## Decomposition of Distributed Nonmonotonic Multi-Context Systems ∗

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Citations: | 7 - 4 self |

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@MISC{Bairakdar_decompositionof,

author = {Seif El-din Bairakdar and Minh Dao-tran and Thomas Eiter and Michael Fink and Thomas Krennwallner},

title = {Decomposition of Distributed Nonmonotonic Multi-Context Systems ∗},

year = {}

}

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### Abstract

Multi-Context Systems (MCS) are formalisms that enable the interlinkage of single knowledge bases, called contexts, via bridge rules. Recently, the evaluation of heterogeneous, nonmonotonic MCS was considered in Dao-Tran et al. (2010), where a fully distributed algorithm was described. In this paper, we continue this line of work and present a decomposition technique for MCS which analyzes the topology of an MCS. It applies pruning techniques to get economically small representations of context dependencies. Orthogonal to this, we characterize minimal interfaces for information exchange between contexts, such that data transmissions can be minimized. We then present a novel evaluation algorithm that operates on a query plan which is compiled with topology pruning and interface minimization. The effectiveness of the optimization techniques is demonstrated by a prototype implementation, which uses an off-the-shelf SAT solver and shows encouraging experimental results.

### Citations

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(Show Context)
Citation Context ...L may be such that KBL is the set of answer set programs over a (propositional) alphabet A, BSL = 2 A contains all subsets of atoms, and ACCL assigns each kb ∈ KBL the set of all its answer sets (see =-=Gelfond and Lifschitz, 1991-=-, for details). Definition 1 A multi-context system (MCS) M = (C1, . . . , Cn) consists of contexts Ci = (Li, kbi, bri), 1 ≤ i ≤ n, where Li = (KBi, BSi, ACCi) is a logic, kbi ∈ KBi is a knowledge bas... |

351 | Notes on formalizing context
- McCarthy
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(Show Context)
Citation Context ...gent systems. There, each context may model the beliefs of an agent while the bridge rules model an agent’s perception of the environment, i.e., other contexts. Among the various MCS proposals (e.g., =-=McCarthy, 1993-=-, Giunchiglia and Serafini, 1994, and Ghidini and Giunchiglia, 2001), the general MCS framework of Brewka and Eiter (2007) is of special interest, as it generalizes previous approaches in contextual r... |

200 | Y.: ASSAT: Computing Answer Sets of a Logic Program by SAT Solvers
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Citation Context ...he partial equilibria starting from a context. • To incorporate bridge rules into the local evaluations, we define loop formulas, inspired by similar compilations of logic programs into SAT theories (=-=Lin and Zhao 2004-=-). They may be added to belief sets abstractly represented as SAT theories to obtain a uniform encoding. We pursue this in particular for MCS whose contexts are answer set programs; notably, cycles in... |

188 | Local models semantics, or contextual reasoning = locality + compatibility
- Ghidini, Giunchiglia
- 2001
(Show Context)
Citation Context ...efs of an agent while the bridge rules model an agent’s perception of the environment, i.e., other contexts. Among the various MCS proposals (e.g., McCarthy, 1993, Giunchiglia and Serafini, 1994, and =-=Ghidini and Giunchiglia, 2001-=-), the general MCS framework of Brewka and Eiter (2007) is of special interest, as it generalizes previous approaches in contextual reasoning and allows for heterogeneous and nonmonotonic MCS, i.e., w... |

179 | Multilanguage hierarchical logics, or: how we can do without modal logics
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(Show Context)
Citation Context ...ere, each context may model the beliefs of an agent while the bridge rules model an agent’s perception of the environment, i.e., other contexts. Among the various MCS proposals (e.g., McCarthy, 1993, =-=Giunchiglia and Serafini, 1994-=-, and Ghidini and Giunchiglia, 2001), the general MCS framework of Brewka and Eiter (2007) is of special interest, as it generalizes previous approaches in contextual reasoning and allows for heteroge... |

