Preferential Semantics for Plausible Subsumption in Possibility Theory

This paper discusses contemporary issues associated with the use of approximate reasoning techniques in knowledge-based systems relying on the theory of possibility. It aims at: providing lines along which comparison of existing systems can be done; pointing out directions toward which future systems should evolve.

Revising knowledge bases (KBs) in description logics (DLs) in a syntax-independent manner is an important, nontrivial problem for the ontology management and DL communities. Several attempts have been made to adapt classical model-based belief revision and update techniques to DLs, but they are restricted in several ways. In particular, they do not provide operators or algorithms for general DL KB revision. The key difficulty is that, unlike propositional logic, a DL KB may have infinitely many models with complex (and possibly infinite) structures, making it difficult to define and compute revisions in terms of models. In this paper, we study general KBs in a specific DL in the DL-Lite family. We introduce the concept of features for such KBs, develop an alternative semantic characterization of KBs using features (instead of models), define two specific revision operators for KBs, and present the first algorithm for computing best approximations for syntax-independent revisions of KBs.

This contribution is a response to the 2025 NASA and DNV challenge on optimization under uncertainty.Three typical engineering problems in the form of parameter identification, forward propagation of uncertainty, and optimization are addressed.The framework of possibility theory is outlined and applied to the problems of the challenge.Given the nature of possibility theory, the results provide a rigorous and deliberately cautious perspective on the challenge problems.Accordingly, this approach is expected to be among the more conservative responses, offering a robust and well-substantiated analysis of uncertainty.The analysis is implemented through a samplingbased approach, returning statistically valid confidence distributions with all prior information explicitly stated.

Evaluating the success of a knowledge acquisition (KA) task is difficult and expensive. Most evaluation approaches rely on the expert themselves, either directly, or indirectly by relying on data previously prepared with the help of experts. In incremental KA, knowledge base (KB) errors are monitored and corrected by an expert. Thus, during its evolution a record of the knowledge based system (KBS) performance is usually easy to keep. We propose to integrate with the incremental KA process, an evaluation process based on a statistical analysis to estimate the effectiveness of the KBS, as the KBS is actually evolved. We tailor such an analysis for Ripple Down Rules (RDR), which is an effective incremental KA methodology where a record of the KBS performance can be easily derived and updated as new cases are processed by the system. An RDR KB is a collection of rules with hierarchical exceptions, which are entered and validated by the expert in the context of their use. This greatly facilitates the knowledge maintenance task which, characteristically in RDR, overlaps with the incremental KA process. The work in this paper aims to overlap evaluation with maintenance and development of the knowledge base. It also minimises the major expense in deploying the RDR KBS, that of keeping a domain expert on-line during maintenance and the initial period of deployment. The expert is not kept on-line longer than it is absolutely necessary. We use the structure and semantics of an evolving RDR KB, combined with proven machine learning statistical methods, to estimate the added value in every KB update, as the KB evolves. Using these values, the decisionmakers in the organisation employing the KBS can apply a cost-benefit analysis of the continuation of the incremental KA process. They can then determine when this process, involving keeping an expert on-line, should be terminated.

Layers of protection analysis in the framework of possibility theory

Breast cancer early diagnosis is a major concern for reducing deadly cases. Automation of microcalcification detection is becoming increasingly important given their tiny scale. At this step, a high false negative rate is observed, leading to high ambiguity. In this context, conventional approaches are unable to handle such ambiguity. Possibility theory offers a powerful paradigm enabling to handle a high uncertainty level. Therefore, in this research,new possibilistic modeling strategy for microcalcification detection is proposed. The developed system is based on k-means clustering followed by a fusion of the corresponding possibility distributions, for decision making. For enhancing classification's accuracy, two aspects may be taken into consideration: scattering within classes and the class discrimination power. A high inter-class variance may be regarded as an evidence of good discrimination. Nevertheless, in case of existing highly scattered classes, miss-classifications of samples at the class margins are still encountered, even at high inter-class variance. Clustering solves this problem by redefining classes in a more compact way. Under this paradigm, the clustering optimization is performed using a criteria based on the Area Under Curve(AUC), where the confidence degree level is based on the consistency principle of Dubois and Prade. The above strategy has been applied for the detection of microcalcifications, based on a set of pyramidal and multi-resolution based features. Validation on the Digital Database for Screening Mammography (DDSM) public dataset has been undertaken. The proposed system, which gives 99.4 % detection accuracy, can be used to assist medical practitioners.

