## A combinatorial approach to conceptual graph projection checking (2004)

Venue: | In Proc. of the 24th Int’l Conf. of the Brit. Comp. Society’s Spec. Group on Artif. Intell. (AI’2004 |

Citations: | 6 - 3 self |

### BibTeX

@INPROCEEDINGS{Croitoru04acombinatorial,

author = {Madalina Croitoru and Ernesto Compatangelo},

title = {A combinatorial approach to conceptual graph projection checking},

booktitle = {In Proc. of the 24th Int’l Conf. of the Brit. Comp. Society’s Spec. Group on Artif. Intell. (AI’2004},

year = {2004},

pages = {130--143},

publisher = {Springer}

}

### OpenURL

### Abstract

We exploit the combinatorial structure of conceptual graphs in order to obtain better execution times when computing projection, which is a core generalisation-specialisation relation over conceptual graphs. We show how the problem of finding this relation can be translated into the Maximum Clique problem. Consequently, approximation techniques developed for the Maximum Clique problem can be used to compute projection in conceptual graphs. We show that there are “simple queries” which can be answered quickly, thus providing efficient reasoning support in a knowledge management environment based on conceptual graphs. 1

### Citations

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Citation Context ...d on semantic networks. They introduce a clear distinction between ontological and asserted knowledge, specifying it in a way that is both readable by humans and computationally tractable by machines =-=[16]-=-. Graph-based formalisms (e.g. CGs) can be successfully applied to solve relevant knowledge management problems such as modelling the articulation of ontologies and representing links between differen... |

138 | A graph-oriented model for articulation of ontology interdependencies
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Citation Context ...isms (e.g. CGs) can be successfully applied to solve relevant knowledge management problems such as modelling the articulation of ontologies and representing links between different ontology versions =-=[11]-=-. As deriving relationships (e.g. subsumption) between linked structures in articulated or versioned ontologies greatly improves multi-ontology management [14], devising a set of inferences that opera... |

29 | Hypertree decompositions: A survey
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Citation Context ... graphs G and H is an NP-complete problem [5, 2]. However, it has been shown that this is polynomially equivalent to other problems, such as (i) conjunctive query containment [4, 15] and query output =-=[8]-=- in databases, (ii) constraint satisfaction [15] in combinatorial optimisation, and clause subsumption [8] in knowledge representation and reasoning. Consequently, algorithms of exponential complexity... |

27 | Multi-level hierarchical retrieval
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Citation Context ... theory. The former combine First-Order Logic and Prolog mechanisms (e.g. resolution) in a reasoning tool [7]. Conversely, the latter translate the reasoning problem into a graph-homomorphism problem =-=[5, 10]-=-.sUnfortunately, deciding whether G ≥ H given two conceptual graphs G and H is an NP-complete problem [5, 2]. However, it has been shown that this is polynomially equivalent to other problems, such as... |

26 | Efficient retrieval from hierarchies of objects using lattice operations
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Citation Context ...ent”. Algorithms devised for computing projection in CGs are either based on logic or on graph theory. The former combine First-Order Logic and Prolog mechanisms (e.g. resolution) in a reasoning tool =-=[7]-=-. Conversely, the latter translate the reasoning problem into a graph-homomorphism problem [5, 10].sUnfortunately, deciding whether G ≥ H given two conceptual graphs G and H is an NP-complete problem ... |

24 |
Conceptual graph matching: A flexible algorithm and experiments
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Citation Context ...ders represented by the support. The time computational complexity of an efficient implementation of this step can be very important in certain applications and depends on the adopted data structures =-=[7, 13]-=-. Our algorithm is similar to the one used in building a jigsaw image by putting the jigsaw pieces together. Our algorithm takes a piece of the jigsaw and checks if it fits in the place we want to put... |

23 | G.: Nested Graphs: A Graph-Based Knowledge Representation Model with FOL Semantics
- Chein, Mugnier, et al.
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(Show Context)
Citation Context ... ≥ H given two conceptual graphs G and H is an NP-complete problem [5, 2]. However, it has been shown that this is polynomially equivalent to other problems, such as (i) conjunctive query containment =-=[4, 15]-=- and query output [8] in databases, (ii) constraint satisfaction [15] in combinatorial optimisation, and clause subsumption [8] in knowledge representation and reasoning. Consequently, algorithms of e... |

