Stream-based inconsistency measurement

Inconsistency measures have been proposed to assess the severity of inconsistencies in knowledge bases of classical logic in a quantitative way. In general, computing the value of inconsistency is a computationally hard task as it is based on the satisfiability problem which is itself NP-complete. In this work, we address the problem of measuring inconsistency in knowledge bases that are accessed in a stream of propositional formulæ. That is, the formulæ of a knowledge base cannot be accessed directly but only once through processing of the stream. This work is a first step towards practicable inconsistency measurement for applications such as Linked Open Data, where huge amounts of information is distributed across the web and a direct assessment of the quality or inconsistency of this information is infeasible due to its size. Here we discuss the problem of stream-based inconsistency measurement on classical logic, in order to make use of existing measures for classical logic. However, it turns out that inconsistency measures defined on the notion of minimal inconsistent subsets are usually not apt to be used in the streaming scenario. In order to address this issue, we adapt measures defined on paraconsistent logics and also present a novel inconsistency measure based on the notion of a hitting set. We conduct an extensive empirical analysis on the behavior of these different inconsistency measures in the streaming scenario, in terms of runtime, accuracy, and scalability. We conclude that for two of these measures, the stream-based variant of the new inconsistency measure and the stream-based variant of the contension inconsistency measure, large-scale inconsistency measurement in streaming scenarios is feasible.     

Approaches to measuring inconsistency for stratified knowledge bases

A number of proposals have been proposed for measuring inconsistency for knowledge bases. However, it is rarely investigated how to incorporate preference information into inconsistency measures. This paper presents two approaches to measuring inconsistency for stratified knowledge bases. The first approach, termed the multi-section inconsistency measure (MSIM for short), provides a framework for characterizing the inconsistency at each stratum of a stratified knowledge base. Two instances of MSIM are defined: the naive MSIM and the stratum-centric MSIM. The second approach, termed the preference-based approach, aims to articulate the inconsistency in a stratified knowledge base from a global perspective. This approach allows us to define measures by taking into account the number of formulas involved in inconsistencies as well as the preference levels of these formulas. A set of desirable properties are introduced for inconsistency measures of stratified knowledge bases and studied with respect to the inconsistency measures introduced in the paper. Computational complexity results for these measures are presented. In addition, a simple but explanatory example is given to illustrate the application of the proposed approaches to requirements engineering.     

A Syntax-based approach to measuring the degree of inconsistency for belief bases

Measuring the degree of inconsistency of a belief base is an important issue in many real-world applications. It has been increasingly recognized that deriving syntax sensitive inconsistency measures for a belief base from its minimal inconsistent subsets is a natural way forward. Most of the current proposals along this line do not take the impact of the size of each minimal inconsistent subset into account. However, as illustrated by the well-known Lottery Paradox, as the size of a minimal inconsistent subset increases, the degree of its inconsistency decreases. Another lack in current studies in this area is about the role of free formulas of a belief base in measuring the degree of inconsistency. This has not yet been characterized well. Adding free formulas to a belief base can enlarge the set of consistent subsets of that base. However, consistent subsets of a belief base also have an impact on the syntax sensitive normalized measures of the degree of inconsistency, the reason for this is that each consistent subset can be considered as a distinctive plausible perspective reflected by that belief base, whilst each minimal inconsistent subset projects a distinctive view of the inconsistency. To address these two issues, we propose a normalized framework for measuring the degree of inconsistency of a belief base which unifies the impact of both consistent subsets and minimal inconsistent subsets. We also show that this normalized framework satisfies all the properties deemed necessary by common consent to characterize an intuitively satisfactory measure of the degree of inconsistency for belief bases. Finally, we use a simple but explanatory example in requirements engineering to illustrate the application of the normalized framework.     

