Abstract Standard Description Logics (DLs) can encode quantitative aspects of an application domain through either number restrictions , which constrain the number of individuals that are in a certain relationship with an individual, or concrete domains , which can be used to assign concrete values to individuals using so-called features. These two mechanisms have been extended towards very expressive DLs, for which reasoning nevertheless remains decidable. Number restrictions have been generalized to more powerful comparisons of sets of role successors in $$\mathcal {ALCSCC}$$ ALCSCC , while the comparison of feature values of different individuals in $$\mathcal {ALC} (\mathfrak {D})$$ ALC ( D ) has been studied in the context of $$\omega $$ ω -admissible concrete domains $$\mathfrak {D}$$ D . In this paper, we combine both formalisms and investigate the complexity of reasoning in the thus obtained DL $$\mathcal {ALCOSCC}(\mathfrak {D})$$ ALCOSCC ( D ) , which additionally includes the ability to refer to specific individuals by name. We show that, in spite of its high expressivity, the consistency problem for this DL is ExpTime -complete, assuming that the constraint satisfaction problem of $$\mathfrak {D}$$ D is also decidable in exponential time. It is thus not higher than the complexity of the basic DL $$\mathcal {ALC}$$ ALC . At the same time, we show that many natural extensions to this DL, including a tighter integration of the concrete domain and number restrictions, lead to undecidability.

Standard automated planning employs first-order formulas under closed-world semantics to achieve a goal with a given set of actions from an initial state. We follow a line of research that aims to incorporate background knowledge into automated planning problems, for example by means of ontologies, which are usually interpreted under open-world semantics. We present a new approach for planning with DL-Lite ontologies that combines the advantages of ontology-based action conditions provided by explicit-input knowledge and action bases (eKABs) and ontology-aware action effects under the coherence update semantics. We show that the complexity of the resulting formalism is not higher than that of previous approaches, and provide an implementation via a polynomial compilation into classical planning. An evaluation on existing and new benchmarks examines the performance of a planning system on different variants of our compilation.

One of the advantages of formalizing domain knowledge in OWL ontologies is that one can use reasoning systems to infer implicit information automatically. However, it is not always straightforward to understand why certain entailments are inferred, and others are not. The popular ontology editor Protégé offers two explanation services to deal with this issue: justifications for OWL 2 DL ontologies, and proofs generated by the reasoner ELK for lightweight OWL 2 EL ontologies. Since justifications are often insufficient for explaining inferences, there is thus only little tool support for more comprehensive explanations in expressive ontology languages, and there is no tool support at all to explain why something was not derived. In this paper, we present Evee, a Java library and a collection of plug-ins for Protégé that offers advanced explanation services for both inferred and missing entailments. Evee explains inferred entailments using proofs in description logics up to ALCH. Missing entailments can be explained using counterexamples and abduction. We evaluated the effectiveness and the interface design of our plug-ins with description logic experts, ontology engineers, and students in two user studies. In these experiments, we were able to not only validate the tool but also gather feedback and insights to improve the existing designs.

State constraints in AI Planning globally restrict the legal environment states. Standard planning languages make closed-domain and closed-world assumptions. Here we address open-world state constraints formalized by planning over a description logic (DL) ontology. Previously, this combination of DL and planning has been investigated for the light-weight DL DL-Lite. Here we propose a novel compilation scheme into standard PDDL with derived predicates, which applies to more expressive DLs and is based on the rewritability of DL queries into Datalog with stratified negation. We also provide a new rewritability result for the DL Horn-ALCHOIQ, which allows us to apply our compilation scheme to quite expressive ontologies. In contrast, we show that in the slight extension Horn-SROIQ no such compilation is possible unless the weak exponential hierarchy collapses. Finally, we show that our approach can outperform previous work on existing benchmarks for planning with DL ontologies, and is feasible on new benchmarks taking advantage of more expressive ontologies.

It is often natural in planning to specify conditions that should be avoided, characterizing dangerous or highly undesirable behavior. PDDL3 supports this with temporal-logic state trajectory constraints. Here we focus on the simpler case where the constraint is a non-temporal formula ? - the avoid condition - that must be false throughout the plan. We design techniques tackling such avoid conditions effectively. We show how to learn from search experience which states necessarily lead into ?, and we show how to tailor abstractions to recognize that avoiding ? will not be possible starting from a given state. We run a large-scale experiment, comparing our techniques against compilation methods and against simple state pruning using ?. The results show that our techniques are often superior.

Natural language generation in real-time settings with raw sensor data is a challenging task. We find that formulating the task as an end-to-end problem leads to two major challenges in content selection – the sensor data is both redundant and diverse across environments, thereby making it hard for the encoders to select and reason on the data. We here present a new corpus for a specific domain that instantiates these properties. It includes handover utterances that an assistant for a semi-autonomous drone uses to communicate with humans during the drone flight. The corpus consists of sensor data records and utterances in 8 different environments. As a structured intermediary representation between data records and text, we explore the use of description logic (DL). We also propose a neural generation model that can alert the human pilot of the system state and environment in preparation of the handover of control.

