## Nested Graphs: A Graph-based Knowledge Representation Model with FOL Semantics (1998)

Venue: | PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON KNOWLEDGE REPRESENTATION (KR'98 |

Citations: | 23 - 5 self |

### BibTeX

@INPROCEEDINGS{Chein98nestedgraphs:,

author = {M. Chein and M.L. Mugnier and G. Simonet},

title = {Nested Graphs: A Graph-based Knowledge Representation Model with FOL Semantics},

booktitle = {PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON KNOWLEDGE REPRESENTATION (KR'98},

year = {1998},

pages = {524--534},

publisher = {Morgan Kaufmann}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present a graph-based KR model issued from Sowa's conceptual graphs but studied and developed with a specific approach. Formal objects are kinds of labelled graphs, which may be simple graphs or nested graphs. The fundamental notion for doing reasonings, called projection (or subsumption), is a kind of labelled graph morphism. Thus, we propose a graphical KR model, where "graphical" is used in the sense of [Sch91], i.e. a model that "uses graph-theoretic notions in an essential and nontrivial way". Indeed, morphism, which is the fundamental notion for any structure, is at the core of our theory. We define two first order logic semantics, which correspond to different intuitive semantics, and prove in both cases that projection is sound and complete with respect to deduction.

### Citations

1539 |
Foundations of Databases
- Abiteboul, Hull, et al.
- 1995
(Show Context)
Citation Context ...::: r n belong to R, ans is not in R, u and u 1 ::: un are tuples of terms (variables or constants of dom), and each variable of u occurs at least once in u 1 ::: un . We follow here the notations of =-=[AHV95]-=-. Now, let S = (TC ; TR ; I) be a support built as follows. TC is restricted to a single type. TR is equal to R [ Ans, where Ans = fans k j ks1g and k stands for the arity of ans. I is equal to dom. E... |

948 | Temporal constraint networks
- Dechter, Meiri, et al.
- 1991
(Show Context)
Citation Context ...G is a tree [Mug95] (or more generally when G has a bounded treewidth). Also note that there is a "strong" equivalence between the subsumption checking problem and the constraint satisfactio=-=n problem [Dec92]-=-, allowing direct transfer of efficient algorithms from one problem to the other [MC96]. Projection is sound and complete with respect to FOL, i.e.: given two SGs G and H defined on S, if G subsumes H... |

351 | Notes on formalizing context
- McCarthy
- 1993
(Show Context)
Citation Context ...s a term and second argument is a formula. \Phi(G) contains the atom descr(e; \Phi(D)), where e is the term associated with c. This logical semantics is similar to the logical semantics of context of =-=[McC93]-=-, [Guh91], with descr playing the same role as the ist predicate. [GW96] defines nested conceptual graphs where concept labels have three fields like ours. But these kinds of nested graphs include nei... |

191 |
Contexts: A Formalization and Some Applications
- Guha
- 1991
(Show Context)
Citation Context ...and second argument is a formula. \Phi(G) contains the atom descr(e; \Phi(D)), where e is the term associated with c. This logical semantics is similar to the logical semantics of context of [McC93], =-=[Guh91]-=-, with descr playing the same role as the ist predicate. [GW96] defines nested conceptual graphs where concept labels have three fields like ours. But these kinds of nested graphs include neither non-... |

102 | Propositional logic of context
- Buvac, Mason
- 1993
(Show Context)
Citation Context ...tial positive conjunctive FOL formulas). But none of the logical semantics proposed in this paper seem to be close to one of the logical formalizations of contextual reasoning (e.g. [McC93], [Guh91], =-=[Buv96]). However-=-, more in-depth comparisons will now have to be done. 8 Conclusion In this paper, a graph-based model for hierarchical structured knowledge, "nested graphs", is presented. Projection --- a l... |

77 |
Indifference Graphs
- Roberts
- 1969
(Show Context)
Citation Context ...ts of this model have two mathematical bases: logic and graph theory. Emphasizing one or the other leads to different research lines. The former, a continuation of Peirce's work on existential graphs =-=[Rob92], investig-=-ates CGs as a diagrammaticssystem of logic (for instance [Sow94] [vdB94]). The later develops CG as a graphical knowledge representation model, where "graphical" is used in the sense of [Sch... |

55 |
Conceptual graphs: fundamental notions. Revue dé Intelligence Artificielle
- Chein, Mugnier
- 1992
(Show Context)
Citation Context ...a graphical knowledge representation model, where "graphical" is used in the sense of [Sch91], i.e. a model that "uses graph-theoretic notions in an essential and nontrivial way" (=-=for instance [LE91] [CM92]-=-). Our work is concerned with this second viewpoint. The basic notion is that of a simple conceptual graph (SG). A SG is a labelled bipartite graph where nodes of one class represent entities, nodes o... |

34 |
Encoding knowledge in partitioned networks
- Hendrix
- 1979
(Show Context)
Citation Context ...here formulas do not belong to classical FOL, and a Gentzen system is defined, which is sound and complete for projection. At first glance, there is some likeness between NGs and partitioned networks =-=[Hen79]-=-. But these two models actually only share a very general notion of grouping. NGs have been introduced for representing hierarchical knowledge and for doing reasonings respecting the levels. In partit... |

27 | Multi-level hierarchical retrieval
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- 1992
(Show Context)
Citation Context ... CG as a graphical knowledge representation model, where "graphical" is used in the sense of [Sch91], i.e. a model that "uses graph-theoretic notions in an essential and nontrivial way&=-=quot; (for instance [LE91]-=- [CM92]). Our work is concerned with this second viewpoint. The basic notion is that of a simple conceptual graph (SG). A SG is a labelled bipartite graph where nodes of one class represent entities, ... |