Description logics provide powerful languages for representing and reasoning about knowledge of static application domains. The main strength of description logics is that they offer considerable expressive power going far beyond propositional logic, while reasoning is still decidable. There is a demand to bring the power and character of description logics into the description and reasoning of dynamic application domains which are characterized by actions. In this paper, based on a combination of the propositional dynamic logic PDL, a family of description logics and an action formalism constructed over description logics, we propose a family of dynamic description logics DDL(X @) for representing and reasoning about actions, where X represents well-studied description logics ranging from the to the , and X @ denotes the extension of X with the @ constructor. The representation power of DDL(X @) is reflected in four aspects. Firstly, the static knowledge of application domains is represented as RBoxes and acyclic TBoxes of the description logic X. Secondly, the states of the world and the pre-conditions of atomic actions are described by ABox assertions of the description logic X @, and the post-conditions of atomic actions are described by primitive literals of X @. Thirdly, starting with atomic actions and ABox assertions of X @, complex actions are constructed with regular program constructors of PDL, so that various control structures on actions such as the "Sequence", "Choice", "Any-Order", "Iterate", "If-Then-Else", "Repeat-While" and "Repeat-Until" can be represented. Finally, both atomic actions and complex actions are used as modal operators for the construction of formulas, so that many properties on actions can be explicitly stated by formulas. A tableau-algorithm is provided for deciding the satisfiability of DDL(X @)-formulas; based on this algorithm, reasoning tasks such as the realizability, executability and projection of actions can be effectively carried out. As a result, DDL(X @) not only offers considerable expressive power going beyond many action formalisms which are propositional, but also provides decidable reasoning services for actions described by it.

Description logics [1] refer to a family of formalisms concentrated around concepts, roles and individuals. They are used in many multiagent and semantic web applications as a foundation for specifying knowledge bases and reasoning about them. One of widely applied description logics is $\mathcal{SHIQ}$ [7,8]. In the current paper we address the problem of inconsistent knowledge. Inconsistencies may naturally appear in the considered application domains, for example as a result of fusing knowledge from distributed sources. We define three three-valued paraconsistent semantics for $\mathcal{SHIQ}$ , reflecting different meanings of concept inclusion of practical importance. We also provide a quite general syntactic condition of safeness guaranteeing satisfiability of a knowledge base w.r.t. three-valued semantics and define a faithful translation of our formalism into a suitable version of a two-valued description logic. Such a translation allows one to use existing tools and $\mathcal{SHIQ}$ reasoners to deal with inconsistent knowledge.

Answering regular path queries in expressive Description Logics via alternating tree-automata

Description logics (DLs) and rule-based systems are two prominent families of knowledge representation formalisms. While DLs are focused on describing and reasoning about conceptual knowledge, rules are focused on answering queries about facts in the knowledge base. So far, research on DLs has been largely isolated from the research on rules. With the advent of the Semantic Web, however, it became apparent that neither formalism alone can cover all the practical use cases. The integration between DLs and rules, however, is technically challenging due to significant differences in the underlying semantic assumptions. In particular, DLs are based on standard first-order semantics and open-world assumption, whereas rules typically employ closed-world semantics based on a variant of circumscription. In my talk, I shall present an overview of the benefits of integrating DLs and rules in a coherent semantic framework, and shall discuss the main challenges in achieving a tight integration. I shall present an overview of the approaches currently discussed in literature. Finally, I shall present in more detail the approach that is based on the nonmonotonic logic MKNF by Lifschitz. This approach is tight in the sense that DLs and rules are given a common model-theoretic semantics. Furthermore, it is faithful in the sense that it is compatible with the original semantics of both DLs and rules. Finally, it is expressive and can naturally capture many of the existing proposals. I shall discuss the definitions of the semantics of the hybrid formalism, present a decision procedure for a particular decidable fragment, and discuss the complexity bounds of reasoning.