Abstract Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying theabsenceof information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption and, therefore, are not suited to deal with the anonymous objects that are common in ontological reasoning. Many real-world applications, like processing electronic health records, also contain a temporal dimension and require efficient reasoning algorithms. Moreover, since medical data are not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps. Our contribution consists of two main parts: In the first part, we introduce a new closed-world semantics for answering conjunctive queries (CQs) with negation over ontologies formulated in the description logic $${\mathcal E}{\mathcal L}{{\mathcal H}_ \bot }$$ , which is based on theminimalcanonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity. In the second part, we extend this minimal-world semantics for answering metric temporal CQs with negation over the lightweight temporal logic and obtain similar rewritability and complexity results.

Abstract Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can explain such an entailment by presenting a proof of the consequence in an appropriate calculus. How comprehensible such a proof is depends not only on the employed calculus, but also on the properties of the particular proof, such as its overall size, its depth, the complexity of the employed sentences and proof steps, etc. For this reason, we want to determine the complexity of generating proofs that are below a certain threshold w.r.t. a given measure of proof quality. Rather than investigating this problem for a fixed proof calculus and a fixed measure, we aim for general results that hold for wide classes of calculi and measures. In previous work, we first restricted the attention to a setting where proof size is used to measure the quality of a proof. We then extended the approach to a more general setting, but important measures such as proof depth were not covered. In the present paper, we provide results for a class of measures called recursive, which yields lower complexities and also encompasses proof depth. In addition, we close some gaps left open in our previous work, thus providing a comprehensive picture of the complexity landscape.

In highly automated driving (HAD), it is still an open question how machines can safely hand over control to humans, and if an advance notice with additional explanations can be beneficial in critical situations. Conceptually, use of formal methods from AI – description logic (DL) and automated planning – in order to more reliably predict when a handover is necessary, and to increase the advance notice for handovers by planning ahead at runtime, can provide a technological support for explanations using natural language generation. However, in this work we address only the user’s perspective with two contributions: First, we evaluate our concept in a driving simulator study (N=23) and find that an advance notice and spoken explanations were preferred over classical handover methods. Second, we propose a framework and an example test scenario specific to handovers that is based on the results of our study.

Planning in the presence of background ontologies is a topic of long-standing interest in AI. It combines the problems of (1) belief update complexity and (2) state-space combinatorics. DL-Lite offers an attractive solution to (1), with belief updates possible at the ABox level. Indeed, it has been shown that DL-Lite planning can be compiled into the commonly used planning language PDDL. Yet that compilation was previously found to be infeasible for off-the-shelf planning systems. Here we analyze the reasons for this problem and find that the bottleneck lies in the planner pre-processes, in particular in the naïve DNF transformations used to compile the PDDL input into the planners' internal representations. Consequently, we design a PDDL pre-compiler realizing a polynomial DNF transformation. We leverage a particular PDDL language feature ("derived predicates") to avoid the need for excessive control structure. Our pre-compiler turns out to be quite effective: the previous bottleneck disappears, and experiments on a broad range of benchmarks demonstrate the first practical technology for DL-Lite planning.

Logic-based approaches to AI have the advantage that their behaviour can in principle be explained by providing their users with proofs for the derived consequences. However, if such proofs get very large, then it may be hard to understand a consequence even if the individual derivation steps are easy to comprehend. This motivates our interest in finding small proofs for Description Logic (DL) entailments. Instead of concentrating on a specific DL and proof calculus for this DL, we introduce a general framework in which proofs are represented as labeled, directed hypergraphs, where each hyperedge corresponds to a single sound derivation step. On the theoretical side, we investigate the complexity of deciding whether a certain consequence has a proof of size at most n along the following orthogonal dimensions: (i) the underlying proof system is polynomial or exponential; (ii) proofs may or may not reuse already derived consequences; and (iii) the number n is represented in unary or binary. We have determined the exact worst-case complexity of this decision problem for all but one of the possible combinations of these options. On the practical side, we have developed and implemented an approach for generating proofs for expressive DLs based on a non-standard reasoning task called forgetting. We have evaluated this approach on a set of realistic ontologies and compared the obtained proofs with proofs generated by the DL reasoner ELK, finding that forgetting-based proofs are often better w.r.t. different measures of proof complexity.

