A Modular Inference System for Probabilistic Description Logics

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...

2015

Bayesian ontology languages are a family of probabilistic ontology languages that allow to encode probabilistic information over the axioms of an ontology with the help of a Bayesian network. The Bayesian ontology language BEL is an extension of the lightweight Description Logic (DL) EL within the above-mentioned framework. We present the system BORN that implements the probabilistic subsumption problem for BEL.

Annals of Mathematics and Artificial Intelligence, 2016

The increasing popularity of the Semantic Web drove to a widespread adoption of Description Logics (DLs) for modeling real world domains. To help the diffusion of DLs, a large number of reasoning algorithms have been developed. Usually these algorithms are implemented in procedural languages such as Java or C++. Most of the reasoners exploit the tableau algorithm which features non-determinism, that is not easily handled by those languages. Prolog directly manages non-determinism, thus is a good candidate for dealing with the tableau's non-deterministic expansion rules. We present TRILL, for "Tableau Reasoner for descrIption Logics in pro-Log", that implements a tableau algorithm and is able to return explanations for queries and their corresponding probability, and TRILL P , for "TRILL powered by Pinpointing formulas", which is able to compute a Boolean formula representing the set of explanations for a query. Reasoning on real world domains also requires the capability of managing probabilistic and uncertain information. We show how TRILL and TRILL P can be used to compute the probability of queries to knowledge bases following DISPONTE semantics. Experiments comparing these with other systems show the feasibility of the approach.

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.

Uncertain information is ubiquitous in real world domains and in the Semantic Web. Recently, the problem of representing this uncertainty in description logics has received an increasing attention. In probabilistic Description Logics, knowledge bases contain numeric parameters that are often difficult to specify for a human. Moreover, the information are incomplete and poorly structured. On the other hand, data is usually available about the domain that can be leveraged for tuning the parameters and learn the structure of the information. In this paper we consider the problem of learning both the structure and the parameters of Probabilistic Description Logics under the DISPONTE semantics. We overview two systems we hve implemented: EDGE, that returns the value of the probabilities associated with axioms tuned using an Expectation Maximization algorithm, and LEAP, that exploits EDGE and the system CELOE to learn both the structure and the parameters of DISPONTE knowledge bases.

Web Semantics: science, …, 2007

In this paper, we present a brief overview of Pellet: a complete OWL-DL reasoner with acceptable to very good performance, extensive middleware, and a number of unique features. Pellet is the first sound and complete OWL-DL reasoner with extensive support for reasoning with individuals (including nominal support and conjunctive query), user-defined datatypes, and debugging support for ontologies. It implements several extensions to OWL-DL including a combination formalism for OWL-DL ontologies, a non-monotonic operator, and preliminary support for OWL/Rule hybrid reasoning. Pellet is written in Java and is open source.

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

2005

Description Logics (DLs) are a family of class based knowledge representation formalisms characterised by the use of various constructors to build complex classes from simpler ones, and by an emphasis on the provision of sound, complete and (empirically) tractable reasoning services. They have a range of applications, but are mostly widely known as the basis for ontology languages such as OWL.

2016

This work reports on our efforts to implement a practical reasoner based on Dung-style argumentation semantics for potentially inconsistent possibilistic ontologies. Our Java-based implementation targets a subset of the description logic programming fragment that we codify in a Racer-like syntax suitably adapted for representing certainty degrees of both axioms and assertions. We introduce our approach with a running example, discuss implementation issues and present time complexity results.

Proceedings of the 11th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management, 2019

The paper proposes a new type of probabilistic description logics with a different interpretation of uncertain knowledge. The basic idea is that the probability of an axiom is not the probability of the axiom to be true in contrast to be false. Instead, it is the probability of the axiom to be true within the same knowledge base, i.e. in contrast to other axioms of the knowledge base to be true. The proposed description logic is evaluated with some sample knowledge bases and the results are discussed in the paper.

2021

Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are not feasible, and a subjective or epistemic approach is required. Aleatoric description logic models uncertainty in the world as aleatoric events, by the roll of the dice, where an agent has subjective beliefs about the bias of these dice. This provides a subjective Bayesian description logic, where propositions and relations are assigned probabilities according to what a rational agent would bet, given a configuration of possible individuals and dice. Aleatoric description logic is shown to generalise the description logic ALC, and can be seen to describe a probability space of interpretations of a restriction of ALC where all roles are functions. Several computational problems are considered and aleatoric description logic is shown to be able to...

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.

One shortcoming of classic Descriptions Logics, DLs, is their inability to encode probabilistic knowledge and reason over it. This is, however, a strong demand of some modern applications, e.g. in biology and healthcare. Therefore, probabilistic extensions of DLs are attracting attention nowadays. We introduce the probabilistic DL SHIQP which extends a known probabilistic DL. We investigate two reasoning problems for TBoxes: deciding consistency and computing tight probability bounds. It turns out that both problems are not harder than reasoning in the classic counterpart SHIQ. We gain insight into complexity sources.

Theory and Practice of Logic Programming, 2019

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 (DLs) 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 TRILL P are systems offering a Prolog implementation of the tableau algorithm. TRILL P 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,...

Journal of Computer Science and Technology, 2015

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PoDLoDA ontologies for short). Given a PoDLoDA ontology, its terminological box is expressed in the description logic programming fragment but its assertional box allows four kinds of statements: an individual is a member of a concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Axioms and statements in PoDLoDA ontologies have a numerical certainty degree attached. A disjunctive assertion expresses a doubt respect to the membership of either individuals to union of concepts or pairs of individuals to the union of roles. Because PoDLoDA ontologies allow to represent incomplete and potentially inconsistent information, instance checking is addressed through an adaptation of Bodanza’s Suppositional Argumentation System that allow...