Probabilistic Query Answering in the Bayesian Description Logic $$\mathcal {BE{}L}$$

Abstract

BEL is a probabilistic description logic (DL) that extends the lightweight DL EL with a joint probability distribution over the axioms, expressed with the help of a Bayesian network (BN). In recent work it has been shown that the complexity of standard logical reasoning in BEL is the same as performing probabilistic inferences over the BN. In this paper we consider conjunctive query answering in BEL. We study the complexity of the three main problems associated to this setting: computing the probability of a query entailment, computing the most probable answers to a query, and computing the most probable context in which a query is entailed. In particular, we show that all these problems are tractable w.r.t. data and ontology complexity.

The Bayesian Ontology Language $$\mathcal {BEL}$$ BEL

“…In case there is knowledge about individuals of the application domain, it is also relevant to answer queries about these individuals and their properties. We have started studying the problem of probabilistic query answering in BEL [17]. However, there still remain many open questions that need to be addressed.…”

Probabilistic Description Logics for Subjective Uncertainty

“…While our possible worlds semantic is in line with standard approaches to probabilistic databases (Suciu, Olteanu, Ré, & Koch, 2011;Dalvi & Suciu, 2012;Fuhr & Rölleke, 1997), in such a setup one typically wants to make strong independence assumptions on the data (that is, between ABox assertions) which we have not considered in this paper. First steps into this direction have been made (Jung & Lutz, 2012;Ceylan & Peñaloza, 2015;Gottlob et al, 2013). Moreover, a very attractive setup for probabilistic reasoning about data is to combine statistical probabilities in the TBox with subjective probabilities in the data, thus transforming knowledge about statistics into subjective beliefs about concrete individuals.…”

Open-world probabilistic databases: Semantics, algorithms, complexity

“…This paradigm is known as ontology-mediated query answering [70], and the open-world assumption is a driving force for ontology-based technologies. The literature on probabilistic extensions of ontology languages is rich, and ontology-mediated queries for probabilistic databases have been investigated in the context of both description logics [71,72] and Datalog ± [73,74,75,40]. Importantly, these models are typically open-domain, i.e., they allow reasoning over infinitely many objects in the domain (unlike our finite-domain assumption).…”