Zese, Riccardo (University of Ferrara)

The last years have seen an exponential increase in the interest for the development of methods for combining probability with Description Logics (DLs). These methods are very useful to model real world domains, where incompleteness and uncertainty are common. This combination has become a fundamental component of the Semantic Web.Our work started with the development of a probabilistic semantics for DL, called DISPONTE, that applies the distribution semantics to DLs. Under DISPONTE we annotate axioms of a theory with a probability, that can be interpreted as the degree of our belief in the corresponding axiom, and we assume that each axiom is independent of the others. Several algorithms have been proposed for supporting the development of the Semantic Web. Efficient DL reasoners, such us Pellet, are able to extract implicit information from the modeled ontologies. Despite the availability of many DL reasoners, the number of probabilistic reasoners is quite small. We developed BUNDLE, a reasoner based on Pellet that allows to compute the probability of queries. BUNDLE, like most DL reasoners, exploits an imperative language for implementing its reasoning algorithm. Nonetheless, usually reasoning algorithms use non-deterministic operators for doing inference. One of the most used approaches for doing reasoning is the tableau algorithm which applies a set of consistency preserving expansion rules to an ABox, but some of these rules are non-deterministic.In order to manage this non-determinism, we developed the system TRILL which performs inference over DISPONTE DLs. It implements the tableau algorithm in the declarative Prolog language, whose search strategy is exploited for taking into account the non-determinism of the reasoning process. Moreover, we developed a second version of TRILL, called TRILL^P, which implements some optimizations for reducing the running time. The parameters of probabilistic KBs are difficult to set. It is thus necessary to develop systems which automatically learn this parameters starting from the information available in the KB. We presented EDGE that learns the parameters of a DISPONTE KB, and LEAP, that learn the structure together with the parameters of a DISPONTE KB. The main objective is to apply the developed algorithms to Big Data. Nonetheless, the size of the data requires the implementation of algorithms able to handle it. It is thus necessary to exploit approaches based on the parallelization and on cloud computing. Nowadays, we are working to improve EDGE and LEAP in order to parallelize them.

Riguzzi, Fabrizio (University of Ferrara) | Bellodi, Elena (University of Ferrara) | Lamma, Evelina (University of Ferrara) | Zese, Riccardo (University of Ferrara)

Modeling real world domains requires ever more frequently to represent uncertain information. The DISPONTE semantics for probabilistic description logics allows to annotate axioms of a knowledge base with a value that represents their probability. In this paper we discuss approaches for performing inference from probabilistic ontologies following the DISPONTE semantics. We present the algorithm BUNDLE for computing the probability of queries. BUNDLE exploits an underlying Description Logic reasoner, such as Pellet, in order to find explanations for a query. These are then encoded in a Binary Decision Diagram that is used for computing the probability of the query.

The last years have seen an exponential increase in the interest for the development of methods for combining probability with Description Logics (DLs). These methods are very useful to model real world domains, where incompleteness and uncertainty are common. This combination has become a fundamental component of the Semantic Web.Our work started with the development of a probabilistic semantics for DL, called DISPONTE, that applies the distribution semantics to DLs. Under DISPONTE we annotate axioms of a theory with a probability, that can be interpreted as the degree of our belief in the corresponding axiom, and we assume that each axiom is independent of the others. Several algorithms have been proposed for supporting the development of the Semantic Web. Efficient DL reasoners, such us Pellet, are able to extract implicit information from the modeled ontologies. Despite the availability of many DL reasoners, the number of probabilistic reasoners is quite small. We developed BUNDLE, a reasoner based on Pellet that allows to compute the probability of queries.

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 Consortium of the 30th International Conference on Logic Programming (ICLP 2014), July 19-22, Vienna, Austria

Cota, Giuseppe, Zese, Riccardo, Bellodi, Elena, Lamma, Evelina, Riguzzi, Fabrizio

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.