Resolving Inconsistencies in Probabilistic Knowledge Bases by Quantitative Modification

There is an increasing need to develop appropriate techniques for merging probabilistic knowledge bases (PKB) in knowledge-based systems. To deal with merging problems, several approaches have been put forward. However, in the proposed models, the representation of the merged probabilistic knowledge base is not similar to the representation of original knowledge bases. The drawback of the solutions is that probabilistic constraints on the set of input knowledge bases must have the same structure and there is no algorithm for implementing the merging process. In this paper, we proposed two algorithms for merging probabilistic knowledge bases represented by various structures. To this aim, the method of constraint deduction is investigated, a set of mean merging operators is proposed and several desirable logical properties are presented and discussed. These are the basis for building algorithms. The complexity of algorithms as well as related propositions are also analysised and discussed.

We present the ARCHIMEDES system for efficient query processing over probabilistic knowledge bases. We design ARCHIMEDES for knowledge bases containing incomplete and uncertain information due to limitations of information sources and human knowledge. Answering queries over these knowledge bases requires efficient probabilistic inference. In this paper, we describe ARCHIMEDES's efficient knowledge expansion and querydriven inference over UDA-GIST, an in-database unified data- and graph-parallel computation framework. With an efficient inference engine, ARCHIMEDES produces reasonable results for queries over large uncertain knowledge bases. We use the Reverb-Sherlock andWikilinks knowledge bases to show ARCHIMEDES achieves satisfactory quality with real-time performance.

The article uses an example of a diagnostic system based on a probabilistic knowledge base and Naive Bayes Classifier inference, analyzing mismatch characteristic of the system’s reasoning and an expert’s reasoning to show the solution extending basic knowledge base with specialized, domain-dependent meta-knowledge. The evaluation of the solution is represented by the expert system dedicated to recognition of hypertension.

Probabilistic Topic Models could be used to extract low-dimension aspects from document collections. However, such models without any human knowledge often produce aspects that are not interpretable. In recent years, a number of knowledge-based models have been proposed, which allow the user to input prior knowledge of the domain to produce more coherent and meaningful topics. In this paper, we incorporate human knowledge in the form of probabilistic knowledge base into topic models. By combining latent Dirichlet allocation, a widely used topic model with Probase, a large-scale probabilistic knowledge base, we improve the semantic coherence significantly. Our evaluation results will demonstrate the effectiveness of our method.

Information extraction and human collaboration techniques are widely applied in the construction of web-scale knowledge bases. However, these knowledge bases are often incomplete or uncertain. In this paper, we present ProbKB, a probabilistic knowledge base designed to infer missing facts in a scalable, probabilistic, and principled manner using a relational DBMS. The novel contributions we make to achieve scalability and high quality are: 1) We present a formal definition and a novel relational model for probabilistic knowledge bases. This model allows an efficient SQL-based inference algorithm for knowledge expansion that applies inference rules in batches; 2) We implement ProbKB on massive parallel processing databases to achieve further scalability; and 3) We combine several quality control methods that identify erroneous rules, facts, and ambiguous entities to improve the precision of inferred facts. Our experiments show that ProbKB system outperforms the state-of-the-art inference engine in terms of both performance and quality.

The probabilistic Description Logic Open image in new window extends the classical Description Logic Open image in new window with probabilistic conditionals of the form (D|C)[p] stating that “D follows from C with probability p.” Conditionals are interpreted based on the aggregating semantics where probabilities are understood as degrees of belief. For reasoning with probabilistic conditional knowledge bases in Open image in new window , the principle of maximum entropy provides a valuable methodology following the idea of completing missing information in a most cautious way. In this paper, we give a guidance on calculating approximations of the maximum entropy distribution for Open image in new window -knowledge bases. For this, we discuss the benefits of solving the dual maximum entropy optimization problem instead of the primal problem. In particular, we show how representations of approximations of the maximum entropy distribution can be derived from the dual problem in time polynomial in the size of the underlying domain. The domain is the crucial quantity in practical applications. For a compact representation of the objective function of the dual maximum entropy optimization problem, we apply the principle of typed model counting.

