Applications of Uncertainty Formalisms

The heterogeneity of uncertainty in the real-world has driven the development of a wide variety of formal approaches to representing and reasoning with uncertainty in knowledge. There is now a shift to analysing the application of many of these formalisms. Here, we briefly consider some of the issues in the application of uncertainty formalisms.

Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with incomplete and uncertain information. In this paper we review some of the most important of these formalisms, describing how they work, and in what ways they differ from one another. We also consider heterogeneous approaches which incorporate two or more approximate reasoning mechanisms within a single reasoning system. These have been proposed to address limitations in the use of individual formalisms.

Therapy planning is a very complex task, being the patient’s therapeutic response affected by several sources of uncertainty. Further-more, the modelling of a patient’s evolution is frequently hampered by the incompleteness of the medical knowledge; it is hence often not possible to derive a mathematical model that is able to take into account the characteristics of the uncertain environment. An interesting way of coping with this class of problems is the Decision-Theoretic Planning approach, i.e. the formulations of policies on the basis of Decision Theory. This approach is able to provide plans in the presence of partial and qualitative information, while preserving a sound mathematical foundation. In this paper we will exploit a novel graphical formalism for representing Decision-Theoretic Planning problems, called Influence View. This method will be tested in an important therapy planning problem: the assessment of the Graft Versus Host Disease prophylaxis after Bone Marrow Transplantation in leukemic children.

This paper studies queries to a database, involving expressions of the form ‘Q A-x’s are B’s’ where A and B are properties which may be fuzzy and with respect to which objects x’s are evaluated, and where Q is a quantifier which may stand for ‘all’, or may leave room for exceptions (‘at least q%’, ‘(at least) most’, etc.). An example of such a query is ‘Find the departments where most young employees are well-paid’. Such queries are discussed from a modeling and evaluation point of view, taking also into consideration what the user intends to ask when (s)he addresses this type of queries to a database system. Clarifying what has to be evaluated is specially important in the case where A is fuzzy, since then the boundaries of A are ill-defined and A may be somewhat empty.

This paper describes the application of uncertainty to a radio communication system. In this particular application, uncertainty information is used to optimise a Reason Maintenance System so that tight deadlines can be met. The advantages of using uncertainty techniques here are the capability of dealing with data which may have been corrupted, and the improved real-time performance. The experiences of using uncertainty techniques in a real application are summarised.

In this chapter we present SPONGIA, a knowledge based system implemented using the Milord II programming environment. SPONGIA deals with the identification of sponges from the Atlanto-Mediterranean biogeographical province. It covers the identification of more than 100 taxa of the phylum Porifera from class to species. The effective handling of uncertainty has been critical to display an efficient performance in SPONGIA. This problem has been managed taking advantage of the multiple techniques provided by Milord II. The use of fuzzy logic makes it possible to accurately represent the imprecise knowledge which constitutes the classificatory theory of Porifera to a large extent. It also provides the user with some means of expressing his state of knowledge with accuracy. Easy design and incremental development of the knowledge base are possible thanks to modularity. Taxonomic knowledge is represented by means of plain modules hierarchically interconnected via submodule declarations and refinement operations. To emulate the reasoning strategies we use generic modules, which can take other modules as parameters. Thanks to the uncertainty handling and reflective deduction mechanisms it has been possible to emulate complex reasoning strategies displayed by experts in sponge systematics. Finally, the strict compartmentation of domain knowledge and knowledge concerning reasoning strategies into modules allows the reusability of pieces of knowledge.

Classically, risk is characterised by a point value probability indicating the likelihood of occurrence of an adverse effect. However, there are domains where the attainability of objective numerical risk characterisations is increasingly being questioned. This paper reviews the arguments in favour of extending classical techniques of risk assessment to incorporate meaningful qualitative and weak quantitative risk characterisations. A technique in which linguistic uncertainty terms are defined in terms of patterns of argument is then proposed. The technique is demonstrated using a prototype computer-based system for predicting the carcinogenic risk due to novel chemical compounds.

