Decomposing ontology in Description Logics by graph partitioning

International audienceIn this paper, we investigate the problem of decomposing an ontology in Description Logics (DLs) based on graph partitioning algorithms. Also, we focus on syntax features of axioms in a given ontology. Our approach aims at decomposing the ontology into many sub ontologies that are as distinct as possible. We analyze the algorithms and exploit parameters of partitioning that influence the efficiency of computation and reasoning. These parameters are the number of concepts and roles shared by a pair of sub-ontologies, the size (the number of axioms) of each sub-ontology, and the topology of decomposition. We provide two concrete approaches for automatically decomposing the ontology, one is called minimal separator based partitioning, and the other is eigenvectors and eigenvalues based segmenting. We also tested on some parts of used TBoxes in the systems FaCT, Vedaall, tambis, ... and propose estimated results.Dans cet article, nous étudions le problème de la décomposition d'une ontologie dans les logiques de description (DL) basés sur des algorithmes de partitionnement de graphe. Nous nous concentrons sur les particularités de syntaxe d'axiomes dans une ontologie donnée. Notre approche vise à décomposer l'ontologie dans un nombre d'ontologies telles qu'elles soient les plus distincts que possible. Nous analysons les algorithmes et exploitons les paramètres de partitionnement qui influencent l'efficacité du calcul et du raisonnement. Ces paramètres sont : le nombre de concepts et rôles partagés par une paire de sous-ontologies, la taille en nombre d'axiomes, de chaque sous-ontologie, et la topologie de la décomposition. Nous proposons deux approches concrètes pour décomposer automatiquement l'ontologie, l'une appelée "partitionnement par séparateur minimal" et l'autre appelée "partitionnement par vecteurs et valeurs propres" sur la base de segmentation. Enfin, nous avons effectué une évaluation de ces algorithmes sur certaines parties de TBoxes utilisées sur le moteur d'inférence FaCT : Vedaall, tambis, ... et étudié des résultats obtenus

Decomposing ontology in Description Logics by graph partitioning

In this paper, we investigate the problem of decomposing an ontology in Description Logics (DLs) based on graph partitioning algorithms. Also, we focus on syntax features of axioms in a given ontology. Our approach aims at decomposing the ontology into many sub ontologies that are as distinct as possible. We analyze the algorithms and exploit parameters of partitioning that influence the efficiency of computation and reasoning. These parameters are the number of concepts and roles shared by a pair of sub-ontologies, the size (the number of axioms) of each sub-ontology, and the topology of decomposition. We provide two concrete approaches for automatically decomposing the ontology, one is called minimal separator based partitioning, and the other is eigenvectors and eigenvalues based segmenting. We also tested on some parts of used TBoxes in the systems FaCT, Vedaall, tambis, ... and propose estimated result

Observing, reporting, and deciding in networks of sentences

In prior work we considered networks of agents who prove facts from their knowledge bases and report them to their neighbors in their common languages in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider\u27s sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when it is possible to prepare in advance a finite plan to generate reports within the network. We obtain conditions under which such a plan exists and is guaranteed to produce the right choice under any new observations

Craig interpolation for networks of sentences

The Craig Interpolation Theorem can be viewed as saying that in first order logic, two agents who can only communicate in their common language can cooperate in building proofs. We obtain generalizations of the Craig Interpolation Theorem for finite sets of agents with the following properties. (1) The agents are vertices of a directed graph. (2) The agents have knowledge bases with overlapping signatures. (3) The agents can only communicate by sending to neighboring agents sentences that they know and that are in the common language of the two agents

Partition-Based Logical Reasoning for First-Order and Propositional Theories

In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and first-order logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is two-fold. First, we are concerned with how to reason effectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the efficiency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions. Many of the reasoning procedures we present are based on the idea of passing messages between partitions. We present algorithms for reasoning using forward (data driven) message-passing and using backward (query driven) message-passing with partitions of logical axioms. Associated with each partition is a reasoning procedure. We characterize a class of reasoning procedures that ensures completeness and soundness of our message-passing algorithms. We also provide a specialized algorithm for propositional satisfiability checking with partitions. Craig’s interpolation theorem serves as a key to proving soundness and completeness of these algorithms. An analysis of these algorithms emphasizes parameters of partitionings that influence the efficiency of computation. These parameters are the number of symbols shared by a pair of partitions, the size (number of symbols) of each partition, and the topology of the partitioning. We provide a principled way for automatically decomposing a given theory into partitions. We provide a greedy algorithm that instantiates this method while exploiting the parameters that influence the efficiency of computation