7 research outputs found
Complexity of Inconsistency-Tolerant Query Answering in Datalog+/- under Cardinality-Based Repairs
This is the author accepted manuscript. The final version is available from Association for the Advancement of Artificial Intelligence (AAAI) via the link in this recordQuerying inconsistent ontological knowledge bases is an important
problem in practice, for which several inconsistencytolerant
query answering semantics have been proposed, including
query answering relative to all repairs, relative to
the intersection of repairs, and relative to the intersection of
closed repairs. In these semantics, one assumes that the input
database is erroneous, and the notion of repair describes a
maximally consistent subset of the input database, where different
notions of maximality (such as subset and cardinality
maximality) are considered. In this paper, we give a precise
picture of the computational complexity of inconsistencytolerant
(Boolean conjunctive) query answering in a wide
range of Datalog± languages under the cardinality-based versions
of the above three repair semantics.This work was supported by the Alan
Turing Institute under the UK EPSRC grant EP/N510129/1,
and by the EPSRC grants EP/R013667/1, EP/L012138/1,
and EP/M025268/1
Query Answer Explanations under Existential Rules
Ontology-mediated query answering is an extensively studied paradigm, which aims at improving
query answers with the use of a logical theory. In this paper, we focus on ontology languages based on
existential rules, and we carry out a thorough complexity analysis of the problem of explaining query
answers in terms of minimal subsets of database facts and related task
Explanations for ontology-mediated query answers
Ontology-mediated query answering is a paradigm that seeks to exploit the semantic knowledge expressed in terms of ontologies to improve query answers over incomplete data sources. In this thesis, we consider explanations for ontology-mediated query answers under the classical semantics. We provide a comprehensive complexity analysis of a wide range of computational problems, associated with explaining ontology-mediated query answers. We study explanations both for positive and negative ontology-mediated query answers under different minimality criteria, both for existential rules and description logics. This allows us to indicate similarities and point out differences in the complexity of explaining ontology-mediated query answers for these different settings.</p
Minimal weighted clones with Boolean support
We study algebraic structures called weighted clones. These structures characterise the computational complexity of discrete optimisation problems of special form, known as valued constraint satisfaction problems. We identify all minimal weighted clones for every Boolean support clone
Explanations for negative query answers under existential rules
Ontology-mediated query answering is an extensively studied paradigm, where the conceptual knowledge provided by an ontology is leveraged towards more enhanced querying of data sources. A major advantage of ontological reasoning is its interpretability, which allows one to derive explanations for query answers. Indeed, explanations have a long history in knowledge representation, and have also been investigated for ontology languages based on description logics and existential rules. Existing works on existential rules, however, merely focus on understanding why a query is entailed, i.e., explaining positive query answers. In this paper, we continue this line of research and address another important problem, namely, explaining why a query is not entailed under existential rules, i.e., explaining negative query answers. We consider various problems related to explaining non-entailments from the abduction literature, and also introduce new problems. For all considered problems, we give a detailed complexity analysis for a wide range of existential rule languages and complexity measures
Preferred explanations for ontologyâmediated queries under existential rules
Recently, explanations for query answers under existential rules have been investigated, where an explanation is an inclusion-minimal subset of a given database that, together with the ontology, entails the query. In this paper, we take a step further and study explanations under different minimality criteria. In particular, we first study cardinality-minimal explanations and hence focus on deriving explanations of minimum size. We then study a more general preference order induced by a weight distribution. We assume that every database fact is annotated with a (penalization) weight, and we are interested in explanations with minimum overall weight. For both preference orders, we study a variety of explanation problems, such as recognizing a preferred explanation, all preferred explanations, a relevant or necessary fact, and the existence of a preferred explanation not containing forbidden sets of facts. We provide a detailed complexity analysis for all the aforementioned problems, thereby providing a more complete picture for explaining query answers under existential rules