19 | Extensions of simple conceptual graphs: the complexity of rules and constraints
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(Show Context)
Citation Context .... Conversely, the latter translate the reasoning problem into a graph-homomorphism problem [5, 10].sUnfortunately, deciding whether G ≥ H given two conceptual graphs G and H is an NP-complete problem =-=[5, 2]-=-. However, it has been shown that this is polynomially equivalent to other problems, such as (i) conjunctive query containment [4, 15] and query output [8] in databases, (ii) constraint satisfaction [... |

15 | Ontology versioning as an element of an ontology-management framework
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Citation Context ...inks between different ontology versions [11]. As deriving relationships (e.g. subsumption) between linked structures in articulated or versioned ontologies greatly improves multi-ontology management =-=[14]-=-, devising a set of inferences that operate on CGs (thereby reasoning with these structures) is an important area of research. Reasoning with and about conceptual graphs, which is logically sound and ... |

14 | Tractable and Decidable Fragments of Conceptual Graphs
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(Show Context)
Citation Context ...n practical applications when the size of the graphs involved is not too large [4]. Extensive research has been done to improve the computational behaviour of algorithms for testing projection in CGs =-=[12, 9, 1]-=-. However, most research results have been influenced by the algorithms used to solve the above mentioned equivalent problems. In this paper, we show how the rich combinatorial structure of CGs can be... |

11 | On Generalization / Specialization for Conceptual Graphs
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(Show Context)
Citation Context ...g a set of inferences that operate on CGs (thereby reasoning with these structures) is an important area of research. Reasoning with and about conceptual graphs, which is logically sound and complete =-=[12]-=-, is based on a conceptual graph operation called projection. This is a labelled graph homomorphism which defines a generalisation-specialisation relation over conceptual graphs. A structure G is more... |

10 | A conceptual graph approach to conceptual schema integration
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(Show Context)
Citation Context ... theory. The former combine First-Order Logic and Prolog mechanisms (e.g. resolution) in a reasoning tool [7]. Conversely, the latter translate the reasoning problem into a graph-homomorphism problem =-=[5, 10]-=-.sUnfortunately, deciding whether G ≥ H given two conceptual graphs G and H is an NP-complete problem [5, 2]. However, it has been shown that this is polynomially equivalent to other problems, such as... |

5 |
A sound and complete CG proof procedure combining projections with analytic tableaux
- Kerdiles, Salvat
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(Show Context)
Citation Context ...n practical applications when the size of the graphs involved is not too large [4]. Extensive research has been done to improve the computational behaviour of algorithms for testing projection in CGs =-=[12, 9, 1]-=-. However, most research results have been influenced by the algorithms used to solve the above mentioned equivalent problems. In this paper, we show how the rich combinatorial structure of CGs can be... |

4 | On Conceptual Graph Projection
- Croitoru, Compatangelo
- 2004
(Show Context)
Citation Context ...roblem that has been investigated using graph homomorphism techniques [5, 2]. Unfortunately, the algorithms that have been devised so far are not exploiting the underlying conceptual graph properties =-=[6]-=-. In fact, results achieved so far do not intuitively provide the user with an understanding of how some of the derived polynomial reductions are connected with particular graph structures. Due to the... |

2 |
et al. The maximum clique problem
- Bomze
- 1999
(Show Context)
Citation Context ...) of conceptual graphs, which is the main contribution of this paper. Such a graph is based on the efficient translation of the problem about deciding whether G ≥ H into the well-known Maximum Clique =-=[3]-=- problem with a matching graph MG→H as input. This translation allows the approximation techniques developed for the Maximum Clique problem to be used in the projection of conceptual graphs. Moreover,... |

2 |
Projection in conceptual graphs and query containment in nr-Datalog
- Simonet, Chein, et al.
- 1998
(Show Context)
Citation Context ... ≥ H given two conceptual graphs G and H is an NP-complete problem [5, 2]. However, it has been shown that this is polynomially equivalent to other problems, such as (i) conjunctive query containment =-=[4, 15]-=- and query output [8] in databases, (ii) constraint satisfaction [15] in combinatorial optimisation, and clause subsumption [8] in knowledge representation and reasoning. Consequently, algorithms of e... |