ABSTRACT. The chase is a fundamental tool for existential rules. Several chase variants are known, which differ on how they handle redundancies possibly caused by the introduction of nulls. Given a chase variant, the halting problem takes as input a set of existential rules and asks if this set of rules ensures the termination of the chase for any factbase. It is well-known that this problem is undecidable for all known chase variants. The related problem of boundedness asks if a given set of existential rules is bounded, i.e., whether there is an upper bound on the depth of the chase, independently from any factbase. This problem is already undecidable in the specific case of datalog rules. However, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound is unknown. Hence, in this paper, we investigate the decidability of the k-boundedness problem, which asks whether a given set of rules is bounded by k.

ABSTRACT. Most query rewriting systems focus on answering Conjunctive Queries that have only positive atoms because the use of negation can easily make the entailment problem undecidable. However, restricting the way we use negation on Conjunctive Queries can make the entailment problem decidable and can also ensure the existence of algorithms based on Query Rewriting that find their answers. In this paper, we propose a definition of Horn Conjunctive Queries to denote queries that have one negated atom. We also present an algorithm based on query rewriting that finds the answers of a Horn Union of Conjunctive Queries. Additionally, we conduct some experiments to compare the performance with other state of the art systems that are able to answer conjunctive queries with negation using tableaux algorithms. The experimental data confirms that our system performs better than the other systems we considered when dealing with big ontologies.

ABSTRACT. The chase procedure is an indispensable tool for several database applications, where its termination guarantees decidability of these tasks. Most previous studies have focused on the skolem chase variant and its termination. It is known that the restricted chase variant is more powerful in termination analysis provided a database is given. But all-instance termination analysis presents a challenge since the critical database and similar techniques do not work. We develop a novel technique to characterize the activeness of all possible cycles of a certain length in the restricted chase procedure which leads to the formulation of a parameterized class called k-safe(cycle), which guarantees all-instance, all-path termination, where the parameter takes a cycle function by which a concrete class of finite restricted chase is instantiated. The approach applies to any class of finite skolem chase that is identified with a condition of acyclicity. More generally, we show how to extend the hierarchy of bounded rule sets under skolem chase without increasing the complexity of data and combined reasoning tasks. Experiments of selected introduced classes show the applicability of the proposed methods on real-world ontologies.

ABSTRACT. SWRL is a semantic web rule language that combines OWL ontologies with Horn Logic rules of the RuleML family of rule languages. Being supported by Protégé as well as by popular rule engines and ontology reasoners, such as Jess, Drools and Pellet, SWRL has become a very popular choice for developing rule-based applications on top of ontologies. However, being doubtful whether SWRL will become a W3C standard, it is difficult to reach out to the industrial world. On the other hand, SPIN has become a de-facto industry standard to rep-resent SPARQL rules and constraints on Semantic Web models, building on the widespread acceptance of the SPARQL query language. In this paper, we argue that the life of existing SWRL rule-based ontology applications can be prolonged by being transformed into SPIN. To this end, we have developed a prototype tool using SWI-Prolog that takes as input an OWL ontology with a SWRL rule base and transforms SWRL rules into SPIN rules in the same ontology, taking into consideration the object-oriented scent of SPIN, i.e. linking rules to the appropri-ate ontology classes as derived by analyzing the rule conditions.

ABSTRACT. RdfRules is a framework for mining logical rules from RDF-style knowledge graphs. The system provides software support for the complete data mining workflows over RDF data: data ingestion, aggregation, transformations, actual rule mining and post-processing of discovered rules, including clustering. As a rule mining algorithm, RdfRules adopts AMIE+ (Galárraga et al, 2015), which has been extended with number of practical features, such as mining across multiple graphs, top-\textit{k} approach and the ability to define fine-grained patterns to reduce the size of the search space. RdfRules is a work-in-progress.

ABSTRACT. PSOA Prova enriches PSOA RuleML with parts of Reaction RuleML. It is implemented by combining PSOATransRun and Prova, a Prolog-based language and engine which supports object orientation, reactive programming as well as several other programming paradigms. A modified Prova engine targeted by PSOA RuleML's PSOATransRun translators is introduced and then extended to top-level assert and retract by allowing KB consult and unconsult at runtime. PSOA is further extended to pure production rules, a conclusion-asserting subset of Production RuleML, hence Reaction RuleML. This is exemplified for a PSOA Prova knowledge base about the British ``Succession to the Crown Act 2013''. These extensions yield a PSOA Prova language and engine available on GitHub. Three formalization approaches for succession are demonstrated.

ABSTRACT. Classification Based on Associations (CBA) algorithm has for two decades been the algorithm of choice for researchers as well as practitioners owing to simplicity of the produced rules, accuracy of models, and also high speed of model building. Two versions of CBA differing in speed – M1 and M2 – were originally proposed by Liu et al in 1998. While the more complex M2 version was originally designated as on average 50% faster, in this article we present benchmarks performed with multiple CBA implementations on the UCI lymph dataset contesting M2 supremacy. The results show that M1 had faster processing speeds in most evaluated setups. M2 was recorded to be faster only when the number of input rules was very small and the number of input instances was large. We hypothesize that the better performance of the M1 version can be attributed to recent advances in optimization of vectorized operations and memory structures in SciKit learn and R, which the M1 can better utilize due to better predispositions for vectorization.

ABSTRACT. The formalization of Air Traffic Control Regulations for the separation of aircraft during approach and departing phases is discussed. Our aim is to demonstrate rules in Positional-Slotted, Object-Applicative (PSOA) RuleML syntax that capture those regulations. This rulebase is combined with aircraft facts, resulting a complete Knowledge Base for the computation of the required separation of aircraft. We provide examples of queries posed in the open-source PSOATransRun system and we show the capabilities and limitations of the Knowledge Base and PSOATransRun.

ABSTRACT. Goal-oriented business decision modeling is driven by the need to simplify communication between business analysts and operational business decision models while extending the capabilities of traditional business rules and decision management systems. The proposed goal-oriented approach aims to creation of business decision models which cover certain business domains and are capable to reach multiple business goals by providing answers to various questions in terms of automatically calculated decision variables. Such decision models can be designed by defining the hierarchy of business goals and sub-goals with relationships between them described in business-friendly decision tables. This paper introduces a new web-based graphical tool “Decision Model Analyzer” that allows human decision modelers (who are assumed to be business analysts and not programmers) to easily add their decision models to the analyzer. Then the analyzer shows all goals supported by the selected decision model, automatically calculates their execution paths, executes the selected goals against various test cases, and explains why certain decisions were made on the way to the goal. The analyzer is publicly available online as a component of the popular open source business rules and decision management system “OpenRules”.

ABSTRACT. For the last two decades, complex event processing under uncertainty has been widely studied, but, nowadays, researches are still facing difficult problems such as combinatorial explosion or lack of expressiveness while inferring about possible outcomes. Numerous approaches have been proposed, like automaton-based methods, stochastic context-free grammars, or mixed methods using first-order logic and probabilistic graphical models.

Each technique has its own pros and cons, which rely on the problem structure and underlying assumptions. In our case, we want to propose a model providing likelihood of a complex event from long data streams produced by a simple, but large system, in a reasonable amount of time. Furthermore, we want this model to allow considering prior knowledge on data streams with a high degree of expressiveness.