to

### Calvanese

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for DLs, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for (conjunctive) query answering over DL-Lite ontologies, by adopting abductive reasoning, that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning taskswe consider existence and recognition of an explanation, and relevance and necessity of a certain assertion for an explanation. We characterize the computational complexity of these problems for subset minimal and cardinality minimal explanations.

### Calvanese

In this paper we study verification of situation calculus action theories against first-order mu-calculus with quantification across situations. Specifically, we consider mu-La and mu-Lp, the two variants of mu-calculus introduced in the literature for verification of data-aware processes. The former requires that quantification ranges over objects in the current active domain, while the latter additionally requires that objects assigned to variables persist across situations. Each of these two logics has a distinct corresponding notion of bisimulation. In spite of the differences we show that the two notions of bisimulation collapse for dynamic systems that are generic, which include all those systems specified through a situation calculus action theory. Then, by exploiting this result, we show that for bounded situation calculus action theories, mu-La and mu-Lp have exactly the same expressive power. Finally, we prove decidability of verification of mu-La properties over bounded action theories, using finite faithful abstractions. Differently from the mu-Lp case, these abstractions must depend on the number of quantified variables in the mu-La formula.

### Calvanese

In this paper, we overview the recently introduced general framework of Description Logic Based Dynamic Systems, which leverages Levesque's functional approach to model systems that evolve the extensional part of a description logic knowledge base by means of actions. This framework is parametric w.r.t. the adopted description logic and the progression mechanism. In this setting, we discuss verification and adversarial synthesis for specifications expressed in a variant of first-order mu-calculus, with a controlled form of quantification across successive states, and present key decidability results under the natural assumption of state-boundedness.

### Calvanese

We study the data complexity of answering conjunctive queries over Description Logic knowledge bases constituted by a TBox and an ABox. In particular, we are interested in characterizing the FO- rewritability and the polynomial tractability boundaries of conjunctive query answering, depending on the expressive power of the DL used to express the knowledge base. What emerges from our complexity analysis is that the Description Logics of the DL-Lite family are essentially the maximal logics allowing for conjunctive query answering through standard database technology.

### Calvanese

In this paper we investigate situation calculus action theories extended with ontologies, expressed as description logics TBoxes that act as state constraints. We show that this combination, while natural and desirable, is particularly problematic: it leads to undecidability of the simplest form of reasoning, namely satisfiability, even for the simplest kinds of description logics and the simplest kind of situation calculus action theories.

### SMT-Based Safety Verification of Data-Aware Processes under Ontologies (Extended Version)

In the context of verification of data-aware processes (DAPs), a formal approach based on satisfiability modulo theories (SMT) has been considered to verify parameterised safety properties of so-called artifact-centric systems. This approach requires a combination of model-theoretic notions and algorithmic techniques based on backward reachability. We introduce here a variant of one of the most investigated models in this spectrum, namely simple artifact systems (SASs), where, instead of managing a database, we operate over a description logic (DL) ontology expressed in (a slight extension of) RDFS. This DL, enjoying suitable model-theoretic properties, allows us to define DL-based SASs to which backward reachability can still be applied, leading to decidability in PSPACE of the corresponding safety problems.

### Mapping Patterns for Virtual Knowledge Graphs

Virtual Knowledge Graphs (VKG) constitute one of the most promising paradigms for integrating and accessing legacy data sources. A critical bottleneck in the integration process involves the definition, validation, and maintenance of mappings that link data sources to a domain ontology. To support the management of mappings throughout their entire lifecycle, we propose a comprehensive catalog of sophisticated mapping patterns that emerge when linking databases to ontologies. To do so, we build on well-established methodologies and patterns studied in data management, data analysis, and conceptual modeling. These are extended and refined through the analysis of concrete VKG benchmarks and real-world use cases, and considering the inherent impedance mismatch between data sources and ontologies. We validate our catalog on the considered VKG scenarios, showing that it covers the vast majority of patterns present therein.

### Answering Regular Path Queries Over SQ Ontologies

We study query answering in the description logic $\mathcal{SQ}$ supporting qualified number restrictions on both transitive and non-transitive roles. Our main contributions are a tree-like model property for $\mathcal{SQ}$ knowledge bases and, building upon this, an optimal automata-based algorithm for answering positive existential regular path queries in 2ExpTime.

### Evidence-based lean logic profiles for conceptual data modelling languages

Multiple logic-based reconstruction of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exists. They mainly cover various fragments of the languages and none are formalised such that the logic applies simultaneously for all three modelling language families as unifying mechanism. This hampers interchangeability, interoperability, and tooling support. In addition, due to the lack of a systematic design process of the logic used for the formalisation, hidden choices permeate the formalisations that have rendered them incompatible. We aim to address these problems, first, by structuring the logic design process in a methodological way. We generalise and extend the DSL design process to apply to logic language design more generally and, in particular, by incorporating an ontological analysis of language features in the process. Second, availing of this extended process, of evidence gathered of language feature usage, and of computational complexity insights from Description Logics (DL), we specify logic profiles taking into account the ontological commitments embedded in the languages. The profiles characterise the minimum logic structure needed to handle the semantics of conceptual models, enabling the development of interoperability tools. There is no known DL language that matches exactly the features of those profiles and the common core is small (in the tractable $\mathcal{ALNI}$). Although hardly any inconsistencies can be derived with the profiles, it is promising for scalable runtime use of conceptual data models.

### Semantic DMN: Formalizing and Reasoning About Decisions in the Presence of Background Knowledge

The Decision Model and Notation (DMN) is a recent OMG standard for the elicitation and representation of decision models, and for managing their interconnection with business processes. DMN builds on the notion of decision table, and their combination into more complex decision requirements graphs (DRGs), which bridge between business process models and decision logic models. DRGs may rely on additional, external business knowledge models, whose functioning is not part of the standard. In this work, we consider one of the most important types of business knowledge, namely background knowledge that conceptually accounts for the structural aspects of the domain of interest, and propose decision requirement knowledge bases (DKBs), where DRGs are modeled in DMN, and domain knowledge is captured by means of first-order logic with datatypes. We provide a logic-based semantics for such an integration, and formalize different DMN reasoning tasks for DKBs. We then consider background knowledge formulated as a description logic ontology with datatypes, and show how the main verification tasks for DMN in this enriched setting, can be formalized as standard DL reasoning services, and actually carried out in ExpTime. We discuss the effectiveness of our framework on a case study in maritime security. This work is under consideration for publication in Theory and Practice of Logic Programming (TPLP).