In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow us to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining description logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there is a growing interest in extending this work to the quantitative case. In this article, we complement existing results on the combination of DLs with metric temporal logics by introducing interval-rigid concept and role names. Elements included in an interval-rigid concept or role name are required to stay in it for some specified amount of time. We investigate several combinations of (metric) temporal logics with A ℒ C by either allowing temporal operators only on the level of axioms or also applying them to concepts. In contrast to most existing work on the topic, we consider a timeline based on the integers and also allow assertional axioms. We show that the worst-case complexity does not increase beyond the previously known bound of 2-E xp S pace and investigate in detail how this complexity can be reduced by restricting the temporal logic and the occurrences of interval-rigid names.

Large-scale knowledge bases are at the heart of modern information systems. Their knowledge is inherently uncertain, and hence they are often materialized as probabilistic databases. However, probabilistic database management systems typically lack the capability to incorporate implicit background knowledge and, consequently, fail to capture some intuitive query answers. Ontology-mediated query answering is a popular paradigm for encoding commonsense knowledge, which can provide more complete answers to user queries. We propose a new data model that integrates the paradigm of ontology-mediated query answering with probabilistic databases, employing a log-linear probability model. We compare our approach to existing proposals, and provide supporting computational results.

Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. We propose a new closed-world semantics for answering conjunctive queries with negation over ontologies formulated in the description logic ELH-bottom, based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity.

We give a survey on recent advances at the forefront of research on probabilistic knowledge bases for representing and querying large-scale automatically extracted data. We concentrate especially on increasing the semantic expressivity of formalisms for representing and querying probabilistic knowledge (i) by giving up the closed-world assumption, (ii) by allowing for commonsense knowledge (and in parallel giving up the tuple-independence assumption), and (iii) by giving up the closed-domain assumption, while preserving some computational properties of query answering in such formalisms.

Probabilistic databases (PDBs) are usually incomplete, e.g., containing only the facts that have been extracted from the Web with high confidence. However, missing facts are often treated as being false, which leads to unintuitive results when querying PDBs. Recently, open-world probabilistic databases (OpenPDBs) were proposed to address this issue by allowing probabilities of unknown facts to take any value from a fixed probability interval. In this paper, we extend OpenPDBs by Datalog+/- ontologies, under which both upper and lower probabilities of queries become even more informative, enabling us to distinguish queries that were indistinguishable before. We show that the dichotomy between P and PP in (Open)PDBs can be lifted to the case of first-order rewritable positive programs (without negative constraints); and that the problem can become NP^PP-complete, once negative constraints are allowed. We also propose an approximating semantics that circumvents the increase in complexity caused by negative constraints.

We investigate ontology-based query answering (OBQA) in a setting where both the ontology and the query can refer to concrete values such as numbers and strings. In contrast to previous work on this topic, the built-in predicates used to compare values are not restricted to being unary. We introduce restrictions on these predicates and on the ontology language that allow us to reduce OBQA to query answering in databases using the so-called combined rewriting approach. Though at first sight our restrictions are different from the ones used in previous work, we show that our results strictly subsume some of the existing first-order rewritability results for unary predicates.

Forming the foundations of large-scale knowledge bases, probabilistic databases have been widely studied in the literature. In particular, probabilistic query evaluation has been investigated intensively as a central inference mechanism. However, despite its power, query evaluation alone cannot extract all the relevant information encompassed in large-scale knowledge bases. To exploit this potential, we study two inference tasks; namely finding the most probable database and the most probable hypothesis for a given query. As natural counterparts of most probable explanations (MPE) and maximum a posteriori hypotheses (MAP) in probabilistic graphical models, they can be used in a variety of applications that involve prediction or diagnosis tasks. We investigate these problems relative to a variety of query languages, ranging from conjunctive queries to ontology-mediated queries, and provide a detailed complexity analysis.

Unification in Description Logics has been introduced as a means to detect redundancies in ontologies. We try to extend the known decidability results for unification in the Description Logic EL to disunification since negative constraints on unifiers can be used to avoid unwanted unifiers. While decidability of the solvability of general EL-disunification problems remains an open problem, we obtain NP-completeness results for two interesting special cases: dismatching problems, where one side of each negative constraint must be ground, and local solvability of disunification problems, where we restrict the attention to solutions that are built from so-called atoms occurring in the input problem. More precisely, we first show that dismatching can be reduced to local disunification, and then provide two complementary NP-algorithms for finding local solutions of (general) disunification problems.

Uncertainty is unavoidable when modeling most application domains. In medicine, for example, symptoms (such as pain, dizziness, or nausea) are always subjective, and hence imprecise and incom-parable. Additionally, concepts and their relation-ships may be inexpressible in a crisp, clear-cut manner. We extend the description logicALC with multi-valued semantics based on lattices that can handle uncertainty on concepts as well as on the axioms of the ontology. We introduce reasoning methods for this logic w.r.t. general concept inclu-sions and show that the complexity of reasoning is not increased by this new semantics. 1