Exploiting partial knowledge of satisfying assignments

Recently Schöning has shown that a simple local-search algorithm for 3SAT achieves the currently best upper bound, i.e., an expected time of 1.334ⁿ. In this paper, we show that this algorithm can be modified to run much faster if there is some kind of imbalance in satisfying assignments and we have a (partial) knowledge about that. Especially if a satisfying assignment has imbalanced 0's and 1's, i.e., p₁n 1's and (1-p₁)n 0's, then we can find a solution in time 1.260ⁿ when and 1.072ⁿ when p₁=0.1. Such an imbalance often exists in SAT instances reduced from other problems. As a concrete example, we investigate a reduction from 3DM and show our new approach is nontrivially faster than its direct algorithms. Preliminary experimental results are also given.     

Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases

There is extensive theoretical work on measures of inconsistency for arbitrary formulae in knowledge bases. Many of these are defined in terms of the set of minimal inconsistent subsets (MISes) of the base. However, few have been implemented or experimentally evaluated to support their viability, since computing all MISes is intractable in the worst case. Fortunately, recent work on a related problem of minimal unsatisfiable sets of clauses (MUSes) offers a viable solution in many cases. In this paper, we begin by drawing connections between MISes and MUSes through algorithms based on a MUS generalization approach and a new optimized MUS transformation approach to finding MISes. We implement these algorithms, along with a selection of existing measures for flat and stratified knowledge bases, in a tool called mimus. We then carry out an extensive experimental evaluation of mimus using randomly generated arbitrary knowledge bases. We conclude that these measures are viable for many large and complex random instances. Moreover, they represent a practical and intuitive tool for inconsistency handling.     

Postulates for logic-based argumentation systems

Logic-based argumentation systems are developed for reasoning with inconsistent information. Starting from a knowledge base encoded in a logical language, they define arguments and attacks between them using the consequence operator associated with the language. Finally, a semantics is used for evaluating the arguments.In this paper, we focus on systems that are based on deductive logics and that use Dung's semantics. We investigate rationality postulates that such systems should satisfy. We define five intuitive postulates: consistency and closure under the consequence operator of the underlying logic of the set of conclusions of arguments of each extension, closure under sub-arguments and exhaustiveness of the extensions, and a free precedence postulate ensuring that the free formulas of the knowledge base (i.e., the ones that are not involved in inconsistency) are conclusions of arguments in every extension. We study the links between the postulates and explore conditions under which they are guaranteed or violated.     

Mathematical programming approaches for generating p-efficient points

Probabilistically constrained problems, in which the random variables are finitely distributed, are non-convex in general and hard to solve. The p-efficiency concept has been widely used to develop efficient methods to solve such problems. Those methods require the generation of p-efficient points (pLEPs) and use an enumeration scheme to identify pLEPs. In this paper, we consider a random vector characterized by a finite set of scenarios and generate pLEPs by solving a mixed-integer programming (MIP) problem. We solve this computationally challenging MIP problem with a new mathematical programming framework. It involves solving a series of increasingly tighter outer approximations and employs, as algorithmic techniques, a bundle preprocessing method, strengthening valid inequalities, and a fixing strategy. The method is exact (resp., heuristic) and ensures the generation of pLEPs (resp., quasi pLEPs) if the fixing strategy is not (resp., is) employed, and it can be used to generate multiple pLEPs. To the best of our knowledge, generating a set of pLEPs using an optimization-based approach and developing effective methods for the application of the p-efficiency concept to the random variables described by a finite set of scenarios are novel. We present extensive numerical results that highlight the computational efficiency and effectiveness of the overall framework and of each of the specific algorithmic techniques.     

Overriding subsuming rules

This paper is concerned with intelligent agents that are able to perform nonmonotonic reasoning, not only with, but also about general rules with exceptions. More precisely, the focus is on enriching a knowledge base Γ with a general rule that is subsumed by other rules already there. Such a problem is important because evolving knowledge needs not follow logic as it is well-known from e.g. the belief revision paradigm. However, belief revision is mainly concerned with the case that the extra information logically conflicts with Γ. Otherwise, the extra knowledge is simply doomed to extend Γ with no change altogether. The problem here is different and may require a change in Γ even though no inconsistency arises. The idea is that when a rule is to be added, it might need to override any rule that subsumes it: preemption must take place. A formalism dedicated to reasoning with and about rules with exceptions is introduced. An approach to dealing with preemption over such rules is then developed. Interestingly, it leads us to introduce several implicants concepts for rules that are possibly defeasible.     

