ABSTRACT. This paper proposes a framework for database repairing that abstracts away from specific choices of language and structure, assuming only a primitive relation between a set of structures and a set of formulas. Within this framework, we define a family of belief change operators that capture an abstract notion of repair, characterized by partial orders and a set of admissible outcomes. This means that, given an initial structure and a set of constraints, the operator can impose extra-logical criteria on the class of admissible structures. In particular, this captures distance-based, subset, and superset repairing.

ABSTRACT. Functional dependencies are an important and well-studied class of database constraints that correspond to a notion expressed by dependence atoms in team logic. In practice, data often contain errors, so in some cases it might be useful to allow the database to have a small number of tuples that violate the desired dependency. Väänänen (2017) studied the axiomatization of a notion of approximate dependence that specifies for each dependence atom how much of the database can be disregarded. We demonstrate that the interaction of approximate dependence atoms is more complicated than previously thought in the sense that there is a semantic consequence that is not captured by the inference rules introduced before. We show that Väänänen's axiomatisation is still complete in the restricted case of unary dependencies. We also consider the complexity of model checking for approximate dependence: it is NP-complete for disjunctions of two atoms and LOGSPACE-hard for individual atoms.

ABSTRACT. We study inconsistency from the perspectives of knowledge representation and statistical inference, and propose a unified framework to relate the two. In statistics, inconsistency arises when data are impossible under a generative model and is typically addressed through flexible modeling or error mechanisms. In logic and computer science, inconsistency corresponds to violations of constraints and is handled via inconsistency-tolerant reasoning. We formalize inconsistency in statistical models in logical terms, enabling the use of repair-based semantics such as AR and CAR. We illustrate the approach in two settings: binary classification with a monotonicity assumption and preference learning with non-transitive comparisons.

ABSTRACT. Physical agents have limited resources and cannot compute all the logical consequences of their beliefs. They therefore possess incomplete deductive abilities, and thus may fail to recognise inconsistencies. This does not prevent them from using and revising their beliefs, and from possibly resolving the undetected inconsistency after some time. However, most multi-agent logics of beliefs represent an agent's beliefs as a logically closed set, and therefore cannot represent inconsistent beliefs without explosion. Here we present a multi-agent logic of belief that can represent agents with incomplete deductive abilities and inconsistent beliefs.

ABSTRACT. We explain that cautious and brave semantics in Consistent Query Answering naturally extend from Boolean queries to numerical queries, where they are known as range semantics. We then apply this extension to numerical queries that are conjunctive queries with aggregation, under primary key constraints. In particular, we highlight results from~\cite{DBLP:journals/pacmmod/KhalfiouiW24, DBLP:conf/icdt/KhalfiouiW26} on computing range semantics via rewriting in aggregate logic.

ABSTRACT. Abduction is the task of computing a sufficient extension of a knowledge base (KB) that entails a conclusion not entailed by the original KB. It serves to compute explanations, or hypotheses, for such missing entailments. Little is known about abduction when erroneous data results in inconsistent KBs. In this paper we investigate abduction under repair semantics, and discuss complexity results on deciding existence of and verifying abductive solutions fulfilling additional criteria that are useful in the presence of inconsistencies. In particular, we consider different repair semantics and the description logics DL-Lite and EL_bot.

ABSTRACT. We present our recent work towards an end-to-end ASP-based system for handling inconsistent data. Our first contribution introduces a declarative rule-based framework for specifying and computing a priority relation between conflicting facts. Such priority relations have been used to define three kinds of optimal repairs (Pareto-, globally-, and completion-optimal), which can be used in place of classical repairs to define repair-based semantics. Our second contribution is an implementation of the optimal repair-based variants of three such semantics (AR, brave and IAR) using answer set programming (ASP) and its extension ASP(Q). In particular, this is the first implementation of the globally-optimal repair-based semantics, which are computationally more challenging. We also implement the grounded semantics, a tractable under-approximation of the optimal repair-based semantics rooted in abstract argumentation. These two components are key steps towards a complete pipeline for handling inconsistent data using priority relations. This extended abstract summarizes the main ideas behind each component and the takeaways from our experiments.

