Patrick Rodler

Veronika Semmelrock, Benedetta Strizzolo, Francesco Zuccato et al.

Combinatorial and optimization problems are fundamental to many industrial AI applications. Solving large-scale real-world instances of such problems typically requires careful problem formalization, specialized solvers, and expert-designed heuristics. Thus, experts need to specify not only what solutions are, but also how they are derived. By introducing the tool CHECKMATE, we show that algorithm generation via code evolution represents a paradigm shift by eliminating the need to formulate the how. CHECKMATE solely relies on the what. Specifically, a formal specification ensures solutions' correctness and enables systematic performance evaluation of the generated programs, while a natural language description guides the evolutionary process. The effectiveness of our method is demonstrated on selected problems from two industrial domains: configuration and scheduling. In all cases, the evolved algorithms consistently outperform state-of-the-art solvers. This underscores the potential of formal methods in guiding code evolution for automatically solving complex real-world problems.

Patrick Rodler

This work proposes a taxonomy for diagnosis computation methods which allows their standardized assessment, classification and comparison. The aim is to (i) give researchers and practitioners an impression of the diverse landscape of available diagnostic techniques, (ii) allow them to easily retrieve the main features as well as pros and cons of the approaches, (iii) enable an easy and clear comparison of the techniques based on their characteristics wrt. a list of important and well-defined properties, and (iv) facilitate the selection of the "right" algorithm to adopt for a particular problem case, e.g., in practical diagnostic settings, for comparison in experimental evaluations, or for reuse, modification, extension, or improvement in the course of research.

Patrick Rodler

In the modern world, we are permanently using, leveraging, interacting with, and relying upon systems of ever higher sophistication, ranging from our cars, recommender systems in e-commerce, and networks when we go online, to integrated circuits when using our PCs and smartphones, the power grid to ensure our energy supply, security-critical software when accessing our bank accounts, and spreadsheets for financial planning and decision making. The complexity of these systems coupled with our high dependency on them implies both a non-negligible likelihood of system failures, and a high potential that such failures have significant negative effects on our everyday life. For that reason, it is a vital requirement to keep the harm of emerging failures to a minimum, which means minimizing the system downtime as well as the cost of system repair. This is where model-based diagnosis comes into play. Model-based diagnosis is a principled, domain-independent approach that can be generally applied to troubleshoot systems of a wide variety of types, including all the ones mentioned above, and many more. It exploits and orchestrates i.a. techniques for knowledge representation, automated reasoning, heuristic problem solving, intelligent search, optimization, stochastics, statistics, decision making under uncertainty, machine learning, as well as calculus, combinatorics and set theory to detect, localize, and fix faults in abnormally behaving systems. In this thesis, we will give an introduction to the topic of model-based diagnosis, point out the major challenges in the field, and discuss a selection of approaches from our research addressing these issues.

Patrick Rodler

Given a system that does not work as expected, Sequential Diagnosis (SD) aims at suggesting a series of system measurements to isolate the true explanation for the system's misbehavior from a potentially exponential set of possible explanations. To reason about the best next measurement, SD methods usually require a sample of possible fault explanations at each step of the iterative diagnostic process. The computation of this sample can be accomplished by various diagnostic search algorithms. Among those, Reiter's HS-Tree is one of the most popular due its desirable properties and general applicability. Usually, HS-Tree is used in a stateless fashion throughout the SD process to (re)compute a sample of possible fault explanations in each iteration, each time given the latest (updated) system knowledge including all so-far collected measurements. At this, the built search tree is discarded between two iterations, although often large parts of the tree have to be rebuilt in the next iteration, involving redundant operations and calls to costly reasoning services. As a remedy to this, we propose DynamicHS, a variant of HS-Tree that maintains state throughout the diagnostic session and additionally embraces special strategies to minimize the number of expensive reasoner invocations. In this vein, DynamicHS provides an answer to a longstanding question posed by Raymond Reiter in his seminal paper from 1987. Extensive evaluations on real-world diagnosis problems prove the reasonability of the DynamicHS and testify its clear superiority to HS-Tree wrt. computation time. More specifically, DynamicHS outperformed HS-Tree in 96% of the executed sequential diagnosis sessions and, per run, the latter required up to 800% the time of the former. Remarkably, DynamicHS achieves these performance improvements while preserving all desirable properties as well as the general applicability of HS-Tree.

