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Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints `a la IFF, possibly annotated with a probability value. We first present the overall abductive language, and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.
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.
In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the Maximum-A-Posteriori (MAP) inference task, which determines the most likely values for a subset of the random variables given evidence on other variables, and the Most Probable Explanation (MPE) task, the instance of MAP where the query variables are the complement of the evidence variables. We present a novel algorithm, included in the PITA reasoner, which tackles these tasks by representing each problem as a Binary Decision Diagram and applying a dynamic programming procedure on it. We compare our algorithm with the version of ProbLog that admits annotated disjunctions and can perform MAP and MPE inference. Experiments on several synthetic datasets show that PITA outperforms ProbLog in many cases. This paper is under consideration for acceptance in Theory and Practice of Logic Programming.
When modeling real world domains we have to deal with information that is incomplete or that comes from sources with different trust levels. This motivates the need for managing uncertainty in the Semantic Web. To this purpose, we introduced a probabilistic semantics, named DISPONTE, in order to combine description logics with probability theory. The probability of a query can be then computed from the set of its explanations by building a Binary Decision Diagram (BDD). The set of explanations can be found using the tableau algorithm, which has to handle non-determinism. Prolog, with its efficient handling of non-determinism, is suitable for implementing the tableau algorithm. TRILL and TRILLP are systems offering a Prolog implementation of the tableau algorithm. TRILLP builds a pinpointing formula, that compactly represents the set of explanations and can be directly translated into a BDD. Both reasoners were shown to outperform state-of-the-art DL reasoners. In this paper, we present an improvement of TRILLP, named TORNADO, in which the BDD is directly built during the construction of the tableau, further speeding up the overall inference process. An experimental comparison shows the effectiveness of TORNADO. All systems can be tried online in the TRILL on SWISH web application at http://trill.ml.unife.it/.
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.
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 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
Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP$^2$ for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.