Meta-Interpretive Learning (MIL) learns logic programs from examples by instantiating meta-rules. The recent Metagol system efficiently solves MIL-problems by relying on the procedural bias imposed by Prolog. Its focus on positive examples, however, effects that Metagol can detect the derivability of negative examples only at a later check, which can severely hit performance. Viewing MIL-problems as combinatorial search problems, they can alternatively be solved by employing Answer Set Programming (ASP). Using a sophisticated ASP solver, we may expect that violations of negative examples can be propagated directly, but such an effect has never been explicitly exploited for general MIL. In fact, a straightforward ASP-encoding of MIL results in a huge search space due to a lack of procedural bias and the need for grounding. To address these challenging issues, we encode MIL in the HEX formalism, which is an extension of ASP that allows us to outsource the background knowledge, and we restrict the search space by modeling the procedural bias. This way, the import of constants from the background knowledge can for a given type of meta-rules be limited to the relevant ones. Moreover, by abstracting from term manipulations in the encoding and exploiting the HEX interface mechanism, the import of such constants can be prevented completely in order to avoid the grounding bottleneck. An experimental evaluation shows promising results.

Meta-Interpretive Learning (MIL) learns logic programs from examples by instantiating meta-rules, which is implemented by the Metagol system based on Prolog. Viewing MIL-problems as combinatorial search problems, they can alternatively be solved by employing Answer Set Programming (ASP), which may result in performance gains as a result of efficient conflict propagation. However, a straightforward ASP-encoding of MIL results in a huge search space due to a lack of procedural bias and the need for grounding. To address these challenging issues, we encode MIL in the HEX-formalism, which is an extension of ASP that allows us to outsource the background knowledge, and we restrict the search space to compensate for a procedural bias in ASP. This way, the import of constants from the background knowledge can for a given type of meta-rules be limited to relevant ones. Moreover, by abstracting from term manipulations in the encoding and by exploiting the HEX interface mechanism, the import of such constants can be entirely avoided in order to mitigate the grounding bottleneck. An experimental evaluation shows promising results.

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.

Meta-Interpretive Learning (MIL) is a recent approach for Inductive Logic Programming (ILP) implemented in Prolog. Alternatively, MIL-problems can be solved by using Answer Set Programming (ASP), which may result in performance gains due to efficient conflict propagation. However, a straightforward MIL-encoding results in a huge size of the ground program and search space. To address these challenges, we encode MIL in the HEX-extension of ASP, which mitigates grounding issues, and we develop novel pruning techniques.

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.

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.

HEX programs extend ASP with external atoms implemented in C++ or Python. DLVHEX is a solver for HEX that permits cyclic reasoning over external atoms and external value invention.Keywords Answer set programming • External source access • Nonmonotonic reasoning 1 Motivation Answer Set Programming (ASP) [1] is a logic programming formalism for knowledge representation and reasoning. However, in many applications, rules are insufficient for representing all reasoning about the domain of interest. Instead, accessing information or computations from the world outside the program is needed. HEX programs [5] extend ASP with special external atoms in rule bodies, whose truth value is determined by an external source using, e.g., imperative code. Consider the following simple example:where the status of some robots is determined by reading and interpreting their battery level. External oracles can perform arbitrary computations to determine their truth value. Two distinguishing features of HEX are:

We consider the problem of classifying visual objects in a scene by exploiting the semantic context. For this task, we define hybrid classifiers (HC) that combine local classifiers with context constraints, and can be applied to collective classification problems (CCPs) in general. Context constraints are represented by weighted ASP constraints using object relations. To integrate probabilistic information provided by the classifier and the context, we embed our encoding in the formalism LP M LN , and show that an optimal labeling can be efficiently obtained from the corresponding LP M LN program by employing an ordinary ASP solver. Moreover, we describe a methodology for constructing an HC for a CCP, and present experimental results of applying an HC for object classification in indoor and outdoor scenes, which exhibit significant improvements in terms of accuracy compared to using only a local classifier.