Patrick Rodler

Various model-based diagnosis scenarios require the computation of most preferred fault explanations. Existing algorithms that are sound (i.e., output only actual fault explanations) and complete (i.e., can return all explanations), however, require exponential space to achieve this task. As a remedy, we propose two novel diagnostic search algorithms, called RBF-HS (Recursive Best-First Hitting Set Search) and HBF-HS (Hybrid Best-First Hitting Set Search), which build upon tried and tested techniques from the heuristic search domain. RBF-HS can enumerate an arbitrary predefined finite number of fault explanations in best-first order within linear space bounds, without sacrificing the desirable soundness or completeness properties. The idea of HBF-HS is to find a trade-off between runtime optimization and a restricted space consumption that does not exceed the available memory. In extensive experiments on real-world diagnosis cases we compared our approaches to Reiter's HS-Tree, a state-of-the-art method that gives the same theoretical guarantees and is as general(ly applicable) as the suggested algorithms. For the computation of minimum-cardinality fault explanations, we find that (1) RBF-HS reduces memory requirements substantially in most cases by up to several orders of magnitude, (2) in more than a third of the cases, both memory savings and runtime savings are achieved, and (3) given the runtime overhead is significant, using HBF-HS instead of RBF-HS reduces the runtime to values comparable with HS-Tree while keeping the used memory reasonably bounded. When computing most probable fault explanations, we observe that RBF-HS tends to trade memory savings more or less one-to-one for runtime overheads. Again, HBF-HS proves to be a reasonable remedy to cut down the runtime while complying with practicable memory bounds.

Patrick Rodler

Various model-based diagnosis scenarios require the computation of the most preferred fault explanations. Existing algorithms that are sound (i.e., output only actual fault explanations) and complete (i.e., can return all explanations), however, require exponential space to achieve this task. As a remedy, to enable successful diagnosis on memory-restricted devices and for memory-intensive problem cases, we propose RBF-HS, a diagnostic search method based on Korf's well-known RBFS algorithm. RBF-HS can enumerate an arbitrary fixed number of fault explanations in best-first order within linear space bounds, without sacrificing the desirable soundness or completeness properties. Evaluations using real-world diagnosis cases show that RBF-HS, when used to compute minimum-cardinality fault explanations, in most cases saves substantial space (up to 98 %) while requiring only reasonably more or even less time than Reiter's HS-Tree, a commonly used and as generally applicable sound, complete and best-first diagnosis search.

Patrick Rodler, Fatima Elichanova

Statistical samples, in order to be representative, have to be drawn from a population in a random and unbiased way. Nevertheless, it is common practice in the field of model-based diagnosis to make estimations from (biased) best-first samples. One example is the computation of a few most probable possible fault explanations for a defective system and the use of these to assess which aspect of the system, if measured, would bring the highest information gain. In this work, we scrutinize whether these statistically not well-founded conventions, that both diagnosis researchers and practitioners have adhered to for decades, are indeed reasonable. To this end, we empirically analyze various sampling methods that generate fault explanations. We study the representativeness of the produced samples in terms of their estimations about fault explanations and how well they guide diagnostic decisions, and we investigate the impact of sample size, the optimal trade-off between sampling efficiency and effectivity, and how approximate sampling techniques compare to exact ones.

Patrick Rodler, Erich Teppan

A common issue for companies is that the volume of product orders may at times exceed the production capacity. We formally introduce two novel problems dealing with the question which orders to discard or postpone in order to meet certain (timeliness) goals, and try to approach them by means of model-based diagnosis. In thorough analyses, we identify many similarities of the introduced problems to diagnosis problems, but also reveal crucial idiosyncracies and outline ways to handle or leverage them. Finally, a proof-of-concept evaluation on industrial-scale problem instances from a well-known scheduling benchmark suite demonstrates that one of the two formalized problems can be well attacked by out-of-the-box model-based diagnosis tools.

