Abstract. Trajectory data have been used in a variety of studies, including human behavior analysis, transportation management, and wildlife tracking. While each study area introduces a different perspective, they share the need to integrate positioning data with domain-specific information. Semantic annotations are necessary to improve discovery, reuse, and integration of trajectory data from different sources. Consequently, it would be beneficial if the common structure encountered in trajectory data could be annotated based on a shared vocabulary, abstracting from domain-specific aspects. Ontology design patterns are an increasingly popular approach to define such flexible and self-contained building blocks of annotations. They appear more suitable for the annotation of interdisciplinary, multi-thematic, and multi-perspective data than the use of foundational and domain ontologies alone. In this paper, we introduce such an ontology design pattern for semantic trajectories. It was developed as a community effort across multiple disciplines and in a data-driven fashion. We discuss the formalization of the pattern using the Web Ontology Language (OWL) and apply the pattern to two different scenarios, personal travel and wildlife monitoring.

The restricted chase is a sound and complete algorithm for conjunctive query answering over ontologies of disjunctive existential rules. We develop acyclicity conditions to ensure its termination. Our criteria cannot always detect termination (the problem is undecidable), and we develop the first cyclicity criteria to show non-termination of the restricted chase. Experiments on real-world ontologies show that our acyclicity notions improve significantly over known criteria.

Abstract. The concepts of scale is at the core of cartographic abstraction and mapping. It defines which geographic phenomena should be displayed, which type of geometry and map symbol to use, which measures can be taken, as well as the degree to which features need to be exaggerated or spatially displaced. In this work, we present an ontology design pattern for map scaling using the Web Ontology Language (OWL) within a particular extension of the OWL RL profile. We explain how it can be used to describe scaling applications, to reason over scale levels, and geometric representations. We propose an axiomatization that allows us to impose meaningful constraints on the pattern, and, thus, to go beyond simple surface semantics. Interestingly, this includes several functional constraints currently not expressible in any of the OWL profiles. We show that for this specific scenario, the addition of such constraints does not increase the reasoning complexity which remains tractable.

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Horn ontologies consisting of existential rules are used in various fields ranging from reasoning over knowledge graphs [7] and Description Logics (DL) ontologies [5,6], to data integration [4] and social network analysis [10]. To solve conjunctive query answering over these logical theories, we can apply the chase algorithm-a sound and complete (albeit non-terminating) bottom-up materialisation procedure where all relevant consequences are precomputed, allowing queries to be directly evaluated over materialised sets of facts.As our main contribution, we extend the in-memory Datalog engine VLog [11] to support Horn existential rules without equality (a fragment that encompasses Horn-SRI in terms of expressivity). Namely, we implement the skolem and the restricted variants of the chase on VLog's architecture. In the skolem chase, rules are replaced by their skolemisation. In the restricted chase, new terms are introduced during the reasoning process only if already derived terms and facts cannot be reused to satisfy the corresponding existential restriction. The latter terminates in many more cases than the former [2,3] and often produces smaller models, but termination depends on the rule application order and its implementation requires value reusability checks. We implement a slightly different version of the restricted chase which leads to termination in more cases [3], by prioritising the exhaustive application of Datalog rules (rules without existentially quantified variables). This enables facts derived from Datalog rules to satisfy some existential restrictions that would otherwise lead to non-termination.In our implementation, we exploit the highly memory-efficient architecture of VLog, based on columnar storage: instead of storing a list of tuples (rows), the data is organised into a tuple of columns (value lists). The columns are ordered lexicographically, enabling fast merge joins and duplicate elimination, as well as data compression schemes for low memory usage. Because updates are slow in columnar tables, VLog operates in appendonly mode, applying one rule per materialisation step, and creating separate tables for the derived facts. To reduce redundant derivations, VLog uses semi-naive evaluation, which only considers rule body matches that were not found up to the previous application of the same rule. We adopted the 1-parallel-restricted chase [1] optimisation, in which the facts derived in the ongoing chase step are not checked for value reusability.We evaluate our implementation using existential rule programs from a recent (skolem and restricted) chase benchmark [1]. In addition, we also use rules obtained from translating data-rich, real world OWL ontologies (UOBM, Reactome, and Uniprot). The test data involves programs with millions of facts and thousands of rules, and predicates with relatively large arities (maximum 11). We test increasing partitions of data for the The full version of this paper was published at IJCAR 2018 [12].