Antonius Weinzierl

Managed multi-context systems

Multi-context systems (MCS) are a powerful framework for interlinking heterogeneous knowledge sources. They model the flow of information among different reasoning components (called contexts) in a declarative way, using so-called bridge rules, where contexts and bridge rules may be nonmonotonic. We considerably generalize MCS to managed MCS (mMCS): while the original bridge rules can only add information to contexts, our generalization allows arbitrary operations on context knowledge bases to be freely defined, e.g., deletion or revision operators. The paper motivates and introduces the generalized framework and presents several interesting instances. Furthermore, we consider inconsistency management in mMCS and complexity issues.

Relational information exchange and aggregation in multi-context systems

Multi-Context Systems (MCSs) are a powerful framework for representing the information exchange between heterogeneous (possibly nonmonotonic) knowledge-bases. Significant recent advancements include implementations for realizing MCSs, e.g., by a distributed evaluation algorithm and corresponding optimizations. However, certain enhanced modeling concepts like aggregates and the use of variables in bridge rules, which allow for more succinct representations and ease system design, have been disregarded so far. We fill this gap introducing open bridge rules with variables and aggregate expressions, extending the semantics ofMCSs correspondingly. The semantic treatment of aggregates allows for alternative definitions when so-called grounded equilibria of an MCS are considered. We discuss options in relation to wellknown aggregate semantics in answer-set programming. Moreover, we develop an implementation by elaborating on the DMCS algorithm, and report initial experimental results.

Preference-based inconsistency assessment in multi-context systems

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.

OMiGA: an open minded grounding on-the-fly answer set solver

We present a new solver for Answer-Set Programs whose main features include grounding on-the-fly and readiness for use in solving distributed answer-set programs. The solver is implemented in Java and uses an underlying Rete network for propagation. Initial experimental results show the benefit of using Rete for this purpose, but also exhibit the need for learning in the presence of grounding on-the-fly.

Comparing inconsistency resolutions in multi-context systems

Inconsistency in heterogeneous knowledge-integration systems with non-monotonic information exchange is a major concern as it renders systems useless at its occurrence. For the knowledge-integration framework of Multi-Context Systems, the problem of finding all possible resolutions to inconsistency has been addressed previously and some basic steps have been proposed to find most preferred resolutions. Here, we refine the techniques of finding preferred resolutions of inconsistency in two directions. First, we extend available qualitative methods using domain knowledge on the intention and category of information exchange to minimize the number of categories that are affected by a resolution. Second, we present a quantitative inconsistency measure for inconsistency resolutions, being suitable for scenarios where no further domain knowledge is available.

Blending Lazy-Grounding and CDNL Search for Answer-Set Solving

Efficient state-of-the-art answer-set solvers are two-phased: first grounding the input program, then applying search based on conflict-driven nogood learning (CDNL). The latter provides superior search performance but the former causes exponential memory requirements for many ASP programs. Lazy-grounding avoids this grounding bottleneck but exhibits poor search performance. The approach here aims for the best of both worlds: grounding and solving are interleaved, but there is a solving component distinct from the grounding component. The solving component works on (ground) nogoods, employs conflict-driven first-UIP learning and enables heuristics. Guessing is on atoms that represent applicable rules, atoms may be one of true, false, or must-be-true, and nogoods have a distinguished head literal. The lazy-grounding component is loosely coupled to the solver and may yield more ground instances than necessary, which avoids re-grounding whenever the solver moves from one search branch to another. The approach is implemented in the new ASP solver Alpha.

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 MCS that 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.

Answer Set Programming with External Source Access

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 real-world problem using Semantic Web technologies, and discuss specifics of the implementation process.

Labeling RDF Graphs for Linear Time and Space Querying

Indices and data structures for web querying have mostly considered tree shaped data, reflecting the view of XML documents as tree-shaped. However, for RDF (and when querying ID/IDREF constraints in XML) data is indisputably graph-shaped. In this chapter, we first study existing indexing and labeling schemes for RDF and other graph datawith focus on support for efficient adjacency and reachability queries. For XML, labeling schemes are an important part of the widespread adoption of XML, in particular for mapping XML to existing (relational) database technology. However, the existing indexing and labeling schemes for RDF (and graph data in general) sacrifice one of the most attractive properties of XML labeling schemes, the constant time (and per-node space) test for adjacency (child) and reachability (descendant). In the second part, we introduce the first labeling scheme for RDF data that retains this property and thus achieves linear time and space processing of acyclic RDF queries on a significantly larger class of graphs than previous approaches (which are mostly limited to tree-shaped data). Finally, we show how this labeling scheme can be applied to (acyclic) SPARQL queries to obtain an evaluation algorithm with time and space complexity linear in the number of resources in the queried RDF graph.

Lazy-Grounding for Answer Set Programs with External Source Access

HEX-programs enrich the well-known Answer Set Programming (ASP) paradigm. In HEX, problems are solved using nonmonotonic logic programs with bidirectional access to external sources. ASP evaluation is traditionally based on grounding the input program first, but recent advances in lazy-grounding make the latter also interesting for HEX, as the grounding bottleneck of ASP may be avoided. We explore this issue and present a new evaluation algorithm for HEX-programs based on lazy-grounding solving for ASP. Nonmonotonic dependencies and value invention (i.e., import of new constants) from external sources make an efficient solution nontrivial. However, illustrative benchmarks show a clear advantage of the new algorithm for grounding-intense programs, which is a new perspective to make HEX more suitable for real-world application needs.