A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the actual context taking place is uncertain. ALCP allows the expression of logical dependencies on the domain and probabilistic dependencies on the possible contexts. In order to draw probabilistic conclusions, we employ the principle of maximum entropy. We provide reasoning algorithms for this logic, and show that it satisfies several desirable properties of probabilistic logics.
Many probabilistic DLs have also been considered in the last decades @cite_15 @cite_6 @cite_20 . Our approach is closest to Bayesian DLs @cite_23 @cite_16 and disponte @cite_14 . The greatest difference with the former lies in the fact that KBs do not require a complete specification of the probability distribution, but only a set of probabilistic constraints. Moreover, the previous formalisms consider only the sceptical degree of belief, while we are interested in the full belief interval. In contrast to disponte , is capable of expressing both, logical and probabilistic dependencies between the axioms in a KB; in addition, disponte requires all uncertainty degrees to be assigned as mutually independent point probabilities, while allows for a more flexible specification.
@cite_14 @cite_6 @cite_23 @cite_15 @cite_16 @cite_20
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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. We propose a new family of probabilistic description logics (DLs) that, in contrast to most existing approaches, are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to certain popular combinations of DLs with temporal logic and are well-suited for capturing subjective probabilities. Our main contribution is a detailed study of the complexity of reasoning in the new family of probabilistic DLs, showing that it ranges from PTIME for weak variants based on the lightweight DL EL to undecidable for some expressive variants based on the DL ALC. We introduce the probabilistic Description Logic ( BEL ). In ( BEL ), axioms are required to hold only in an associated context. The probabilistic component of the logic is given by a Bayesian network that describes the joint probability distribution of the contexts. We study the main reasoning problems in this logic; in particular, we (i) prove that deciding positive and almost-sure entailments is not harder for ( BEL ) than for the BN, and (ii) show how to compute the probability, and the most likely context for a consequence. Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give an overview of approaches in this context to managing probabilistic uncertainty, possibilistic uncertainty, and vagueness in expressive description logics for the Semantic Web. The DL-Litefamily of tractable description logics lies between the semantic web languages RDFS and OWL Lite. In this paper, we present a probabilistic generalization of the DL-Litedescription logics, which is based on Bayesian networks. As an important feature, the new probabilistic description logics allow for flexibly combining terminological and assertional pieces of probabilistic knowledge. We show that the new probabilistic description logics are rich enough to properly extend both the DL-Litedescription logics as well as Bayesian networks. We also show that satisfiability checking and query processing in the new probabilistic description logics is reducible to satisfiability checking and query processing in the DL-Litefamily. Furthermore, we show that satisfiability checking and answering unions of conjunctive queries in the new logics can be done in LogSpace in the data complexity. For this reason, the new probabilistic description logics are very promising formalisms for data-intensive applications in the Semantic Web involving probabilistic uncertainty.