Reasoning with Probabilistic Ontologies

We present BUNDLE, a reasoner able to perform reasoning on probabilistic knowledge bases according to the semantics DISPONTE. In DISPONTE the axioms of a probabilistic ontology can be annotated with an epistemic or a statistical probability. The epistemic probability represents a degree of confidence in the axiom, while the statistical probability considers the populations to which the axiom is applied. BUNDLE exploits an underlying OWL DL reasoner, which is Pellet, that is able to return explanations for a query. However, it can work well with any reasoner able to return explanations for a query. The explanations are encoded in a Binary Decision Diagram from which the probability of the query is computed.

Uncertainty Reasoning for the Semantic Web III, 2014

We present a semantics for Probabilistic Description Logics that is based on the distribution semantics for Probabilistic Logic Programming. The semantics, called DISPONTE, allows to express assertional probabilistic statements. We also present two systems for computing the probability of queries to probabilistic knowledge bases: BUNDLE and TRILL. BUNDLE is based on the Pellet reasoner while TRILL exploits the declarative Prolog language. Both algorithms compute a propositional Boolean formula that represents the set of explanations to the query. BUNDLE builds a formula in Disjunctive Normal Form in which each disjunct corresponds to an explanation while TRILL computes a general Boolean pinpointing formula using the techniques proposed by Baader and Peñaloza. Both algorithms then build a Binary Decision Diagram (BDD) representing the formula and compute the probability from the BDD using a dynamic programming algorithm. We also present experiments comparing the performance of BUNDLE and TRILL.

2020

While there exist several reasoners for Description Logics, very few of them can cope with uncertainty. BUNDLE is an inference framework that can exploit several OWL (non-probabilistic) reasoners to perform inference over Probabilistic Description Logics. In this chapter, we report the latest advances implemented in BUNDLE. In particular, BUNDLE can now interface with the reasoners of the TRILL system, thus providing a uniform method to execute probabilistic queries using different settings. BUNDLE can be easily extended and can be used either as a standalone desktop application or as a library in OWL API-based applications that need to reason over Probabilistic Description Logics. The reasoning performance heavily depends on the reasoner and method used to compute the probability. We provide a comparison of the different reasoning settings on several datasets.

2011

We present DISPONTE, a semantics for probabilistic ontologies that is based on the distribution semantics for probabilistic logic programs. In DISPONTE each axiom of a probabilistic ontology is annotated with a probability. The probabilistic theory defines thus a distribution over normal theories (called worlds) obtained by including an axiom in a world with a probability given by the annotation. The probability of a query is computed from this distribution with marginalization. We also present the system BUNDLE for reasoning over probabilistic OWL DL ontologies according to the DISPONTE semantics. BUNDLE is based on Pellet and uses its capability of returning explanations for a query. The explanations are encoded in a Binary Decision Diagram from which the probability of the query is computed.

2018

While many systems exist for reasoning with Description Logics knowledge bases, very few of them are able to cope with uncertainty. BUNDLE is a reasoning system, exploiting an underlying non-probabilistic reasoner (Pellet), able to perform inference w.r.t. Probabilistic Description Logics. In this paper, we report on a new modular version of BUNDLE that can use other OWL (non-probabilistic) reasoners and various approaches to perform probabilistic inference. BUNDLE can now be used as a standalone desktop application or as a library in OWL API-based applications that need to reason over Probabilistic Description Logics. Due to the introduced modularity, BUNDLE performance now strongly depends on the method and OWL reasoner chosen to obtain the set of justifications. We provide an evaluation on several datasets as the inference settings vary.

2013

Uncertain information is ubiquitous in the Semantic Web, due to methods used for collecting data and to the inherently distributed nature of the data sources. It is thus very important to develop probabilistic Description Logics (DLs) so that the uncertainty is directly represented and managed at the language level. The DISPONTE semantics for probabilistic DLs applies the distribution semantics of probabilistic logic programming to DLs. In DISPONTE, axioms are labeled with numeric parameters representing their probability. These are often difficult to specify or to tune for a human. On the other hand, data is usually available that can be leveraged for setting the parameters. In this paper, we present EDGE that learns the parameters of DLs following the DISPONTE semantics. EDGE is an EM algorithm in which the required expectations are computed directly on the binary decision diagrams that are built for inference. Experiments on two datasets show that EDGE achieves higher areas under...

The interest in the combination of probability with logics for modeling the world has rapidly increased in the last few years. One of the most effective approaches is the Distribution Semantics which was adopted by many logic programming languages and in Descripion Logics. In this paper, we illustrate the work we have done in this research field by presenting a probabilistic semantics for description logics and reasoning and learning algorithms. In particular, we present in detail the system TRILL P , which computes the probability of queries w.r.t. probabilistic knowledge bases, which has been implemented in Prolog. Note: An extended abstract / full version of a paper accepted to be presented at the Doctoral

The adoption of Description Logics for modeling real world domains within the Semantic Web is exponentially increased in the last years, also due to the availability of a large number of reasoning algorithms. Most of them exploit the tableau algorithm which has to manage non-determinism, a feature that is not easy to handle using procedural languages such as Java or C++. Reasoning on real world domains also requires the capability of managing probabilistic and uncertain information. We thus present TRILL, for "Tableau Reasoner for descrIption Logics in proLog" and TRILL P , for "TRILL powered by Pinpointing formulas", which implement the tableau algorithm and return the probability of queries. TRILL P , instead of the set of explanations for a query, computes a Boolean formula representing them, speeding up the computation.

One of the major weaknesses of current research on the Semantic Web (SW) is the lack of proper means to represent and reason with uncertainty. A number of recent efforts from the SW community, the W3C, and others have recently emerged to address this gap. Such efforts have the positive side effect of bringing together two fields of research that have been apart for historical reasons, the artificial intelligence and the SW communities. One example of the potential research gains of this convergence is the current development of Probabilistic OWL (PR-OWL), an extension of the OWL Web Ontology Language that provides a framework to build probabilistic ontologies, thus enabling proper representation and reasoning with uncertainty within the SW context. PR-OWL is based on Multi-Entity Bayesian Networks (MEBN), a first-order probabilistic logic that combines the representational power of first-order logic (FOL) and Bayesian Networks (BN). However, PR-OWL and MEBN are still in development, lacking a software tool that implements their underlying concepts. The development of UnBBayes-MEBN, an open source, Java-based application that is currently in alpha phase (public release March 08), addresses this gap by providing both a GUI for building probabilistic ontologies and a reasoner based on the PR-OWL/MEBN framework. This work focuses on the major challenges of UnBBayes-MEBN implementation, describes the features already implemented, and provides an overview of the major algorithms, mainly the one used for building a Situation Specific Bayesian Network (SSBN) from a MEBN Theory.

2012

We present DISPONTE, a semantics for probabilistic ontologies that is based on the distribution semantics for probabilistic logic programs. In DISPONTE the axioms of a probabilistic ontology can be annotated with an epistemic or a statistical probability. The epistemic probability represents a degree of confidence in the axiom, while the statistical probability considers the populations to which the axiom is applied.