This paper describes the use of the Dempster-Shafer theory of evidence to construct an information retrieval model that aims to capture four essential features of information: structure, significance, uncertainty and partiality. We show that Dempster-Shafer’s initial framework allows the representation of the structure and the significance of information, and that the notion of refinement later introduced by Shafer allows the representation of the uncertainty and the partiality of information. An implementation of the model is briefly discussed.

This paper describes the application of Fuzzy Logic to Connection Admission Control (CAC) in Asynchronous Transfer Mode (ATM) broadband communications networks. CAC is a traffic control function that decides whether or not to admit a new connection on to the network, subject to ensuring the required quality of service of all the connections. Observations of the traffic in the ATM link (examples) are used to acquire knowledge on the behaviour of the ATM traffic. From this knowledge, the Fuzzy Logic based CAC (FCAC) can, then, infer the maximum expected ratio of cells lost per cells sent for a given connection in the presence of a particular traffic scenario. Uncertainty measures associated with each of the fuzzy rules enable to measure the uncertainty generated by the number of positive and negative examples for a rule. This way, not only the matching rule(s) for a certain input but also the uncertainty measure for this rule(s) will influence the fuzzily inferred output. A study is made to evaluate the cell loss ratio for an ATM link carrying variable bit rate traffic; the results obtained with the FCAC are compared with results obtained using analytical CAC algorithms.

Autonomous robots need the ability to move purposefully and without human intervention in real-world environments that have not been specifically engineered for them. These environments are characterized by the pervasive presence of uncertainty: the need to cope with this uncertainty constitutes a major challenge for autonomous robots. In this note, we discuss this challenge, and present some specific solutions based on our experience on the use of fuzzy logic in mobile robots. We focus on three issues: how to realize robust motion control; how to flexibly execute navigation plans; and how to approximately estimate the robot’s location.

This paper discusses the difficulties in applying uncertainty management techniques to real world problems. Automated Inspection is a process where the data used to model the environment is uncertain. There is an existing body of knowledge within the research community which enables such uncertain information to be expressed. Although there have been successful applications in fields such as medical diagnosis, there are also problems in industry which currently cannot be solved. The process of industrial inspection is an environment where the method for applying uncertainty management techniques is not intuitive. The nature of the uncertainty and the difficulty in applying the theoretical techniques to real world problems shall be the focus of the following discussion.

This paper describes a modelling language which is suitable for the correlation of information when the underlying functional model of the system is incomplete or uncertain and the temporal dependencies are imprecise. An implementation of this approach is outlined using cost functions. If the cost functions satisfy certain criteria then an efficient and incremental approach to the control computation is possible. Possibilistic logic and probability theory (as it is used in the applications targetted) satisfy the criteria.

Decision making under uncertainty is central to reasoning by practical intelligent systems, and attracts great controversy. The most widely accepted approach is to represent uncertainty in terms of prior and conditional probabilities of events and the utilities of consequences of actions, and to apply standard decision theory to calculate degrees of belief and expected utilities of actions. Unfortunately, as has been observed many times, reliable probabilities are often not easily available. Furthermore the benefits of a quantitative probabilistic representation can be small by comparison with the restrictions imposed by the formalism. In this paper we summarise an approach to reasoning under uncertainty by constructing arguments for and against particular options and then describe an extension of this approach to reasoning about the expected values of actions.

In this paper logical techniques developed to formalize the analysis of multi-interpretable information, in particular belief set operators and selection operators, are applied to an ecological domain. A knowledge-based decision support system is described that determines the abiotic (chemical and physical) characteristics of a site on the basis of samples of plant species that are observed. The logical foundation of this system is described in terms of a belief set operator and a selection operator. Moreover, it is shown how the belief set operator that corresponds to the system can be represented by a normal default theory.

This paper contains two parts: we first investigate the idea of reasoning, in a “local” way, with prioritized and possibly inconsistent knowledge bases. Priorities are not given globally between all the beliefs in the knowledge base, but locally within each minimal set of pieces of information responsible for inconsistencies. This local stratification offers more flexibility for representing priorities between beliefs. When this stratification is available, we show that the task of coping with inconsistency is greatly simplified, since it determines what beliefs must be removed in order to restore consistency in the knowledge base. Three local approaches are developed in this paper. The second part of the paper applies one of these three approaches to default reasoning. Our proposal for defining the specificity relation inside conflicts allows us to infer plausible conclusions which cannot be obtained if a global stratification is used. In each part, we provide a comparative study with existing inconsistency-handling approaches and with various default reasoning systems, respectively.

