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Conservative Extensions in Horn Description Logics with Inverse Roles

Journal of Artificial Intelligence Research

We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF . The same results hold for inseparability and entailment.


Knowledge Graphs @ ICLR 2020

#artificialintelligence

It's great to see more research and more datasets on complex QA and reasoning tasks. Whereas last year we saw a surge of multi-hop reading comprehension datasets (e.g., HotpotQA), this year at ICLR there is a strong line-up of papers dedicated to studying compositionality and logical complexity: and here KGs are of big help! Keysers et al study how to measure compositional generalization of QA models, i.e., when train and test splits operate on the same set of entities (broadly, logical atoms), but the composition of such atoms is different. The authors design a new large KGQA dataset CFQ (Compositional Freebase Questions) comprised of about 240K questions of 35K SPARQL query patterns. Several fascinating points 1) the questions are annotated with EL Description Logic (yes, those were the times around 2005 when DL meant mostly Description Logic, not Deep Learning); 2) as the dataset is positioned towards semantic parsing, all questions already have linked Freebase IDs (URIs), so you don't need to plug in your favourite Entity Linking system (like ElasticSearch).


Detecting fake news for the new coronavirus by reasoning on the Covid-19 ontology

arXiv.org Artificial Intelligence

In the context of the Covid-19 pandemic, many were quick to spread deceptive information. I investigate here how reasoning in Description Logics (DLs) can detect inconsistencies between trusted medical sources and not trusted ones. The not-trusted information comes in natural language (e.g. "Covid-19 affects only the elderly"). To automatically convert into DLs, I used the FRED converter. Reasoning in Description Logics is then performed with the Racer tool.


CQE in Description Logics Through Instance Indistinguishability (extended version)

arXiv.org Artificial Intelligence

We study privacy-preserving query answering in Description Logics (DLs). Specifically, we consider the approach of controlled query evaluation (CQE) based on the notion of instance indistinguishability. We derive data complexity results for query answering over DL-Lite$_{\mathcal{R}}$ ontologies, through a comparison with an alternative, existing confidentiality-preserving approach to CQE. Finally, we identify a semantically well-founded notion of approximated query answering for CQE, and prove that, for DL-Lite$_{\mathcal{R}}$ ontologies, this form of CQE is tractable with respect to data complexity and is first-order rewritable, i.e., it is always reducible to the evaluation of a first-order query over the data instance.


Reasoning about Typicality and Probabilities in Preferential Description Logics

arXiv.org Artificial Intelligence

In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) D, whose intuitive meaning is that "normally/typically Cs are also Ds". This extension is based on a minimal model semantics corresponding to a notion of rational closure, built upon preferential models. We recall the basic concepts underlying preferential Description Logics. We also present two extensions of the preferential semantics: on the one hand, we consider probabilistic extensions, based on a distributed semantics that is suitable for tackling the problem of commonsense concept combination, on the other hand, we consider other strengthening of the rational closure semantics and construction to avoid the so called "blocking of property inheritance problem".


Large-scale Ontological Reasoning via Datalog

arXiv.org Artificial Intelligence

Reasoning over OWL 2 is a very expensive task in general, and therefore the W3C identified tractable profiles exhibiting good computational properties. Ontological reasoning for many fragments of OWL 2 can be reduced to the evaluation of Datalog queries.


Axiom Pinpointing

arXiv.org Artificial Intelligence

Axiom pinpointing refers to the task of finding the specific axioms in an ontology which are responsible for a consequence to follow. This task has been studied, under different names, in many research areas, leading to a reformulation and reinvention of techniques. In this work, we present a general overview to axiom pinpointing, providing the basic notions, different approaches for solving it, and some variations and applications which have been considered in the literature. This should serve as a starting point for researchers interested in related problems, with an ample bibliography for delving deeper into the details.


When is Ontology-Mediated Querying Efficient?

arXiv.org Artificial Intelligence

In ontology-mediated querying, description logic (DL) ontologies are used to enrich incomplete data with domain knowledge which results in more complete answers to queries. However, the evaluation of ontology-mediated queries (OMQs) over relational databases is computationally hard. This raises the question when OMQ evaluation is efficient, in the sense of being tractable in combined complexity or fixed-parameter tractable. We study this question for a range of ontology-mediated query languages based on several important and widely-used DLs, using unions of conjunctive queries as the actual queries. For the DL ELHI extended with the bottom concept, we provide a characterization of the classes of OMQs that are fixed-parameter tractable. For its fragment EL extended with domain and range restrictions and the bottom concept (which restricts the use of inverse roles), we provide a characterization of the classes of OMQs that are tractable in combined complexity. Both results are in terms of equivalence to OMQs of bounded tree width and rest on a reasonable assumption from parameterized complexity theory. They are similar in spirit to Grohe's seminal characterization of the tractable classes of conjunctive queries over relational databases. We further study the complexity of the meta problem of deciding whether a given OMQ is equivalent to an OMQ of bounded tree width, providing several completeness results that range from NP to 2ExpTime, depending on the DL used. We also consider the DL-Lite family of DLs, including members that admit functional roles.


Querying and Repairing Inconsistent Prioritized Knowledge Bases: Complexity Analysis and Links with Abstract Argumentation

arXiv.org Artificial Intelligence

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.


An Overview of Distance and Similarity Functions for Structured Data

arXiv.org Artificial Intelligence

The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts and make generalizations. While distance functions for propositional representations have been thoroughly studied, work on distance functions for structured representations, such as graphs, frames or logical clauses, has been carried out in different communities and is much less understood. Specifically, a significant amount of work that requires the use of a distance or similarity function for structured representations of data usually employs ad-hoc functions for specific applications. Therefore, the goal of this paper is to provide an overview of this work to identify connections between the work carried out in different areas and point out directions for future work.