Specifying and Exploiting Non-Monotonic Domain-Specific Declarative Heuristics in Answer Set Programming

Domain-specific heuristics are an essential technique for solving combinatorial problems efficiently. Current approaches to integrate domain-specific heuristics with Answer Set Programming (ASP) are unsatisfactory when dealing with heuristics that are specified non-monotonically on the basis of partial assignments. Such heuristics frequently occur in practice, for example, when picking an item that has not yet been placed in bin packing. Therefore, we present novel syntax and semantics for declarative specifications of domain-specific heuristics in ASP. Our approach supports heuristic statements that depend on the partial assignment maintained during solving, which has not been possible before. We provide an implementation in ALPHA that makes ALPHA the first lazy-grounding ASP system to support declaratively specified domain-specific heuristics. Two practical example domains are used to demonstrate the benefits of our proposal. Additionally, we use our approach to implement informed} search with A*, which is tackled within ASP for the first time. A* is applied to two further search problems. The experiments confirm that combining lazy-grounding ASP solving and our novel heuristics can be vital for solving industrial-size problems

Konsistenz-Management unter Praeferenzen fuer Multi-Kontext Systeme und Erweiterungen

Abweichender Titel laut Übersetzung der Verfasserin/des VerfassersZsfassung in dt. SpracheMulti-Context Systems (MCS) are a versatile and powerful framework for heterogeneous, nonmonotonic knowledge-integration. MCS allow information exchange between legacy information systems, i.e., knowledge bases. Inconsistency occurs easily in such scenarios since it is impossible to foresee all effects and consequences of the information exchange. Inconsistency makes an MCS useless, just as in other formal systems; thus, inconsistency management is a major issue. Resolving inconsistency by purely technical means is guaranteed to yield a consistent system, but it can easily result in a system where the remaining information exchange leads to unwanted or even dangerous conclusions. Consider, for example, an MCS that is employed in a hospital and the billing subsystem became inconsistent because of a patient with insufficient insurance. Automatically resolving the inconsistency by declaring the patient to be healthy and sending her home instead of administering proper treatment surely is a solution, but it hardly is a valid one. On the other hand, manually resolving all inconsistencies is not feasible since there usually exist too many possible resolutions to consider each of them individually. This thesis therefore addresses the issues of inconsistency management in MCS with a focus on using preferences to identify and automatically select preferred and valid resolutions of inconsistency, to aid a human operator by significantly reducing the number of possible resolutions to consider. The novelty of this approach is on the one hand a technique to enable meta-reasoning about inconsistency resolutions within the MCS framework, i.e., preferences expressed in any knowledge formalism can be incorporated to identify preferred resolutions and filter unwanted ones. On the other hand, an extension of the MCS framework is introduced to enable the use of legacy inconsistency management methods directly at each information system. This thesis consists of three main parts. The first investigates basic notions to identify and explain inconsistency in MCS. These notions are called diagnosis and explanation of inconsistency. Refined notions are investigated and shown to be reducible to the basic notions, and splitting-set based conditions are analyzed which allow to modularly obtain diagnoses and explanations from parts of a given MCS. Finally, a logic program is given that computes all explanations of an MCS. The second part of this thesis is dedicated to the identification and selection of most-preferred diagnoses and the filtering of unwanted diagnoses. Several transformation-based approaches are introduced which allow a transformed MCS to reason about the diagnoses of the original MCS, i.e., these approaches enable meta-reasoning on diagnoses in MCS. The necessary extended notions of diagnosis are shown to be of the same complexity as the basic notion, except for one, which is of higher complexity but still shown to be worst-case optimal. Therefore, the new meta-reasoning approach incurs no unnecessary complexity-wise cost. In the third part, the MCS framework is extended to incorporate existing, formalism-specific methods of inconsistency management (e.g., belief revision for classical logics, or updates for logic programs). In such an MCS where each knowledge base comes with local inconsistency management, the overall system can only become inconsistent due to cyclic information exchange. Furthermore, the extended framework is reducible to ordinary MCS and checking consistency in the extended framework is of the same computational complexity as in ordinary MCS.21

Preference-based inconsistency management in multi-context systems

Multi-Context Systems (MCS) are a powerful framework for interlinking possibly heterogeneous, autonomous knowledge bases, where information can be exchanged among knowledge bases by designated bridge rules with negation as failure. An acknowledged issue with MCS is inconsistency that arises due to the information exchange. To remedy this problem, inconsistency removal has been proposed in terms of repairs, which modify bridge rules based on suitable notions for diagnosis of inconsistency. In general, multiple diagnoses and repairs do exist; this leaves the user, who arguably may oversee the inconsistency removal, with the task of selecting some repair among all possible ones. To aid in this regard, we extend the MCS framework with preference information for diagnoses, such that undesired diagnoses are filtered out and diagnoses that are most preferred according to a preference ordering are selected. We consider preference information at a generic level and develop meta-reasoning techniques on diagnoses in MCSthat can be exploited to reduce preference-based selection of diagnoses to computing ordinary subset-minimal diagnoses in an extended MCS. We describe two meta-reasoning encodings for preference orders: the first is conceptually simple but may incur an exponential blowup. The second is increasing only linearly in size and based on duplicating the original MCS. The latter requires nondeterministic guessing if a subset-minimal among all most preferred diagnoses should be computed. However, a complexity analysis of diagnoses shows that this is worst-case optimal, and that in general, preferred diagnoses have the same complexity as subset-minimal ordinary diagnoses. Furthermore, (subset-minimal) filtered diagnoses and (subset-minimal) ordinary diagnoses also have the same complexity.Peer reviewe

Enhancing Lazy Grounding with Lazy Normalization in Answer-Set Programming

Answer-Set Programming (ASP) is an expressive rule-based knowledge-representation formalism. Lazy grounding is a solving technique that avoids the well-known grounding bottleneck of traditional ASP evaluation but is restricted to normal rules, severely limiting its expressive power. In this work, we introduce a framework to handle aggregates by normalizing them on demand during lazy grounding, hence relieving the restrictions of lazy grounding significantly. We term our approach as lazy normalization and demonstrate its feasibility for different types of aggregates. Asymptotic behavior is analyzed and correctness of the presented lazy normalizations is shown. Benchmark results indicate that lazy normalization can bring up-to exponential gains in space and time as well as enable ASP to be used in new application areas

Towards Lightweight Completion Formulas for Lazy Grounding in Answer Set Programming

status: accepte