Representation and extraction of information by probabilistic logic

The methods for determining OWA operator weights have aroused wide attention. We first review the main existing methods for determining OWA operator weights. We next introduce the principle of maximum entropy for setting up probability distributions on the basis of partial knowledge and prove that Xu's normal distribution-based method obeys the principle of maximum entropy. Finally, we propose an argument-dependent approach based on normal distribution, which assigns very low weights to these “false” or “biased” opinions and can relieve the influence of the unfair arguments. A numerical example is provided to illustrate the application of the proposed approach. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 209–221, 2007.

Combining probabilistic logic programming with the power of maximum entropy

Probability theory provides a sound and convenient machinery to be used for knowledge representation and automated reasoning (see, for instance, [Cox46, DPT90, DP91b, LS88, Pea88, TGK92]). In many cases, only relatively few relationships between relevant variables are known, due to incomplete information. Or maybe, an abstractional representation is intended, incorporating only fundamental relationships. In both cases, the knowledge explicitly stated is not sufficient to determine uniquely a probability distribution. One way to cope with this indetermination is to calculate upper and lower bounds for probabilities (cf. [Nil86, TGK92, DPT90]). This method, however, brings about two problems: Sometimes the inferred bounds are quite bad, and one has to handle intervals instead of single values.An alternative way that provides best expectation values for the unknown probabilities and guarantees a logically sound reasoning is to use the principle of maximum entropy resp. the principle of minimum cross entropy to represent all available probabilistic knowledge by a unique distribution (see Section 2.5; cf. [Sho86, Kul68, Jay83a, GHK94]). Here we assume the available knowledge to constitute of a (consistent) set R of conditionals, each equipped with a probability, usually providing only incomplete probabilistic knowledge.The aim of this chapter is to establish a direct and constructive link between probabilistic conditionals and their suitable representation via distributions, taking prior knowledge into account if necessary.We develope the following four principles which mark the corner-stones for using quantified conditionals consistently for probabilistic knowledge representation and updating: (P1) The principle of conditional preservation: this is to express that prior conditional dependencies shall be preserved “as far as possible” under adaptation; (P2) the idea of a functional concept which underlies the adaptation and which allows us to calculate a posterior distribution from prior and new knowledge (P3) the principle of logical coherence 1: posterior distributions shall be used coherently as priors for further inferences (P4) the principle of representation invariance: the resulting distribution shall not depend upon the actual probabilistic representation of the new information. KeywordsWeight FactorPosterior DistributionPrior DistributionRepresentation InvariancePositive DistributionThese 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.

We investigate the task of recognizing objects of daily use in human environments purely based on object descriptions given in natural language. In particular, we present an approach to transform phrases stated in natural language that describe such objects by their visual appearance into formal, semantic representations of their perceptual characteristics, which in turn can be used in a robot perception system in order to identify objects that the robot has never encountered before. To this end, we learn probabilistic first-order knowledge bases from encyclopedic articles and online dictionaries, which contain textual descriptions of a vast amount of everyday objects. We demonstrate the applicability of the approach on a robotic system in a proof-of-concept evaluation on a selected set of object descriptions acquired from the internet.

We propose a method of probability logic reasoning with threshold-surety to the problem of making inference from a knowledge base in experts system, which treats a finite set of premises in the knowledge base as assertions that are true with probability at least some primary threshold, and consider as a finite set of alternative conclusions those assertions probabilistically entailed to have probability at least some suitable threshold. Based on comparative probability theory, we construct a probability entailment relation between premises and conclusions, and use the method of fuzzy c-partition and the maximum fuzzy entropy principle to select the threshold values. An illustrative example of application of our method shows how we make inferences from knowledge base.

Minimum Cross Entropy and Informational Approaches for Spectrum Estimation

In defense of the maximum entropy inference process

The principle of maximum entropy inductively completes the knowledge given by a knowledge base \(\mathcal R\), and it has been suggested to view learning as an operation being inverse to inductive knowledge completion. While a corresponding learning approach has been developed when \(\mathcal R\) is based on propositional logic, in this paper we describe an extension to a relational setting. It allows to learn relational FO-PCL knowledge bases containing both generic conditionals as well as specific conditionals referring to exceptional individuals from a given probability distribution.KeywordsMaximum EntropyBelief RevisionPredicate SymbolRelational SettingHorn ClauseThese 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.