Patrick Rodler

We challenge existing query-based ontology fault localization methods wrt. assumptions they make, criteria they optimize, and interaction means they use. We find that their efficiency depends largely on the behavior of the interacting expert, that performed calculations can be inefficient or imprecise, and that used optimization criteria are often not fully realistic. As a remedy, we suggest a novel (and simpler) interaction approach which overcomes all identified problems and, in comprehensive experiments on faulty real-world ontologies, enables a successful fault localization while requiring fewer expert interactions in 66 % of the cases, and always at least 80 % less expert waiting time, compared to existing methods.

Patrick Rodler

In his seminal paper of 2004, Ulrich Junker proposed the QuickXPlain algorithm, which provides a divide-and-conquer computation strategy to find within a given set an irreducible subset with a particular (monotone) property. Beside its original application in the domain of constraint satisfaction problems, the algorithm has since then found widespread adoption in areas as different as model-based diagnosis, recommender systems, verification, or the Semantic Web. This popularity is due to the frequent occurrence of the problem of finding irreducible subsets on the one hand, and to QuickXPlain's general applicability and favorable computational complexity on the other hand. However, although (we regularly experience) people are having a hard time understanding QuickXPlain and seeing why it works correctly, a proof of correctness of the algorithm has never been published. This is what we account for in this work, by explaining QuickXPlain in a novel tried and tested way and by presenting an intelligible formal proof of it. Apart from showing the correctness of the algorithm and excluding the later detection of errors (proof and trust effect), the added value of the availability of a formal proof is, e.g., (i) that the workings of the algorithm often become completely clear only after studying, verifying and comprehending the proof (didactic effect), (ii) the shown proof methodology can be used as a guidance for proving other recursive algorithms (transfer effect), and (iii) the possibility of providing "gapless" correctness proofs of systems that rely on (results computed by) QuickXPlain, such as numerous model-based debuggers (completeness effect).

Patrick Rodler

Reiter's HS-Tree is one of the most popular diagnostic search algorithms due to its desirable properties and general applicability. In sequential diagnosis, where the addressed diagnosis problem is subject to successive change through the acquisition of additional knowledge about the diagnosed system, HS-Tree is used in a stateless fashion. That is, the existing search tree is discarded when new knowledge is obtained, albeit often large parts of the tree are still relevant and have to be rebuilt in the next iteration, involving redundant operations and costly reasoner calls. As a remedy to this, we propose DynamicHS, a variant of HS-Tree that avoids these redundancy issues by maintaining state throughout sequential diagnosis while preserving all desirable properties of HS-Tree. Preliminary results of ongoing evaluations in a problem domain where HS-Tree is the state-of-the-art diagnostic method suggest significant time savings achieved by DynamicHS by reducing expensive reasoner calls.

Patrick Rodler, Dietmar Jannach, Konstantin Schekotihin et al.

Real-world semantic or knowledge-based systems, e.g., in the biomedical domain, can become large and complex. Tool support for the localization and repair of faults within knowledge bases of such systems can therefore be essential for their practical success. Correspondingly, a number of knowledge base debugging approaches, in particular for ontology-based systems, were proposed throughout recent years. Query-based debugging is a comparably recent interactive approach that localizes the true cause of an observed problem by asking knowledge engineers a series of questions. Concrete implementations of this approach exist, such as the OntoDebug plug-in for the ontology editor Protégé. To validate that a newly proposed method is favorable over an existing one, researchers often rely on simulation-based comparisons. Such an evaluation approach however has certain limitations and often cannot fully inform us about a method's true usefulness. We therefore conducted different user studies to assess the practical value of query-based ontology debugging. One main insight from the studies is that the considered interactive approach is indeed more efficient than an alternative algorithmic debugging based on test cases. We also observed that users frequently made errors in the process, which highlights the importance of a careful design of the queries that users need to answer.

