Complexity of Non-Monotonic Logics

Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been considered, e.g., extension with default rules, extension with modal belief operators, or modification of the semantics. In this survey we consider a logical formalism from each of the above possibilities, namely Reiter's default logic, Moore's autoepistemic logic and McCarthy's circumscription. Additionally, we consider abduction, where one is not interested in inferences from a given knowledge base but in computing possible explanations for an observation with respect to a given knowledge base. Complexity results for different reasoning tasks for propositional variants of these logics have been studied already in the nineties. In recent years, however, a renewed interest in complexity issues can be observed. One current focal approach is to consider parameterized problems and identify reasonable parameters that allow for FPT algorithms. In another approach, the emphasis lies on identifying fragments, i.e., restriction of the logical language, that allow more efficient algorithms for the most important reasoning tasks. In this survey we focus on this second aspect. We describe complexity results for fragments of logical languages obtained by either restricting the allowed set of operators (e.g., forbidding negations one might consider only monotone formulae) or by considering only formulae in conjunctive normal form but with generalized clause types. The algorithmic problems we consider are suitable variants of satisfiability and implication in each of the logics, but also counting problems, where one is not only interested in the existence of certain objects (e.g., models of a formula) but asks for their number.Comment: To appear in Bulletin of the EATC

Constraint-Driven Fault Diagnosis

Constraint-Driven Fault Diagnosis (CDD) is based on the concept of constraint suspension [6], which was proposed as an approach to fault detection and diagnosis. In this chapter, its capabilities are demonstrated by describing how it might be applied to hardware systems. With this idea, a model-based fault diagnosis problem may be considered as a Constraint Satisfaction Problem (CSP) in order to detect any unexpected behavior and Constraint Satisfaction Optimization Problem (COP) constraint optimization problem in order to identify the reason for any unexpected behavior because the parsimony principle is taken into accountMinisterio de Ciencia y Tecnología TIN2015-63502-C3-2-

Explanation in constraint satisfaction: A survey

Much of the focus on explanation in the field of artificial intelligence has focused on machine learning methods and, in particular, concepts produced by advanced methods such as neural networks and deep learning. However, there has been a long history of explanation generation in the general field of constraint satisfaction, one of the AI's most ubiquitous subfields. In this paper we survey the major seminal papers on the explanation and constraints, as well as some more recent works. The survey sets out to unify many disparate lines of work in areas such as model-based diagnosis, constraint programming, Boolean satisfiability, truth maintenance systems, quantified logics, and related areas

Automated model-based spreadsheet debugging

Spreadsheets are interactive data organization and calculation programs that are developed in spreadsheet environments like Microsoft Excel or LibreOffice Calc. They are probably the most successful example of end-user developed software and are utilized in almost all branches and at all levels of companies. Although spreadsheets often support important decision making processes, they are, like all software, prone to error. In several cases, faults in spreadsheets have caused severe losses of money. Spreadsheet developers are usually not educated in the practices of software development. As they are thus not familiar with quality control methods like systematic testing or debugging, they have to be supported by the spreadsheet environment itself to search for faults in their calculations in order to ensure the correctness and a better overall quality of the developed spreadsheets. This thesis by publication introduces several approaches to locate faults in spreadsheets. The presented approaches are based on the principles of Model-Based Diagnosis (MBD), which is a technique to find the possible reasons why a system does not behave as expected. Several new algorithmic enhancements of the general MBD approach are combined in this thesis to allow spreadsheet users to debug their spreadsheets and to efficiently find the reason of the observed unexpected output values. In order to assure a seamless integration into the environment that is well-known to the spreadsheet developers, the presented approaches are implemented as an extension for Microsoft Excel. The first part of the thesis outlines the different algorithmic approaches that are introduced in this thesis and summarizes the improvements that were achieved over the general MBD approach. In the second part, the appendix, a selection of the author's publications are presented. These publications comprise (a) a survey of the research in the area of spreadsheet quality assurance, (b) a work describing how to adapt the general MBD approach to spreadsheets, (c) two new algorithmic improvements of the general technique to speed up the calculation of the possible reasons of an observed fault, (d) a new concept and algorithm to efficiently determine questions that a user can be asked during debugging in order to reduce the number of possible reasons for the observed unexpected output values, and (e) a new method to find faults in a set of spreadsheets and a new corpus of real-world spreadsheets containing faults that can be used to evaluate the proposed debugging approaches

Diagnosing Tree Structured Systems

This paper introduces the algorithm TREE DIAG for computing minimal diagnoses for tree structured systems. Diagnoses are computed by descending into the tree, enumerating the input combinations that might be reponsible for a given incorrect observation, and combining the diagnoses for the subtrees generating these inputs into diagnoses for the whole system. We prove soundness and correctness of the algorithm and show experimental results that indicate that it compares favorably to Reiter's hitting-set-based algorithm and El Fattah and Dechter's SAB. Extensions of the algorithm related to general acyclic systems, use of fault modes and the practical application to the software diagnosis domain are discussed. Keywords: Model-Based Diagnosis, Algorithms 1 Introduction Since the beginning of model-based diagnosis research, several attempts have been made to make model-based diagnosis of large systems feasible. This has been done by introducing probability measurements ([dK91]), by comput..

Diagnosing tree-structured systems☆☆Part of this work has been published in preliminary form in the Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI-97).

AbstractThis paper introduces the TREE/TREE∗ algorithm for computing minimal diagnoses for tree-structured systems. Diagnoses are computed by descending into the tree, enumerating the input combinations that might be responsible for a given incorrect observation, and combining the diagnoses for the subtrees generating these inputs into diagnoses for the whole system. Algorithm TREE diagnoses systems containing functional components and algorithm TREE∗ diagnoses more general constraint-based components. We prove soundness and correctness of the algorithms and show experimental results that indicate that they compare favorably to Reiter's hitting-set-based algorithm and El Fattah and Dechter's SAB. Extensions of the algorithms such as use of fault modes are discussed