Epistemic and Statistical Probabilistic Ontologies

Across a wide range of domains, there is an urgent need for a wellfounded approach to incorporating uncertain and incomplete knowledge into formal domain ontologies. Although this subject is receiving increasing attention from ontology researchers, there is as yet no broad consensus on the definition of a probabilistic ontology and on the most suitable approach to extending current ontology languages to support uncertainty. This paper presents two contributions to developing a coherent framework for probabilistic ontologies: (1) a formal definition of a probabilistic ontology, and (2) an extension of the OWL Web Ontology Language that is consistent with our formal definition. This extension, PR-OWL, is based on Multi-Entity Bayesian Networks (MEBN), a first-order Bayesian logic that unifies Bayesian probability with First-Order Logic. As such, PR-OWL combines the full representation power of OWL with the flexibility and inferential power of Bayesian logic.

IGI Global eBooks, 2018

During the past years, ontologies are widely used for representing knowledge of complex domains. Despite that the ontologies (classical ontologies) have become standard for representing knowledge; however, they are not able to represent and reason with uncertainty which is one of the characteristics of the world that must be handled. Probabilistic Ontologies have come to remedy this defect. This paper is part of this framework in which the authors have proposed a new method of probabilistic ontology construction, named Prob-Ont, by integrating uncertainty to elements of OWL ontology (especially to instances and/or relations). As a case study, the authors have constructed a probabilistic ontology for the domain of scientific documentation system (dblp).

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

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.

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.

Advances in Soft Computing, 2008

This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.

This paper addresses a major weakness of current technologies for the Semantic Web, namely the lack of a principled means to represent and reason about uncertainty. This not only hinders the realization of the original vision for the Semantic Web, but also creates a barrier to the development of new, powerful features for general knowledge applications that require proper treatment of uncertain phenomena. We propose to extend OWL, the ontology language recommended by the World Wide Web Consortium (W3C), to provide the ability to express probabilistic knowledge. The new language, PR-OWL, will allow legacy ontologies to interoperate with newly developed probabilistic ontologies. PR-OWL will move beyond the current limitations of deterministic classical logic to a full first-order probabilistic logic. By providing a principled means of modeling uncertainty in ontologies, PR-OWL will serve as a supporting tool for many applications that can benefit from probabilistic inference within an ontology language, thus representing an important step toward the W3C's vision for the Semantic Web.

2014

: The use of ontologies is on the rise, as they facilitate interoperability and provide support for automation. Today, ontologies are popular in areas such as the Semantic Web, knowledge engineering, Artificial Intelligence and knowledge management. However, many real world problems in these disciplines are burdened by incomplete information and other sources of uncertainty which traditional ontologies cannot represent. Therefore, a means to incorporate uncertainty is a necessity. Probabilistic ontologies extend current ontology formalisms to provide support for representing and reasoning with uncertainty. Traditional ontologies provide a hierarchical structure of entity classes and a formal way of expressing their relationships with first-order expressivity, which supports logical reasoning. However, they lack built-in, principled support to adequately account for uncertainty. Applying simple probability annotations to ontologies fails to convey the structure of the probabilistic r...

The use of ontologies is on the rise, as they facilitate interoperability and provide support for automation. Today, ontologies are popular for research in areas such as the Semantic Web, knowledge engineering, artificial intelligence and knowledge management. However, many real world problems in these disciplines are burdened by incomplete information and other sources of uncertainty which traditional ontologies cannot represent. Therefore, a means to incorporate uncertainty is a necessity. Probabilistic ontologies extend current ontology formalisms to provide support for representing and reasoning with uncertainty. Representation of uncertainty in real-world problems requires probabilistic ontologies, which integrate the inferential reasoning power of probabilistic representations with the first-order expressivity of ontologies. This paper introduces a systematic approach to probabilistic ontology development through a reference architecture which captures the evolution of a traditional ontology into a probabilistic ontology implementation for real-world problems. The Reference Architecture for Probabilistic Ontology Development catalogues and defines the processes and artifacts necessary for the development, implementation and evaluation of explicit, logical and defensible probabilistic ontologies developed for knowledgesharing and reuse in a given domain.

2002

Probabilistic computation has proven to be a challenging and interesting area of research, both from the theoretical perspective of denotational semantics and the practical perspective of reasoning about probabilistic algorithms. On the theoretical side, the probabilistic powerdomain of Jones and Plotkin represents a significant advance. Further work, especially by Alvarez-Manilla, has greatly improved our understanding of the probabilistic powerdomain, and has helped clarify its relation to classical measure and integration theory. On the practical side, many researchers such as Kozen, Segala, Desharnais, and Kwiatkowska, among others, study problems of verification for probabilistic computation by defining various suitable logics for the classes of processes under study. The work reported here begins to bridge the gap between the domain theoretic and verification (model checking) perspectives on probabilistic computation by exhibiting sound and complete logics for probabilistic powerdomains that arise directly from given logics for the underlying domains. The category in which the construction is carried out generalizes Scott's Information Systems by taking account of full classical sequents. Via Stone duality, following Abramsky's Domain Theory in Logical Form, all known interesting categories of domains are embedded as subcategories. So the results reported here properly generalize similar constructions on specific categories of domains. The category offers a promising universe of semantic domains characterized by a very rich structure and good preservation properties of standard constructions. Furthermore, because the logical constructions make use of full classical sequents, the morphisms have a natural non-deterministic interpretation. Thus the category is a natural one in which to investigate the relationship between probabilistic and non-deterministic computation. We discuss the problem of integrating probabilistic and non-deterministic computation after presenting the construction of logics for probabilistic powerdomains.