We provide two approaches for explaining inconsistency in multi-context systems, where decentralized and heterogeneous system parts interact via nonmonotonic bridge rules. Inconsistencies arise easily in such scenarios, and nonmonotonicity calls for specific methods of inconsistency analysis. Both our approaches characterize inconsistency in terms of involved bridge rules: either by pointing out rules which need to be altered for restoring consistency, or by finding combinations of rules which cause inconsistency. We show duality and modularity properties, give precise complexity characterizations, and provide algorithms for computation using HEXprograms. Our results form a basis for inconsistency management in heterogeneous knowledge integration systems.

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Answer Set Programming (ASP) is a well-known declarative problem solving approach based on nonmonotonic logic programs, which has been successfully applied to a wide range of applications in artificial intelligence and beyond. To address the needs of modern applications, HEXprograms were introduced as an extension of ASP with external atoms for accessing information outside programs via an API style bi-directional interface mechanism. To evaluate such programs, conflict-driving learning algorithms for SAT and ASP solving have been extended in order to capture the semantics of external atoms. However, a drawback of the state-of-the-art approach is that external atoms are only evaluated under complete assignments (i.e., input to the external source) while in practice, their values often can be determined already based on partial assignments alone (i.e., from incomplete input to the external source). This prevents early backtracking in case of conflicts, and hinders more efficient evaluation of HEX-programs. We thus extend the notion of external atoms to allow for three-valued evaluation under partial assignments, while the two-valued semantics of the overall HEX-formalism remains unchanged. This paves the way for three enhancements: first, to evaluate external sources at any point during model search, which can trigger learning knowledge about the source behavior and/or early backtracking in the spirit of theory propagation in SAT modulo theories (SMT). Second, to optimize the knowledge learned in terms of so-called nogoods, which roughly speaking are impossible input-output configurations. Shrinking nogoods to their relevant input part leads to more effective search space pruning. And third, to make a necessary minimality check of candidate answer sets more efficient by exploiting early external evaluation calls. As this check usually accounts for a large share of the total runtime, optimization is here particularly important. We further present an experimental evaluation of an implementation of a novel HEX-algorithm that incorporates these enhancements using a benchmark suite. Our results demonstrate a clear efficiency gain over the state-of-the-art HEX-solver for the benchmarks, and provide insights regarding the most effective combinations of solver configurations.

Answer set programming (ASP) is an established knowledge representation formalism. Lazy grounding avoids the so-called grounding bottleneck of ASP by interleaving grounding and solving; this technique was recently extended to work with conflict-driven clause learning. Unfortunately, it often happens that such a lazy grounding ASP system, at the fixpoint of the evaluation, arrives at an assignment that contains literals that are true but unjustified. The system then is unable to determine the actual causes of the situation and falls back to chronological backtracking, potentially wasting an exponential amount of time. In this paper, we show how top-down query mechanisms can be used to analyze the situation, learn a new clause or nogood, and backjump further in the search tree. Contributions include a rephrasing of lazy grounding in terms of justifications and algorithms to construct relevant justifications without grounding. Initial experiments indicate that the newly developed techniques indeed allow for an exponential speed-up.

Abstract. Resolving inconsistency in knowledge-integration systems is a major issue, especially when interlinking heterogeneous, autonomous sources. The latter can be done using a multi-context system, also in presence of non-monotonicity. Recent work considered diagnosis and explanation of inconsistency in such systems in terms of faulty information exchange. To discriminate between different solutions, we consider inconsistency assessment using preference. We present means to a) filter undesired diagnoses b) select the most preferred ones given an arbitrary preference order and c) use CP-nets for efficient selection. Furthermore, we show how to incorporate the assessment into a Multi-Context System by a transformational approach. In a range of settings, the complexity does not increase compared to the basic case and key properties like decentralized information exchange and information hiding are preserved.

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Access to external information is an important need for Answer Set Programming (ASP), which is a booming declarative problem solving approach these days. External access not only includes data in different formats, but more general also the results of computations, and possibly in a two-way information exchange. Providing such access is a major challenge, and in particular if it should be supported at a generic level, both regarding the semantics and efficient computation. In this article, we consider problem solving with ASP under external information access using the dlvhex system. The latter facilitates this access through special external atoms, which are two-way API style interfaces between the rules of the program and an external source. The dlvhex system has a flexible plugin architecture that allows one to use multiple predefined and user-defined external atoms which can be implemented, e.g., in Python or C++. We consider how to solve problems using the ASP paradigm, and specifically discuss how to use external atoms in this context, illustrated by examples. As a showcase, we demonstrate the development of a HEX program for a concrete realworld problem using Semantic Web technologies, and discuss specifics of the implementation process.