORLD DATA BASES

ON CLOSED WORLD DATA BASES

The lesson of chapter 3 is that theorem-proving in the predicate calculus constitutes a poor mechanism for reasoning about a complex, dynamic environment such as the one we inhabit. In particular, we drew attention to the problem of representing negative information — information about the non-existence of objects or events or processes or influences. Negative information, we argued, must sometimes be encoded by the mere absence of positive information to the contrary: propositions which are not given, or which are not deducible from those which are given, should be assumed to be false. This type of assumption is sometimes referred to as a closed world assumption, and the logical properties of closed world assumptions occupy centre stage in one important strand in AI research. They also form the topic of this chapter.

Given a sublattice ∑ of 1st-order sentences, the notions of the ∑-closed world assumption, the generalized ∑-closed world assumption and ∑-irreducibility of an arbitrary theory are investigated. It is shown that for a theory T there exists a finite number of ∑ irreducible extensions whose intersection equals T iff there exists a finite ∑-testclass for T, i.e. a finite set of models of T such that any sentence σ ∈ ∑ follows from T iff σ holds in all of these models. In this case, an axiomatizability result for the irreducible components is proved.

Logic programs, deductive databases, and more generally non-monotonic theories, use various forms of default negation, not F , whose major distinctive feature is that not F is assumed “by default”, i.e., it is assumed in the absence of sufficient evidence to the contrary. The meaning of “sufficient evidence” depends on the specific semantics used. For example, in Reiter’s Closed World Assumption, CWA [32], not A is assumed for atomic A if A is not provable, or, equivalently, if there is a minimal model in which A is false. On the other hand, in Minker’s Generalized Closed World Assumption, GCWA [18, 16], or in McCarthy’s Circumscription, CIRC [17], not A is assumed only if A is false in all minimal models. In Clark’s Predicate Completion semantics for logic programs [7], this form of negation is called negation-as-failure because not A is derivable whenever attempts to prove A finitely fail. The more recent semantics proposed for logic programs and deductive databases, such as the stable semantics [14], well-founded semantics [34], partial stable or stationary semantics [27] and static semantics [30], propose even more sophisticated meanings for default negation, closely related to more general nonmonotonic formalisms such as Default Logic, DL [33], AutoEpistemic Logic, AEL [19], and AutoEpistemic logic of Beliefs, AEB [29]. Under all of these semantics, however, default negation “not ” significantly differs from classical negation “¬”. For example, the formula charged(x) ∧ ¬guilty(x) ⊃ acquitted(x) says that a person charged with a crime should be acquitted if he or she is actually proven to be not guilty. On the other hand, the formula charged(x) ∧ not guilty(x) ⊃ acquitted(x) says that one should be acquitted of any charges by default unless sufficient evidence of that person’s guilt is demonstrated.

Incomplete information is usually present in a database in the form of null values. Several other forms of incompleteness such as fuzzy information, partial values and disjunctive information have been studied extensively. Most of the research on indefinite information has been carried out under the Closed World Assumption(CWA). In this paper, we present a data structure that supports the opposite view, the Open World Assumption(OWA), where negative information is explicitly represented in a relation. We allow disjunctions at the tuple level to appear in two forms: A or B and notA or notB, thus obtaining a gain in expressivity. Wenot define a generalization of the relational algebra that handles this kind of information.

This paper proposes a framework for building product information model (PIM) and product rule model (PRM), and integrated reasoning based on Description Frame Logic (DFL) [1] for collaborative product engineering environments. Most of the previous research has focused either on building ontology for PIM or on building a rule base for PRM respectively, not on both of them. Some research on product engineering has tried to build both ontology language and rule-language. But, the research is/has been limited to using both languages in a homogeneous approach under open world assumption (OWA) such as Web Ontology Language (OWL)/Semantic Web Rule Language (SWRL), which has some drawbacks to accommodate the requirements of enhanced expressivity for collaborative product engineering. We adopt Description Frame Logic (DFL) framework to integrate product semantics in PIM and engineering-specific knowledge in PRM based on description logic (DL) and logic programming (LP) under both open world assumption (OWA) and closed world assumption (CWA). This enables to secure seamless and interactive reasoning between PIM and PRM. We also include rule-expressions and constraint checking with DL for PIM while we include DL-expression in rules and LP’s non-logical features for PRM. This provides enhancement of expressiveness required for product engineering. Additionally, we show the benefits of the proposed framework with a case study.