Policy-based inconsistency management in relational databases

Though inconsistency management in databases and AI has been studied extensively for years, it does not allow the user to specify how he wants to resolve inconsistencies. In real-world applications, users may want to manage or resolve inconsistencies based not only on the data, but their own knowledge of the risks involved in decision making based on faulty data. Each user should be empowered to use reasonable policies to deal with his data and his mission needs. In this paper, we start by providing an axiomatic definition of inconsistency management policies (IMPs) that puts this power in the hands of users. Any function satisfying these axioms is an IMP. We then define three broad families of IMPs, and derive several results that show (i) how these policies relate to postulates for the revision of belief bases and to recent research in the area of consistent query answering, and (ii) how they interact with standard relational algebra operators. Finally, we present several approaches to efficiently implement an IMP-based framework.     

Learning by developing knowledge networks

A central challenge for research on how we should prepare students to manage crossing boundaries between different knowledge settings in life long learning processes is to identify those forms of knowledge that are particularly relevant here. In this paper, we develop by philosophical means the concept of adialectical system as a general framework to describe the development of knowledge networks that mark the starting point for learning processes, and we use semiotics to discuss (a) the epistemological thesis that any cognitive access to our world of objects is mediated by signs and (b)diagrammatic reasoning andabduction as those forms of practical knowledge that are crucial for the development of knowledge networks. The richness of this theoretical approach becomes evident by applying it to an example of learning in a biological research context. At the same time, we take a new look at the role of mathematical knowledge in this process.     

Responsibility for inconsistency

It is desirable to identify the degree of responsibility of each part of a knowledge base for the inconsistency of that base to make some necessary trade-off decisions on restoring the consistency of that base. In this paper, we propose a measurement for the degree of responsibility of each formula in a knowledge base for the inconsistency of that base. This measurement is given in terms of minimal inconsistent subsets of a knowledge base. Moreover, it can be well explained in the context of causality and responsibility presented by Chockler and Halpern [1].     

Some topologies on a Šerstnev probabilistic normed space

In this paper we will introduce two other topologies, coarser than the so-called strong topology, on a class of Šerstnev probabilistic normed spaces, and obtain some important properties of these topologies. We will show that under the first topology, denoted by τ₀, our probabilistic normed space is decomposable into the topological direct sum of a normable subspace and the subspace of probably null elements. Under the second topology, which is in fact the inductive limit topology of a family of locally convex topologies, the dual space becomes a locally convex topological vector space.     

Networks of probabilistic events in discrete time

The usual methods of applying Bayesian networks to the modeling of temporal processes, such as Dean and Kanazawa’s dynamic Bayesian networks (DBNs), consist in discretizing time and creating an instance of each random variable for each point in time. We present a new approach called network of probabilistic events in discrete time (NPEDT), for temporal reasoning with uncertainty in domains involving probabilistic events. Under this approach, time is discretized and each value of a variable represents the instant at which a certain event may occur. This is the main difference with respect to DBNs, in which the value of a variable V_i represents the state of a real-world property at time t_i. Therefore, our method is more appropriate for temporal fault diagnosis, because only one variable is necessary for representing the occurrence of a fault and, as a consequence, the networks involved are much simpler than those obtained by using DBNs. In contrast, DBNs are more appropriate for monitoring tasks, since they explicitly represent the state of the system at each moment. We also introduce in this paper several types of temporal noisy gates, which facilitate the acquisition and representation of uncertain temporal knowledge. They constitute a generalization of traditional canonical models of multicausal interactions, such as the noisy OR-gate, which have been usually applied to static domains. We illustrate the approach with the example domain of modeling the evolution of traffic jams produced on the outskirts of a city, after the occurrence of an event that obliges traffic to stop indefinitely.     

Asymptotics of Plancherel measures for the infinite-dimensional unitary group

We study a two-dimensional family of probability measures on infinite Gelfand-Tsetlin schemes induced by a distinguished family of extreme characters of the infinite-dimensional unitary group. These measures are unitary group analogs of the well-known Plancherel measures for symmetric groups.We show that any measure from our family defines a determinantal point process on Z₊×Z, and we prove that in appropriate scaling limits, such processes converge to two different extensions of the discrete sine process as well as to the extended Airy and Pearcey processes.     