Patrick Rodler, Michael Eichholzer

When ontologies reach a certain size and complexity, faults such as inconsistencies, unsatisfiable classes or wrong entailments are hardly avoidable. Locating the incorrect axioms that cause these faults is a hard and time-consuming task. Addressing this issue, several techniques for semi-automatic fault localization in ontologies have been proposed. Often, these approaches involve a human expert who provides answers to system-generated questions about the intended (correct) ontology in order to reduce the possible fault locations. To suggest as informative questions as possible, existing methods draw on various algorithmic optimizations as well as heuristics. However, these computations are often based on certain assumptions about the interacting user. In this work, we characterize and discuss different user types and show that existing approaches do not achieve optimal efficiency for all of them. As a remedy, we suggest a new type of expert question which aims at fitting the answering behavior of all analyzed experts. Moreover, we present an algorithm to optimize this new query type which is fully compatible with the (tried and tested) heuristics used in the field. Experiments on faulty real-world ontologies show the potential of the new querying method for minimizing the expert consultation time, independent of the expert type. Besides, the gained insights can inform the design of interactive debugging tools towards better meeting their users' needs.

Patrick Rodler, Wolfgang Schmid

Given a malfunctioning system, sequential diagnosis aims at identifying the root cause of the failure in terms of abnormally behaving system components. As initial system observations usually do not suffice to deterministically pin down just one explanation of the system's misbehavior, additional system measurements can help to differentiate between possible explanations. The goal is to restrict the space of explanations until there is only one (highly probable) explanation left. To achieve this with a minimal-cost set of measurements, various (active learning) heuristics for selecting the best next measurement have been proposed. We report preliminary results of extensive ongoing experiments with a set of selection heuristics on real-world diagnosis cases. In particular, we try to answer questions such as "Is some heuristic always superior to all others?", "On which factors does the (relative) performance of the particular heuristics depend?" or "Under which circumstances should I use which heuristic?"

Patrick Rodler, Wolfgang Schmid, Konstantin Schekotihin

Model-Based Diagnosis deals with the identification of the real cause of a system's malfunction based on a formal system model and observations of the system behavior. When a malfunction is detected, there is usually not enough information available to pinpoint the real cause and one needs to discriminate between multiple fault hypotheses (called diagnoses). To this end, Sequential Diagnosis approaches ask an oracle for additional system measurements. This work presents strategies for (optimal) measurement selection in model-based sequential diagnosis. In particular, assuming a set of leading diagnoses being given, we show how queries (sets of measurements) can be computed and optimized along two dimensions: expected number of queries and cost per query. By means of a suitable decoupling of two optimizations and a clever search space reduction the computations are done without any inference engine calls. For the full search space, we give a method requiring only a polynomial number of inferences and show how query properties can be guaranteed which existing methods do not provide. Evaluation results using real-world problems indicate that the new method computes (virtually) optimal queries instantly independently of the size and complexity of the considered diagnosis problems and outperforms equally general methods not exploiting the proposed theory by orders of magnitude.

Patrick Rodler

Active Learning (AL) methods have proven cost-saving against passive supervised methods in many application domains. An active learner, aiming to find some target hypothesis, formulates sequential queries to some oracle. The set of hypotheses consistent with the already answered queries is called version space. Several query selection measures (QSMs) for determining the best query to ask next have been proposed. Assuming binaryoutcome queries, we analyze various QSMs wrt. to the discrimination power of their selected queries within the current version space. As a result, we derive superiority and equivalence relations between these QSMs and introduce improved versions of existing QSMs to overcome identified issues. The obtained picture gives a hint about which QSMs should preferably be used in pool-based AL scenarios. Moreover, we deduce properties optimal queries wrt. QSMs must satisfy. Based on these, we demonstrate how efficient heuristic search methods for optimal queries in query synthesis AL scenarios can be devised.

Patrick Rodler, Wolfgang Schmid, Konstantin Schekotihin

In this work we present strategies for (optimal) measurement selection in model-based sequential diagnosis. In particular, assuming a set of leading diagnoses being given, we show how queries (sets of measurements) can be computed and optimized along two dimensions: expected number of queries and cost per query. By means of a suitable decoupling of two optimizations and a clever search space reduction the computations are done without any inference engine calls. For the full search space, we give a method requiring only a polynomial number of inferences and guaranteeing query properties existing methods cannot provide. Evaluation results using real-world problems indicate that the new method computes (virtually) optimal queries instantly independently of the size and complexity of the considered diagnosis problems.

