ABSTRACT. Ontology-based data access (OBDA) is a popular paradigm for data integration. In this paradigm, multiple data sources are integrated through mappings to an ontology. These data sources can be heterogeneous (databases, language models, knowledge graph embedding models, etc) and the information retrieved from them may have different levels of trust. So, when answering queries, one may well be interested in not only obtaining the answers but also knowing why/how these answers were obtained. Provenance here refers to the origin of a query result, in particular, which tuples in a database or which data sources were relevant for answering a query. This corresponds to a notion of explanation explored in the context of databases using commutative semirings. In this talk, I will present work on semiring provenance in the context of ontology-based data access. The focus will be on ontologies expressed in DL-Lite and solutions to determine the provenance of a query within the OBDA setting.

ABSTRACT. Different attribution scores have been proposed to quantify the relevance of database tuples for query answering in databases; e.g. Causal Responsibility, the Shapley Value, the Banzhaf Power-Index, and the Causal Effect. They have been analyzed in isolation. This work is a first investigation of score alignment depending on the query and the database; i.e. on whether they induce compatible rankings of tuples. We concentrate mostly on causality-based scores; and provide a syntactic dichotomy result for queries: on one side, pairs of scores are always aligned, on the other, they are not always aligned. It turns out that the presence of exogenous tuples makes a crucial difference in this regard.

ABSTRACT. The optimal repair property, which says that there is a finite set of optimal (i.e., entailment-maximal) repairs that covers all repairs, has turned out to be useful both in the context of ontology engineering and in belief change. We provide abstract order-theoretic conditions that guarantee the existence of finite sets of optimal repairs covering all repairs, and illustrate their use with abstract examples as well as with more practical examples from the realm of Description Logic (DL). The order-theoretic view on optimal repairs also reveals that there is a strong similarity between the optimal repair property and the existence of a finite complete set of unifiers for unification modulo equational theories. Applying Siekmann's proposal to divide unification problems into the unification types unitary, finitary, infinitary, and zero to repair problems, we obtain a more fine-grained classification of repair problems. For the DL examples introduced in this paper, we observe that types unitary, finitary and zero can occur, but none of these examples provides us with an infinitary repair problem. However, we also show that unification problems can actually be viewed as repair problems in the abstract framework introduced in our previous work on contractions based on optimal repairs. Thus, within this framework, known results on unification types of certain equational theories provide us with examples of repair problems of these types.

ABSTRACT. Belief expansion is the operation of incorporating new information into a belief base or theory. If a belief state can draw on a set of fundamental beliefs, new pieces of information are often not simply added but explicitly tied to fundamental beliefs by means of explanations. Abductive expansion is an AGM-style belief change operation that augments a theory with an underlying explanation by means of abduction. AGM-style belief change, presupposes deductively closed theories and thus makes no distinction between the explanation and the explained. In this paper, we extend abductive expansion to belief bases, which do not presuppose deductive closure. Within bases, abduced information is introduced in response to unexplained inputs and can therefore be explicitly identified as a newly formed belief. We provide an axiomatic characterization along with constructive methods.

ABSTRACT. We show that revision by single sentences and multiple revision are, in general, mutually irreducible processes. The result is given for revision in base logics, a framework for studying revision in arbitrary classical logics for various notions of bases. Within this framework, we demonstrate that revision by single sentences can not be represented as multiple revision. The result employs general relational semantics for base revision. In combination with the well-known result that multiple revision is irreducible to sentence revision, we obtain that sentence revision and multiple revision are mutually irreducible.

ABSTRACT. In this paper we investigate splitting notions for conditional belief bases that allow us to localize reasoning and computations to only the relevant parts of a belief base. The focus of our investigations lies on splitting notions for c-representations, which are special kinds of Spohn’s ranking models for belief bases and which can be specified via a constraint satisfaction problem. We extend the notion of constraint splittings for c-representations to conditional constraint splittings, covering also cases where the subbases may share conditionals. Inspired by conditional syntax splittings, we identify the subclass of safe conditional constraint splittings, allowing us to solve the constraint systems of the subbases independently from each other. We elaborate the relationships of constraint and safe conditional constraint splittings to safe and generalized safe conditional syntax splittings and also to safe covers, which have been proposed for localized computation of c-representations. Additionally, we generalize solution splittings for c-representations to safe conditional c-solution splittings and show how they relate to conditional constraint splittings.