ABSTRACT. Causal Assumption-based Argumentation (ABA) has been proposed as a causal discovery method with increased guarantees on the correspondence of the discovered causal graphs to a subset of the input constraints that drive the search for the causal relations. Heuristics are currently used to identify the optimal subset of constraints and infer the most likely corresponding graphs. Minimal Unsatisfiable Sets (MUSes) and Minimal Correction Sets (MCSes) have been explored in the Answer Set Programming (ASP) literature to create explanations and repair logic programs (LPs). We leverage the correspondence of stable semantics between ABA and LPs to investigate the benefits and drawbacks of MUSes and MCSes when applied to the causal discovery task carried out by Causal ABA. We define the notion of optimal MCSes and show how they can be computed by leveraging standard optimisation constructs such as weak constraints. We then empirically show that optimal MCSes, integrated into Causal ABA for causal discovery, substantially (i) increase the identification rate of true constraints; (ii) reduce the number of compatible causal graphs in output; (iii) improve graph reconstruction according to standard metrics.

ABSTRACT. We propose a family of local inconsistency measures for graph databases subject to Regular Path Constraints, grounded in an origin-based semantics that scopes constraint evaluation to a designated subset of nodes. We formalize this notion, study the properties of the proposed measures with respect to a set of postulates, and illustrate their behavior on a running example. Our framework enables fine-grained inconsistency assessment, surfacing localized violations that global measures may fail to detect.

ABSTRACT. We present our ongoing work on implementing and benchmarking scalable SAT-based procedures for query answering under variants of three well-known inconsistency-tolerant semantics (AR, brave and IAR) based on two notions of optimal repairs (Pareto- and completion-optimal) that exploit a priority relation between conflicting facts. We focus in particular on comparing different SAT encodings that can handle non-binary conflicts.

ABSTRACT. Description logic (DL) knowledge bases (KBs) built by hand or (semi)automatically using machine learning or information retrieval tools may contain errors, often detected when reasoning derives an inconsistency. However, not all errors cause an inconsistency, but such errors may be noticed when reasoning produces a consequence that follows from the KB, but does not hold in the application domain modelled by the KB. In fact, some application-relevant DL KBs such as the large medical ontology SNOMED CT are even written in DL dialects such as E L that cannot even express an inconsistency. Getting rid of an inconsistency or an unwanted consequence by removing a minimal amount of information from the KB is usually called repair in the DL literature. Instead of producing a single new KB as repair, inconsistency-tolerant reasoning takes all repairs of a detected inconsistency into account, e.g., by producing only consequences that follow from all (in a certain way preferred) repairs. This notion can be extended to repairs that remove an unwanted consequence, but this variant has been investigated in less detail. The purpose of this paper is to show that certain results for inconsistency-tolerant reasoning can easily be transferred to error-tolerant reasoning. To this purpose, it concentrates on results that link inconsistency-tolerant reasoning for prioritized KBs to certain notions of extensions in argumentation frameworks (AFs). The paper shows that these results, originally proved for inconsistency-tolerant reasoning in certain DL-Lite dialects, can easily be transferred to error-tolerant reasoning for KBs written in the DL EL.

ABSTRACT. When using datalogMTL over a dense timeline and inconsistent data, there can be several kinds of repairs as recently defined in [BBK-IJCAI25]. One of such kind is pointwise repairs for which no method for deciding existence for DatalogMTL is known. In this paper, we consider datalogMTL^\diamondminus, a fragment of datalogMTL, which has diamond minus as the only temporal operator and a bounded dataset. We develop a computation algorithm that returns pointwise repairs for this setting.

ABSTRACT. In this work, we provide an overview of our recent work on SHACL validation, satisfiability and containment, and specifically relate it to the setting in which SHACL constraints are paired with an ontology. This allows for combining employing database constraints to detect inconsistencies with domain knowledge to reduce gaps in the data: both standard techniques to address current data plagued by quality issues.