The main goal of this paper is to propose a distributed paradigm for reasoning with multiple ontologies connected by semantic mappings. The contribution of the paper to this goal is twofold. From the theoretical point of view we characterize the problem of global subsumption (i.e. the problem of subsumption in a set of local ontologies connected by semantic mappings) as a suitable fixpoint combination of operators that compute subsumptions in the local ontologies. This allows us to define a sound and complete algorithm for global subsumptions which calls black-boxes sub-routines for local subsumptions. The second contribution is the description of a prototype implementation of such algorithm in a peer-to-peer architecture.

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Abstract. In this paper, we tackle the satisfiability problem for multi-context systems. First, we establish a satisfiability algorithm based on an encoding into propositional logic. Then, we propose a distributed decision procedure that maximally exploits the potential amenity of localizing reasoning and restricting it to relevant contexts. We show that the latter approach is computationally superior to our translation-based procedure, and outline how off-the-shelf efficient reasoning procedures can be used to implement our algorithm. 1

Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies a given formula. Their long-term goal is to produce practical tools to solve combinatorial search problems, especially those in NP. In this framework, a problem is encoded in a logic, an instance of the problem is represented by a finite structure, and a solver generates solutions to the problem. This approach relies on propositionalisation of high-level specifications, and on the efficiency of modern SAT solvers. Here, we propose an efficient algorithm which combines grounding with partial evaluation. Since the MX framework is based on classical logic, we are able to take advantage of known results for the so-called guarded fragments. In the case of k-guarded formulas with inductive definitions under a natural restriction, the algorithm performs much better than naive grounding by relying on connections between k-guarded formulas and tree decompositions. 1

We propose a sound and complete satisfiability algorithm for propositional multi-context systems. In essence, the algorithm is a distribution policy built on top of local reasoning procedures, one for each context, which can be implemented by (a diversity of) customized state-of-the-art SAT solvers. The foremost intuition that has motivated our algorithm, and the very potential strength of contextual reasoning, is that of keeping reasoning as local as possible. In doing so, we improve on earlier established complexity results by Massacci. Moreover, our approach could be applied to enhance recent proposals by Amir and Mcilraith towards a new partitionbased reasoning paradigm; particularly, our formalism allows for a more expressive description of interpartition relations, and we provide an algorithm that is explicitly designed to deal with this expressiveness.

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Recent years have seen the advent of large and complex ontologies, most notably in the medical domain. As a consequence, structuring mechanisms for ontologies are nowadays viewed as an indispensible tool. A basic such mechanism is the automatic decomposition of the vocabulary of an ontology into independent parts. In this paper, we study decompositions that are syntax independent in the sense that the resulting partitioning depends only on the meaning of the vocabulary items, but not on the concrete syntactic form of the axioms in the ontology. We present the first systematic investigation of decompositions of this type in the context of ontologies. Specifically, we focus on ontologies formulated in description logics and provide a variety of results that range from theorems stating the existence of unique finest decompositions to complexity results and algorithms computing decompositions. We also investigate the relationship between the existence of unique finite decompositions and a variant of the Craig interpolation property called parallel interpolation.

Abstract. The use of Description Logic as the basis for Semantic Web Languages has led to new requirements with respect to scalable and nonstandard reasoning. In this paper, we address the problem of scalable reasoning by proposing a distributed, complete and terminating algorithm that decides satisfiability of terminologies in ALC. The algorithm is based on recent results on applying resolution to description logics. We show that the resolution procedure proposed by Tammet can be distributed amongst multiple resolution solvers by assigning unique sets of literals to individual solvers. This results provides the basis for a highly scalable reasoning infrastructure for Description logics. 1

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Decentralized reasoning is receiving increasing attention due to the distributed nature of knowledge on the Web. We address the problem of answering queries to distributed propositional reasoners which may be mutually inconsistent. This paper provides a formal characterization of a prioritized peerto-peer query answering framework that exploits a priority ordering over the peers, as well as a distributed entailment relation as an extension to established work on argumentation frameworks. We develop decentralized algorithms for computing query answers according to distributed entailment and prove their soundness and completeness. To improve the efficiency of query answering, we propose an ordering heuristic that exploits the peers ’ priority ordering and empirically evaluate its effectiveness. 1