Patrick Rodler, Wolfgang Schmid, Kostyantyn Shchekotykhin

In many model-based diagnosis applications it is impossible to provide such a set of observations and/or measurements that allow to identify the real cause of a fault. Therefore, diagnosis systems often return many possible candidates, leaving the burden of selecting the correct diagnosis to a user. Sequential diagnosis techniques solve this problem by automatically generating a sequence of queries to some oracle. The answers to these queries provide additional information necessary to gradually restrict the search space by removing diagnosis candidates inconsistent with the answers. During query computation, existing sequential diagnosis methods often require the generation of many unnecessary query candidates and strongly rely on expensive logical reasoners. We tackle this issue by devising efficient heuristic query search methods. The proposed methods enable for the first time a completely reasoner-free query generation while at the same time guaranteeing optimality conditions, e.g. minimal cardinality or best understandability, of the returned query that existing methods cannot realize. Hence, the performance of this approach is independent of the (complexity of the) diagnosed system. Experiments conducted using real-world problems show that the new approach is highly scalable and outperforms existing methods by orders of magnitude.

Patrick Rodler

A broad variety of knowledge-based applications such as recommender, expert, planning or configuration systems usually operate on the basis of knowledge represented by means of some logical language. Such a logical knowledge base (KB) enables intelligent behavior of such systems by allowing them to automatically reason, answer queries of interest or solve complex real-world problems. Nowadays, where information acquisition comes at low costs and often happens automatically, the applied KBs are continuously growing in terms of size, information content and complexity. These developments foster the emergence of errors in these KBs and thus pose a significant challenge on all people and tools involved in KB evolution, maintenance and application. If some minimal quality criteria such as logical consistency are not met by some KB, it becomes useless for knowledge-based applications. To guarantee the compliance of KBs with given requirements, (non-interactive) KB debuggers have been proposed. These however often cannot localize all potential faults, suggest too large or incorrect modifications of the faulty KB or suffer from poor scalability due to the inherent complexity of the KB debugging problem. As a remedy to these issues, based on a well-founded theoretical basis this work proposes complete, sound and optimal methods for the interactive debugging of KBs that suggest the one (minimally invasive) error correction of the faulty KB that yields a repaired KB with exactly the intended semantics. Users, e.g. domain experts, are involved in the debugging process by answering automatically generated queries whether some given statements must or must not hold in the domain that should be modeled by the problematic KB at hand.

Patrick Rodler

Many AI applications rely on knowledge encoded in a locigal knowledge base (KB). The most essential benefit of such logical KBs is the opportunity to perform automatic reasoning which however requires a KB to meet some minimal quality criteria such as consistency. Without adequate tool assistance, the task of resolving such violated quality criteria in a KB can be extremely hard, especially when the problematic KB is large and complex. To this end, interactive KB debuggers have been introduced which ask a user queries whether certain statements must or must not hold in the intended domain. The given answers help to gradually restrict the search space for KB repairs. Existing interactive debuggers often rely on a pool-based strategy for query computation. A pool of query candidates is precomputed, from which the best candidate according to some query quality criterion is selected to be shown to the user. This often leads to the generation of many unnecessary query candidates and thus to a high number of expensive calls to logical reasoning services. We tackle this issue by an in-depth mathematical analysis of diverse real-valued active learning query selection measures in order to determine qualitative criteria that make a query favorable. These criteria are the key to devising efficient heuristic query search methods. The proposed methods enable for the first time a completely reasoner-free query generation for interactive KB debugging while at the same time guaranteeing optimality conditions, e.g. minimal cardinality or best understandability for the user, of the generated query that existing methods cannot realize. Further, we study different relations between active learning measures. The obtained picture gives a hint about which measures are more favorable in which situation or which measures always lead to the same outcomes, based on given types of queries.