Rich preference-based argumentation frameworks

An argumentation framework is seen as a directed graph whose nodes are arguments and arcs are attacks between the arguments. Acceptable sets of arguments, called extensions, are computed using a semantics. Existing semantics are solely based on the attacks and do not take into account other important criteria like the intrinsic strengths of arguments.The contribution of this paper is three fold. First, we study how preferences issued from differences in strengths of arguments can help in argumentation frameworks. We show that they play two distinct and complementary roles: (i) to repair the attack relation between arguments, (ii) to refine the evaluation of arguments. Despite the importance of both roles, only the first one is tackled in existing literature. In a second part of this paper, we start by showing that existing models that repair the attack relation with preferences do not perform well in certain situations and may return counter-intuitive results. We then propose a new abstract and general framework which treats properly both roles of preferences. The third part of this work is devoted to defining a bridge between the argumentation-based and the coherence-based approaches for handling inconsistency in knowledge bases, in particular when priorities between formulae are available. We focus on two well-known models, namely the preferred sub-theories introduced by Brewka and the demo-preferred sets defined by Cayrol, Royer and Saurel. For each of these models, we provide an instantiation of our abstract framework which is in full correspondence with it.     

Extension of the notion of collision and avalanche effect to sequences of k symbols

In recent papers [14], [15] I studied collision and avalanche effect in families of finite pseudorandom binary sequences. Motivated by applications, Mauduit and Sárk?zy in [13] generalized and extended this theory from the binary case to k-ary sequences, i.e., to k symbols. They constructed a large family of k-ary sequences with strong pseudorandom properties. In this paper our goal is to extend the study of the pseudorandom properties mentioned above to k-ary sequences. The aim of this paper is twofold. First we will extend the definitions of collision and avalanche effect to k-ary sequences, and then we will study these related properties in a large family of pseudorandom k-ary sequences with ??small?? pseudorandom measures.     

A generalization of local divergence measures

In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures.     

Patterns in Rational Base Number Systems

Number systems with a rational number a/b>1 as base have gained interest in recent years. In particular, relations to Mahler’s $\frac{3}{2}$ -problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base a/b and use representations w.r.t. this base to construct normal numbers in base a in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the adèle ring $\mathbb{A}_{\mathbb{Q}}$ and Fourier analysis in $\mathbb{A}_{\mathbb{Q}}$ . With help of these tools we are able to reformulate our results as estimation problems for character sums.     

A novel differential evolution algorithm for binary optimization

Differential evolution (DE) is one of the most powerful stochastic search methods which was introduced originally for continuous optimization. In this sense, it is of low efficiency in dealing with discrete problems. In this paper we try to cover this deficiency through introducing a new version of DE algorithm, particularly designed for binary optimization. It is well-known that in its original form, DE maintains a differential mutation, a crossover and a selection operator for optimizing non-linear continuous functions. Therefore, developing the new binary version of DE algorithm, calls for introducing operators having the major characteristics of the original ones and being respondent to the structure of binary optimization problems. Using a measure of dissimilarity between binary vectors, we propose a differential mutation operator that works in continuous space while its consequence is used in the construction of the complete solution in binary space. This approach essentially enables us to utilize the structural knowledge of the problem through heuristic procedures, during the construction of the new solution. To verify effectiveness of our approach, we choose the uncapacitated facility location problem (UFLP)—one of the most frequently encountered binary optimization problems—and solve benchmark suites collected from OR-Library. Extensive computational experiments are carried out to find out the behavior of our algorithm under various setting of the control parameters and also to measure how well it competes with other state of the art binary optimization algorithms. Beside UFLP, we also investigate the suitably of our approach for optimizing numerical functions. We select a number of well-known functions on which we compare the performance of our approach with different binary optimization algorithms. Results testify that our approach is very efficient and can be regarded as a promising method for solving wide class of binary optimization problems.