125 | Conflict-driven answer set solving
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Citation Context ... Pentium Core2 Duo 2.53GHz processor with 4GB RAM. We compare response times of DMCSOPT to DMCS. We used the development version of clasp (2010-01-31) as a SAT solver, which accepts DIMACS CNF input (=-=Gebser et al. 2007-=-). Specifically, all generated instantiations of multicontext systems have contexts with ASP logics. We use the translation defined in (Dao-Tran et al. 2010) to create SAT instances at contexts Ck and... |

118 |
Graph Theory
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- 2008
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Citation Context ...ponents. The latter form a tree representation of the MCS, and we can apply edge removal techniques in each component. In the following, we will use standard terminology from graph theory (see, e.g., =-=Bondy and Murty, 2008-=-) and assume that graphs are directed by default. For any graph G and set S ⊆ E(G) of edges, we denote by G\S the subgraph of G that has no edges from S. For a vertex v ∈ V (G), we denote by G\v the s... |

65 | A uniform integration of higher-order reasoning and external evaluations in answer set programming
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(Show Context)
Citation Context ...states of such a management system. Moreover, multi-context systems allow to model bidirectional input and output for external knowledge sources that goes beyond the import interface of HEX-programs (=-=Eiter et al. 2005-=-). Roughly, MCS can be divided into monotonic and nonmonotonic MCS. Examples of the former kind are (McCarthy 1993; Giunchiglia and Serafini 1994; Ghidini and Giunchiglia 2001) (see also (Serafini and... |

63 | Drago: Distributed reasoning architecture for the semantic web
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(Show Context)
Citation Context ...rt from being not truly distributed, an extension to nonmonotonic MCS is non-obvious; also, no caching was used. Distributed tableaux algorithms for reasoning in distributed ontologies are defined in =-=[14, 15]-=-. They can be used to decide consistency of distributed description logic knowledge bases, provided that the distributed TBox is acyclic. The DRAGO system is an implementation of this approach. The au... |

45 | Loop formulas for disjunctive logic programs - Lee, Lifschitz |

44 |
Distributed Reasoning in a Peer-to-Peer Setting: Application to the Semantic
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- 2006
(Show Context)
Citation Context ...n be used to decide consistency of distributed description logic knowledge bases, provided that the distributed TBox is acyclic. The DRAGO system is an implementation of this approach. The authors of =-=[1]-=- presented a framework of peer-to-peer inference systems. Local theories of propositional clause sets share atoms, and a special algorithm can be usedfor consequence finding. As we pursue the dual pr... |

44 | Equilibria in heterogeneous nonmonotonic multi-context systems
- Brewka, Eiter
- 2007
(Show Context)
Citation Context ... This demonstrates that our optimization techniques are effective and bring MCS closer to applications. Preliminaries We recall some basic notions of heterogeneous nonmonotonic multi-context systems (=-=Brewka and Eiter 2007-=-). A logic is, viewed abstractly, a tuple L = (KBL, BSL, ACCL), where • KBL is a set of well-formed knowledge bases, each being a set (of formulas), • BSL is a set of possible belief sets, each being ... |

35 | Why are there so many loop formulas - Lifschitz, Razborov - 2003 |

34 | Networked Graphs: A Declarative Mechanism for SPARQL - Schenk, Staab - 2008 |

31 | Aspects of distributed and modular ontology reasoning
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- 2005
(Show Context)
Citation Context ...rt from being not truly distributed, an extension to nonmonotonic MCS is non-obvious; also, no caching was used. Distributed tableaux algorithms for reasoning in distributed ontologies are defined in =-=[14, 15]-=-. They can be used to decide consistency of distributed description logic knowledge bases, provided that the distributed TBox is acyclic. The DRAGO system is an implementation of this approach. The au... |