Patrick Rodler

Many AI applications rely on knowledge about a relevant real-world domain that is encoded by means of some logical knowledge base (KB). The most essential benefit of logical KBs is the opportunity to perform automatic reasoning to derive implicit knowledge or to answer complex queries about the modeled domain. The feasibility of meaningful reasoning requires KBs to meet some minimal quality criteria such as logical consistency. Without adequate tool assistance, the task of resolving violated quality criteria in KBs can be extremely tough even for domain experts, especially when the problematic KB includes a large number of logical formulas or comprises complicated logical formalisms. Published non-interactive debugging systems often cannot localize all possible faults (incompleteness), suggest the deletion or modification of unnecessarily large parts of the KB (non-minimality), return incorrect solutions which lead to a repaired KB not satisfying the imposed quality requirements (unsoundness) or suffer from poor scalability due to the inherent complexity of the KB debugging problem. Even if a system is complete and sound and considers only minimal solutions, there are generally exponentially many solution candidates to select one from. However, any two repaired KBs obtained from these candidates differ in their semantics in terms of entailments and non-entailments. Selection of just any of these repaired KBs might result in unexpected entailments, the loss of desired entailments or unwanted changes to the KB. This work proposes complete, sound and optimal methods for the interactive debugging of KBs that suggest the one (minimally invasive) error correction of the faulty KB that yields a repaired KB with exactly the intended semantics. Users, e.g. domain experts, are involved in the debugging process by answering automatically generated queries about the intended domain.

Patrick Rodler, Kostyantyn Shchekotykhin, Philipp Fleiss et al.

The best currently known interactive debugging systems rely upon some meta-information in terms of fault probabilities in order to improve their efficiency. However, misleading meta information might result in a dramatic decrease of the performance and its assessment is only possible a-posteriori. Consequently, as long as the actual fault is unknown, there is always some risk of suboptimal interactions. In this work we present a reinforcement learning strategy that continuously adapts its behavior depending on the performance achieved and minimizes the risk of using low-quality meta information. Therefore, this method is suitable for application scenarios where reliable prior fault estimates are difficult to obtain. Using diverse real-world knowledge bases, we show that the proposed interactive query strategy is scalable, features decent reaction time, and outperforms both entropy-based and no-risk strategies on average w.r.t. required amount of user interaction.

Patrick Rodler, Kostyantyn Shchekotykhin, Philipp Fleiss et al.

Efficient ontology debugging is a cornerstone for many activities in the context of the Semantic Web, especially when automatic tools produce (parts of) ontologies such as in the field of ontology matching. The best currently known interactive debugging systems rely upon some meta information in terms of fault probabilities, which can speed up the debugging procedure in the good case, but can also have negative impact on the performance in the bad case. The problem is that assessment of the meta information is only possible a-posteriori. Consequently, as long as the actual fault is unknown, there is always some risk of suboptimal interactive diagnoses discrimination. As an alternative, one might prefer to rely on a tool which pursues a no-risk strategy. In this case, however, possibly well-chosen meta information cannot be exploited, resulting again in inefficient debugging actions. In this work we present a reinforcement learning strategy that continuously adapts its behavior depending on the performance achieved and minimizes the risk of using low-quality meta information. Therefore, this method is suitable for application scenarios where reliable a-priori fault estimates are difficult to obtain. Using problematic ontologies in the field of ontology matching, we show that the proposed risk-aware query strategy outperforms both active learning approaches and no-risk strategies on average in terms of required amount of user interaction.

Kostyantyn Shchekotykhin, Philipp Fleiss, Patrick Rodler et al.

Modern ontology debugging methods allow efficient identification and localization of faulty axioms defined by a user while developing an ontology. The ontology development process in this case is characterized by rather frequent and regular calls to a reasoner resulting in an early user awareness of modeling errors. In such a scenario an ontology usually includes only a small number of conflict sets, i.e. sets of axioms preserving the faults. This property allows efficient use of standard model-based diagnosis techniques based on the application of hitting set algorithms to a number of given conflict sets. However, in many use cases such as ontology alignment the ontologies might include many more conflict sets than in usual ontology development settings, thus making precomputation of conflict sets and consequently ontology diagnosis infeasible. In this paper we suggest a debugging approach based on a direct computation of diagnoses that omits calculation of conflict sets. Embedded in an ontology debugger, the proposed algorithm is able to identify diagnoses for an ontology which includes a large number of faults and for which application of standard diagnosis methods fails. The evaluation results show that the approach is practicable and is able to identify a fault in adequate time.