We present an implementation platform for query-answering in default logics, supporting local proof procedures. We describe the salient features of the corresponding system, called XRay, and provide some major theoretical underpinnings. The deductive power of XRay stems from its usage of Prolog Technology Theorem Proving Techniques (PTTP). This is supported by further enhancements, such as default lemma handling, regularity-based truncations of the underlying search space, and further configurable features. The computational value of these enhancements is backed up by a series of experiments that provide us with valuable insights into their inuence on XRay’s performance. The generality of the approach, allowing for a (simultaneous) treatment of different default logics, stems from a novel model-based approach to consistency checking.

The present study treats model-based diagnosis as an uncertain reasoning problem. To handle the uncertainty in model-based diagnosis effectively, a probabilistic approach serves as a point of departure. The use of probabilities in diagnosis has proved beneficial to the performance of diagnostic engines.

We extend the use of probabilities to reflect the aging processes affecting component lifetimes. Unexpected failures signal unusual operating conditions possibly due to the failure of other subsystems. The diagnostic system architecture proposed here is capable of detecting failures that are difficult to detect using a conventional diagnostic engine. Moreover, ascribing a statistical interpretation to nonmonotonic reasoning, allows us to use a hybrid (probabilistic-logical) inference engine at the heart of this system.

Graphical modelling is an important tool for the efficient representation and analysis of uncertain information in knowledge-based systems. While Bayesian networks and Markov networks from probabilistic graphical modelling have been well-known for about ten years, the field of possibilistic graphical modelling appears to be a new promising area of research. Possibilistic networks provide an alternative approach compared to probabilistic networks, whenever it is necessary to model uncertainty and imprecision as two different kinds of imperfect information. Imprecision in the sense of multivalued data has often to be considered in situations where information is obtained from human observations or non-precise measurement units. In this contribution we present a comparison of the background and perspectives of probabilistic and possibilistic graphical models, and give an overview on the current state of the art of possibilistic networks with respect to propagation and learning algorithms, applicable to data mining and data fusion problems.

Modal logics are often criticised for their coarse grain representation of knowledge of possibilities about assertions. That is to say, if two assertions are possible in the current world, their further properties are indistinguishable in the modal formalism even if an agent knows that one of them is true in twice as many possible worlds as compared to the other one. Epistemic logic, that is the logic of knowledge and belief, cannot avoid this shortcomings because it inherits the syntax and semantics of modal logics. In this paper, we develop an extended formalism of modal epistemic logic which will allow an agent to represent its degrees of support about an assertion. The degrees are drawn from qualitative or quantitative dictionaries which are accumulated from agent’s a priori knowledge about the application domain. A possible-world semantics of the logic is developed by using the accessibility hyperelation and the soundness and completeness results are stated. The abstract syntax and semantics are illustrated and motivated by an example from the medical domain.

In this paper we begin the analysis and formalisation of common sense reasoning about safety. To begin with we analyse absolute safety, and use and extend the framework of Dynamic Logic in order to develop a formal possible-worlds semantics and logic for it. We then extend the analysis to normal safety. We introduce Defeasible Dynamic Logic in order to give possible-worlds semantics and logic for normal safety, and define a preferential entailment relation defined in order to represent common sense reasoning about the normal termination of actions. We conclude with a discussion of the relationship between safety, obligation, rationality and risk, and outline some extensions to the present work.

This paper proposes assumption-based systems as an efficient and convenient way to encode uncertain information. Assumption based systems are obtained from propositional logic by including a special type of propositional symbol called assumption. Assumptions are needed to express the uncertainty of the given information. Assumption-based systems can be used to judge hypotheses qualitatively or quantitatively. This paper shows how assumption-based systems are obtained from causal networks, it describes how symbolic arguments for hypotheses can be computed efficiently, and it presents ABEL, a modeling language for assumption-based systems and an interactive tool for probabilistic assumption-based reasoning.