27 | S.: Modularity Aspects of Disjunctive Stable Models
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(Show Context)
Citation Context ...M ′ , we obtain the equilibria of M. Theorem 5 may be generalized to contexts with extensions of ASP logics that have loop formula characterizations, like those in (Ferraris, Lee, and Lifschitz 2006; =-=Janhunen et al. 2009-=-). Furthermore, we have developed such a characterization for modular logic programs (DaoTran et al. 2009), which feature modules akin to imperative programs and have increased expressiveness. Note th... |

23 |
formal theories of context in
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- 2004
(Show Context)
Citation Context ... et al. 2005). Roughly, MCS can be divided into monotonic and nonmonotonic MCS. Examples of the former kind are (McCarthy 1993; Giunchiglia and Serafini 1994; Ghidini and Giunchiglia 2001) (see also (=-=Serafini and Bouquet 2004-=-) for a comparison of these approaches), while (Brewka, Roelofsen, and Serafini 2007; Brewka and Eiter 2007) are nonmonotonic MCS. The general MCS framework of Brewka and Eiter (2007) is of special in... |

21 | A generalization of the Lin-Zhao theorem - Ferraris, Lee, et al. - 2006 |

16 | Contextual default reasoning - Brewka, Roelofsen, et al. - 2007 |

14 | The distributed breakout algorithms - Hirayama, Yokoo - 2005 |

12 | Modular nonmonotonic logic programming revisited - Dao-Tran, Eiter, et al. - 2009 |

7 | Many hands make light work: localized satisfiability for multicontext systems
- Roelofsen, Serafini, et al.
(Show Context)
Citation Context ... a small amount of models have to be shipped. In B↔ we can see that already small instances produce many models and the price is that the network is under heavy load. 6 Related Work and Conclusion In =-=[13]-=-, the authors described evaluation of monotone MCS with classical theories using SAT solvers for the contexts in parallel. They used a (co-inductive) fixpoint strategy to check MCS satisfiability, whe... |

6 | Finding explanations of inconsistency in multi-context systems
- Eiter, Fink, et al.
- 2010
(Show Context)
Citation Context ...t’s perception of the environment, i.e., other contexts. Data integration from different knowledge sources is in general a driving force for MCS applications. One possibility is the example given in (=-=Eiter et al. 2010-=-) for finding explanations of inconsistencies in MCS. Another real life application is project costs and time management, which typically ∗ This research has been supported by the Austrian Science Fun... |

4 |
P.: Strategies for contextual reasoning with conflicts in Ambient Intelligence
- Bikakis, Antoniou, et al.
- 2011
(Show Context)
Citation Context ...nal clause sets share atoms, and a special algorithm can be usedfor consequence finding. As we pursue the dual problem of model building, application for our needs is not straightforward. Similarly, =-=[3]-=- developed a distributed algorithm for query evaluation in a MCS framework based on defeasible logic. Here, contexts are built using defeasible rules, and the algorithm can determine for a given liter... |

3 |
Backtracking through biconnected components of a constraint graph
- Baget, Tognetti
- 2001
(Show Context)
Citation Context ...s (not) a logical conclusion of the MCS, or whether it cannot be proved that l is a logical conclusion. Again, applying this approach to model building is not easy. Biconnected components are used in =-=[2]-=- to decompose constraint satisfaction problems. The decomposition is used to localize the computation of a single solution in the components of undirected constraint graphs. Likened to our approach, w... |

2 |
Logic programming with social features. Theo. Pract. Logic Progr
- Buccafurri, Caminiti
- 2008
(Show Context)
Citation Context ... agreement. Ms. 1 decides which option to take based on the information she gets from Mr. 2 and Mr. 3. Similar scenarios have already been investigated in the realm of multi-agent systems (see, e.g., =-=[6]-=- on social answer set programming). We do not aim at introducing a new semantics for such scenarios; our example is meant to be a plain showcase application of MCS. We stress that MCS have potential a... |

1 | Distributed Defeasible Reasoning in Multi-Context Systems - Bikakis, Antoniou - 2008 |