Formulation of efficient algorithms to check implication and satisfibality for relational queries is an important research issue. Implication and satisfibality checking can be used to find query containment in semantic cache query processing and other similar applications. Description logic (DL) is a formalism used to model knowledge of a domain in the form of concepts and a rich set of associations between these concepts in the T-Boxes. Reasoning on these knowledge bases can be performed in order to find explicit relation as well as discover implicit relations. Sound and Complete subsumption algorithms exist for reasoning facts represented in Description Logic. The most common reasoning (which can be used for other sort of reasoning, too) is the determination of a subsumption relation between the logical expressions of T-boxes. In this paper, we propose an algorithm to translate relational queries in to description logic ALC(D), so that DL subsumption algorithms can be applied on these translated queries to find query containment. Working of the algorithm is demonstrated with the help of a case study. Conversion of relational query into DL will also help in optimization of cache size for the storage of semantics by eliminating redundant semantics in the cache. Hence, the sound and complete reasoning services of DL can be used for relational query containment.

Research in verification and validation (V&V) of knowledge based systems (KBS) has emerged as a distinct field in the last decade and is intended to address issues associated with KBS quality aspects and to credit such applications to the same degree as conventional applications. Part of the knowledge and techniques developed are now ready to be transferred to industry for the implementation of software certification. Certification is probably the most advanced use of the V&V methods, techniques and knowledge that have been developed so far. The paper approaches the challenging issues of certifying the knowledge base (KB) component of a KBS. KB certification uses a number of different certification methods such as static analysis, testing, inspection, and modeling to assess the quality of the KB component. Although these methods are currently used in KBS development, it is not yet clear how they would be applied by an independent certification organization to arrive at a pass/fail decision. The article discusses the components of KB certification and identifies application areas directly connected with industrial needs.

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition.We start by investigating a notion ofdefeasible subsumptionin the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for bothpreferentialandrationalsubsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level ofentailmentand present an algorithm for the computation ofrational closureof a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DLALC.

In the process of information semantic integration for product design and manufacturing, it is very important to express the product information semantic. Description logics (DLs) are a family of state-of-the-art knowledge representation languages, and a decidable subset of first-order logic. Firstly, by analyzing the characteristics of product information, proposed a semantic information description framework based on description logics for product information integration, which is divided into three levels: basic description logic, classic extended logic and unusual extended logic. Then, in the framework, reducer was taken for example to illustrate the application of their description logic in product design and manufacturing formal semantic information. Finally, based on description logic, discussed reasoning problems of product design and manufacturing information.

Knowledge-based technology is being applied to complex problem-solving and critical tasks in many application domains. Concerns have naturally arisen as to the dependability of knowledge-base systems (KBSs). As with any software, attention to quality and safety must be paid throughout the development of a KBS, and rigorous verification and validation (V&V) techniques must be employed. Research in KBS V&V has emerged as a distinct field only in the last decade and is intended to address issues associated with KBS quality aspects and to credit such applications with the same degree of dependability as conventional applications. However, a major drawback of the current state of acceptance of KBS software is the lack of standardization. Although standards do exist for software, extensions are needed to cope with specific KBS software characteristics. This paper advocates the idea that, although quality assessment of KBS software is still a challenging issue, KBS software is not an impossible one. Some V&V techniques based on specific KBS software properties are described in this paper which aims at indicating KBS acceptability requirements may be specified and evaluated, being at the same time a good basis for certification.