Metamodeling helps in specifying conceptual modelling requirements with the notion of meta-classes (for instance, classes that are instances of other classes) and meta-properties (relations between metaconcepts). These notions can be expressed in OWL Full. However, OWL Full is so expressive for metamodeling that it leads to undecidability [13]. OWL 2 DL and its sub-profiles guarantee decidability, but they provide a very restricted form of metamodeling [7] and give no semantic support due to the prevalent Direct Semantics (DS). Consider an example adapted from [6], concerning the modeling of biological species, stating that all golden eagles are eagles, all eagles are birds, and Harry is an instance of GoldenEagle, which further can be inferred as an instance of Eagle and Bird. However, in the species domain one can not just express properties of and relationships among species, but also express properties of the species themselves. For example "GoldenEagle is listed in the IUCN Red List of endangered species" states that GoldenEagle as a whole class is an endangered species. Note that this is also not a subclass relation, as Harry is not an endangered species. To formally model this expression, we can declare GoldenEagle to be an instance of new class EndangeredSpecies.

Over the last decades the development of ASP has brought about an expressive modeling language powered by highly performant systems. At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting constructs and inferences. This is even more severe when it comes to hybrid ASP languages and systems that are often needed to handle real-world applications. We address this challenge and introduce the concept of abstract and structured theories that allow us to formally elaborate upon their integration with ASP. We then use this concept to make precise the semantic characterization of CLINGO's theory-reasoning framework and establish its correspondence to the logic of Here-and-there with constraints. This provides us with a formal framework in which we can elaborate formal properties of existing hybridizations of CLINGO such as CLINGCON, CLINGOM[DL], and CLINGO[LP].

HEX-programs are an extension of answer set programs (ASP) with external sources. To this end, external atoms provide a bidirectional interface between the program and an external source. The traditional evaluation algorithm for HEX-programs is based on guessing truth values of external atoms and verifying them by explicit calls of the external source. The approach was optimized by techniques that reduce the number of necessary verification calls or speed them up, but the remaining external calls are still expensive. In this paper we present an alternative evaluation approach based on inlining of external atoms, motivated by existing but less general approaches for specialized formalisms such as DL-programs. External atoms are then compiled away such that no verification calls are necessary. The approach is implemented in the dlvhex reasoner. Experiments show a significant performance gain. Besides performance improvements, we further exploit inlining for extending previous (semantic) characterizations of program equivalence from ASP to HEX-programs, including those of strong equivalence, uniform equivalence and H, B -equivalence. Finally, based on these equivalence criteria, we characterize also inconsistency of programs wrt. extensions. Since well-known ASP extensions (such as constraint ASP) are special cases of HEX, the results are interesting beyond the particular formalism. Under consideration in Theory and Practice of Logic Programming (TPLP).

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, HEX-programs 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 a well-known problem solving approach based on nonmonotonic logic programs. HEX-programs extend ASP with external atoms for accessing arbitrary external information, which can introduce values that do not appear in the input program. In this work we consider inconsistent ASP- and HEX-programs, i.e., programs without answer sets. We study characterizations of inconsistency, introduce a novel notion for explaining inconsistencies in terms of input facts, analyze the complexity of reasoning tasks in context of inconsistency analysis, and present techniques for computing inconsistency reasons. This theoretical work is motivated by two concrete applications, which we also present. The first one is the new modeling technique of query answering over subprograms as a convenient alternative to the well-known saturation technique. The second application is a new evaluation algorithm for HEX-programs based on conflict-driven learning for programs with multiple components: while for certain program classes previous techniques suffer an evaluation bottleneck, the new approach shows significant, potentially exponential speedup in our experiments. Since well-known ASP extensions such as constraint ASP and DL-programs correspond to special cases of HEX, all presented results are interesting beyond the specific formalism.

HEX-programs extend of answer-set programs (ASP) with ex-ternal sources. In previous work, notions of equivalence ofASP programs under extensions have been developed. Mostwell-known are strong equivalence, which is given for pro-grams P and Q if P ∪ R and Q ∪ R have the same answersets for arbitrary programs R, and uniform equivalence, whichis given if this is guaranteed for sets R of facts. More fine-grained approaches exist, which restrict the set of atoms inthe added program R. In this paper we provide a characteriza-tion of equivalence of HEX -programs. Since well-known ASPextensions (e.g. constraint ASP) amount to special cases ofHEX , the results are interesting beyond the particular formal-ism. Based on this, we further characterize inconsistency ofprograms wrt. program extensions. We then discuss possibleapplications of the results for algorithms improvements.

HEX-programs are an extension of answer set programming(ASP) towards external sources. To this end, external atomsprovide a bidirectional interface between the program and anexternal source. Traditionally, HEX -programs are evaluatedusing a rewriting to ordinary ASP programs which guess truthvalues of external atoms; this yields answer set candidateswhose guesses are verified by evaluating the source. Despitethe integration of learning techniques into this approach, whichreduce the number of candidates and of necessary verificationcalls, the remaining external calls are still expensive. In thispaper we present an alternative approach based on inliningof external atoms, motivated by existing but less general approaches for specialized formalisms such as DL-programs. External atoms are then compiled away such that no verification calls are necessary. To this end, we make use of supportsets, which describe conditions on input atoms that are sufficient to satisfy an external atom. The approach is implementedin the DLVHEX reasoner. Experiments show a significant performance gain.

As software systems are getting increasingly connected, there is a need for equipping nonmonotonic logic programs with access to external sources that are possibly remote and may contain information in heterogeneous formats. To cater for this need, HEX programs were designed as a generalization of answer set programs with an API style interface that allows to access arbitrary external sources, providing great flexibility. Efficient evaluation of such programs however is challenging, and it requires to interleave external computation and model building; to decide when to switch between these tasks is difficult, and existing approaches have limited scalability in many real-world application scenarios. We present a new approach for the evaluation of logic programs with external source access, which is based on a configurable framework for dividing the non-ground program into possibly overlapping smaller parts called evaluation units. The latter will be processed by interleaving external evaluation and model building using an evaluation graph and a model graph, respectively, and by combining intermediate results. Experiments with our prototype implementation show a significant improvement compared to previous approaches. While designed for HEX-programs, the new evaluation approach may be deployed to related rule-based formalisms as well.

Answer set programs (ASP) with external evaluations are a declarative means to capture advanced applications. However, their evaluation can be expensive due to external source accesses. In this paper we consider HEX-programs that provide external atoms as a bidirectional interface to external sources and present a novel evaluation method based on support sets, which informally are portions of the input to an external atom that will determine its output for any completion of the partial input. Support sets allow one to shortcut the external source access, which can be completely eliminated. This is particularly attractive if a compact representation of suitable support sets is efficiently constructible. We discuss some applications with this property, among them description logic programs over DL-Lite ontologies, and present experimental results showing that support sets can significantly improve efficiency.

HEX-programs extend logic programs under the answer set semantics with external computations through external atoms. As reasoning from ground Horn programs with nonmonotonic external atoms of polynomial complexity is already on the second level of the polynomial hierarchy, minimality checking of answer set candidates needs special attention. To this end, we present an approach based on unfounded sets as a generalization of related techniques for ASP programs. The unfounded set detection is expressed as a propositional SAT problem, for which we provide two different encodings and optimizations to them. We then integrate our approach into a previously developed evaluation framework for HEX-programs, which is enriched by additional learning techniques that aim at avoiding the reconstruction of the same or related unfounded sets. Furthermore, we provide a syntactic criterion that allows one to skip the minimality check in many cases. An experimental evaluation shows that the new approach significantly decreases runtime.