Ana Ozaki

Metric Temporal Description Logics with Interval-Rigid Names

In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining Description Logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there has recently been a growing interest in extending this work to the quantitative case. In this paper, we complement existing results on the combination of DLs with metric temporal logics over the natural numbers by introducing interval-rigid names. This allows to state that elements in the extension of certain names stay in this extension for at least some specified amount of time.

Attributed Description Logics: Ontologies for Knowledge Graphs

In modelling real-world knowledge, there often arises a need to represent and reason with meta-knowledge. To equip description logics (DLs) for dealing with such ontologies, we enrich DL concepts and roles with finite sets of attribute–value pairs, called annotations, and allow concept inclusions to express constraints on annotations. We show that this may lead to increased complexity or even undecidability, and we identify cases where this increased expressivity can be achieved without incurring increased complexity of reasoning. In particular, we describe a tractable fragment based on the lightweight description logic \(\mathcal {EL}\), and we cover \(\mathcal {SROIQ}\), the DL underlying OWL 2 DL.

Attributed Description Logics: Reasoning on Knowledge Graphs.

In modelling real-world knowledge, there often arises a need to represent and reason with metaknowledge. To equip description logics (DLs) for dealing with such ontologies, we enrich DL concepts and roles with finite sets of attribute–value pairs, called annotations, and allow concept inclusions to express constraints on annotations. We investigate a range of DLs starting from the lightweight description logic EL, covering the prototypicalALCH, and extending to the very expressive SROIQ, the DL underlying OWL 2 DL.

Preserving Constraints with the Stable Chase

Conjunctive query answering over databases with constraints – also known as (tuple-generating) dependencies – is considered a central database task. To this end, several versions of a construction called chase have been described. Given a set Sigma of dependencies, it is interesting to ask which constraints not contained in Sigma that are initially satisfied in a given database instance are preserved when computing a chase over Sigma. Such constraints are an example for the more general class of incidental constraints, which when added to Sigma as new dependencies do not affect certain answers and might even speed up query answering. After formally introducing incidental constraints, we show that deciding incidentality is undecidable for tuple-generating dependencies, even in cases for which query entailment is decidable. For dependency sets with a finite universal model, the core chase can be used to decide incidentality. For the infinite case, we propose the stable chase, which generalises the core chase, and study its relation to incidental constraints.

Theorem Proving for Metric Temporal Logic over the Naturals

We study translations from Metric Temporal Logic (MTL) over the natural numbers to Linear Temporal Logic (LTL). In particular, we present two approaches for translating from MTL to LTL which preserve the ExpSpace complexity of the satisfiability problem for MTL. In each of these approaches we consider the case where the mapping between states and time points is given by (1) a strict monotonic function and by (2) a non-strict monotonic function (which allows multiple states to be mapped to the same time point). Our translations allow us to utilise LTL solvers to solve satisfiability and we empirically compare the translations, showing in which cases one performs better than the other.

Exact learning of multivalued dependency formulas

Abstract The transformation of a relational database schema into fourth normal form, which minimizes data redundancy, relies on the correct identification of multivalued dependencies. In this work, we study the learnability of multivalued dependency formulas (MVDF), which correspond to the logical theory behind multivalued dependencies. As we explain, MVDF lies between propositional Horn and 2-Quasi-Horn. We prove that MVDF is polynomially learnable in Angluin et al.s exact learning model with membership and equivalence queries, provided that counterexamples and membership queries are formulated as 2-Quasi-Horn clauses. As a consequence, we obtain that the subclass of 2-Quasi-Horn theories which are equivalent to MVDF is polynomially learnable.

Exact Learning of Multivalued Dependencies

The transformation of a relational database schema into fourth normal form, which minimizes data redundancy, relies on the correct identification of multivalued dependencies. In this work, we study the learnability of multivalued dependency formulas MVDF, which correspond to the logical theory behind multivalued dependencies. As we explain, MVDF lies between propositional Horn and 2-Quasi-Horn. We prove that MVDF is polynomially learnable in Angluin et al.s exact learning model with membership and equivalence queries, provided that counterexamples and membership queries are formulated as 2-Quasi-Horn clauses. As a consequence, we obtain that the subclass of 2-Quasi-Horn theories which are equivalent to MVDF is polynomially learnable.