Quantifying uncertainty is a hot topic for uncertain information processing in the framework of evidence theory, but there is limited research on belief entropy in the open world assumption. In this paper, an uncertainty measurement method that is based on Deng entropy, named Open Deng entropy (ODE), is proposed. In the open world assumption, the frame of discernment (FOD) may be incomplete, and ODE can reasonably and effectively quantify uncertain incomplete information. On the basis of Deng entropy, the ODE adopts the mass value of the empty set, the cardinality of FOD, and the natural constant e to construct a new uncertainty factor for modeling the uncertainty in the FOD. Numerical example shows that, in the closed world assumption, ODE can be degenerated to Deng entropy. An ODE-based information fusion method for sensor data fusion is proposed in uncertain environments. By applying it to the sensor data fusion experiment, the rationality and effectiveness of ODE and its application in uncertain information fusion are verified.

In this paper we consider approaches to updating databases containing null values and incomplete information. Our approach distinguishes between modeling incompletely known worlds and modeling changes in these worlds. As an alternative to the open and closed world assumptions, we propose the expanded closed world assumption. Under this assumption, we discuss how to perform updates on databases containing set nulls, marked nulls, and simple conditional tuples, and address some issues of refining incompletely specified information.

We study the semantics of disjunctive logic programs that simultaneously contain multiple kinds of default negations. We introduce operators not G, not W, and not STB in the language of logic programs to represent the Generalized Closed World Assumption, the Weak Generalized Closed World Assumption, and the stable negation, respectively. The notion of stratification involving different kinds of negations is defined and the meaning of stratified programs with multiple negations is described. The class of stratified programs is extended to the class of quasi-stratified programs and the semantics of the latest class is studied.

Although negative conclusions are presented implicitly in Normal Hybrid Probabilistic Programs (NHPP) [26] through the closed world assumption, representing and reasoning with explicit negation is needed in NHPP to allow the ability to reason with incomplete knowledge. In this paper we extend the language of NHPP to explicitly encode classical negation in addition to non-monotonic negation. The semantics of the extended language is based on the answer set semantics of traditional logic programming [9]. We show that the proposed semantics is a natural extension to the answer set semantics of traditional logic programming [9]. In addition, the proposed semantics is reduced to stable probabilistic model semantics of NHPP [26]. The importance of that is computational methods developed for NHPP can be applied to the proposed language. Furthermore, we show that some commonsense probabilistic knowledge can be easily represented in the proposed language.KeywordsLogic ProgramLogic ProgrammingClassical NegationIncomplete KnowledgeProbability IntervalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

One of the most famous authors of the method is Tomas Mikolov. His software and method of theoretical application are the major ones for our consideration today. It is better to pay attention that it is more mathematically oriented. The use of embedding models to turn KGs into vector space has become a well-known field of research. In recent years, a plethora of embedding learning approaches have been proposed in the literature. Many of these models rely on data already stored in the input KG. Following the closed world assumption, the knowledge not presented in the KG cannot be judged untrue; instead, it may only be labeled as unknown. On the other hand, embedding models, like most machine learning algorithms, require negative instances to learn embeddings efficiently. To deal with this, a variety of negative sample generating strategies have been developed. The author himself had more to do with mathematics, and his method concerns, first of all, a mathematical solution for a theoretical, and then a practical solution for creating this and the method we are analyzing. Dense vector word representations have lately gained popularity as fixed-length features for machine learning algorithms, and Mikolov’s system is now widely used. We investigate one of its main components, Negative Sampling, and offer efficient distributed methods that allow us to scale to indicate and exclude the possibility of probability loss in a similar value. Furthermore, this method is laser-focused on a single action in the broad sense for processing the recognition of the above-mentioned vector or words. It is important to pay attention to mathematical theory and understand the importance of the neural network in this field.

Querying big data is the cornerstone of the application of big data. From a database perspective, query is the function defined by domain, range and a specified semantics. For querying big data, the domain is the big data and becomes quite complicated with characteristics of large volume, heterogeneous types, strong timeliness, weak authenticity, etc. To describe and analyze querying big data theoretically, we propose the definitions of big data and big data system, which includes querying big data. Aforementioned characteristics of big data lead to a break-through in normal form qualification and Closed World Assumption (CWA) related to traditional database. Therefore, this paper also points out several challenges according to those characteristics of domain and analyzes them in detail using the first-order language. Since the complexity of domain makes traditionally tractable queries infeasible, this paper analyzes and summarizes the classification of queries on relational big data according to their structure and computational complexity.