22 |
Conceptual graphs for a database interface
- Sowa
- 1976
(Show Context)
Citation Context ...d for representing knowledge. In artificial intelligence, they have been investigated under the name of semantic networks (see for instance [Leh92] for an overview of recent research in this domain). =-=[Sow76]-=- proposed a model of this family, named conceptual graphs (CGs), which was developed in [Sow84]. The formal aspects of this model have two mathematical bases: logic and graph theory. Emphasizing one o... |

17 |
Représenter des connaissances et raisonner avec des graphes », Revue d'intelligence artificielle
- Mugnier, Chein
- 1996
(Show Context)
Citation Context ...here is a "strong" equivalence between the subsumption checking problem and the constraint satisfaction problem [Dec92], allowing direct transfer of efficient algorithms from one problem to =-=the other [MC96]-=-. Projection is sound and complete with respect to FOL, i.e.: given two SGs G and H defined on S, if G subsumes H then \Phi(S); \Phi(H) ffl \Phi(G) (soundness [Sow84]); conversely, if H is in normal f... |

16 | Positive Nested Conceptual Graphs
- Chein, Mugnier
(Show Context)
Citation Context ...Simple(H) and conversely). We conclude with the soundness and completeness result on SG ref s. 2 7 Related works In the conceptual graph domain, several kinds of CGs with complex nodes have been used =-=[CM97]-=-. Most of them follow the formalism proposed by [Sow94]. Briefly, a specific relation type called description and a special concept type called Graph are introduced. Concept nodes of type Graph may ha... |

11 |
CoGITo: une plate-forme de développement de logiciels sur les graphes conceptuels
- Haemmerlé
- 1995
(Show Context)
Citation Context ... with respect to deduction in both cases. We are developing a workbench, called CoGITo, for building knowledge-based applications, in which every piece of knowledge is described by nested graphs (see =-=[Hae95]-=- [CCC + 97] for a previous version based on simple graphs). This workbench forms the skeleton of a modelization language for an industrial application we are currently involved in [BBV97]. Acknowledge... |

11 | On Generalization / Specialization for Conceptual Graphs
- Mugnier
- 1995
(Show Context)
Citation Context ... GsH (G subsumes H) if there is a projection from G to H . This relation is a preorder, but not an order. Subsumption checking is an NP-complete problem [CM92]. It becomes polynomial when G is a tree =-=[Mug95] (or more -=-generally when G has a bounded treewidth). Also note that there is a "strong" equivalence between the subsumption checking problem and the constraint satisfaction problem [Dec92], allowing d... |

11 |
On generalization/specialization for conceptual graphs
- Mugnier
- 1995
(Show Context)
Citation Context ...: G H (G subsumes H) if there is a projection from G to H. This relation is a preorder, but not an order. Subsumption checking is an NP-complete problem [CM92]. It becomes polynomial when G is a tree =-=[Mug95]-=- (or more generally when G has a bounded treewidth). Also note that there is a \strong" equivalence between the subsumption checking problem and the constraint satisfaction problem [Dec92], allowing d... |

10 |
Logical foundations for representing object-oriented systems
- Sowa
- 1993
(Show Context)
Citation Context ...ess and completeness result on SG ref s. 2 7 Related works In the conceptual graph domain, several kinds of CGs with complex nodes have been used [CM97]. Most of them follow the formalism proposed by =-=[Sow94]-=-. Briefly, a specific relation type called description and a special concept type called Graph are introduced. Concept nodes of type Graph may have a graph as referent. Adding an internal information ... |

7 |
A Logic for Nested Graphs
- Preller, Mugnier, et al.
- 1998
(Show Context)
Citation Context ...non-trivial graph-theoretic operations (such as projection) for reasoning purposes, nor FOL logical semantics. Another logical semantics for nested graphs, but without co-reference links, is given in =-=[PMC95]-=-. A specific logical language is proposed, where formulas do not belong to classical FOL, and a Gentzen system is defined, which is sound and complete for projection. At first glance, there is some li... |

6 |
Modeling and simulating human behaviors with conceptual graphs
- Bos, Botella, et al.
- 1997
(Show Context)
Citation Context ...e are currently involved in. In this application, NGs are used to represent and simulate the required behavior of human agents in case of emergency situations, for instance a fire in a chemical plant =-=[BBV97]-=-. This behavior is described by NGs which represent situations, pre-conditions and postconditions of actions to be performed, each of these elements being themselves described by NGs. Knowledge is str... |

4 |
Quanti cational Logic of Context
- Buvac
- 1996
(Show Context)
Citation Context ...tial positive conjunctive FOL formulas). But none of the logical semantics proposed in this paper seem to be close to one of the logical formalizations of contextual reasoning (e.g. [McC93], [Guh91], =-=[Buv96]-=-). However, more in-depth comparisons will now have to be done. 8 Conclusion In this paper, a graph-based model for hierarchical structured knowledge, \nested graphs", is presented. Projection | a lab... |

3 |
Semantic Networks are in the eye of the Beholder
- Schubert
- 1991
(Show Context)
Citation Context ...he fundamental notion for doing reasonings, called projection (or subsumption), is a kind of labelled graph morphism. Thus, we propose a graphical KR model, where "graphical " is used in the=-= sense of [Sch91], i.e. a m-=-odel that "uses graph-theoretic notions in an essential and nontrivial way". Indeed, morphism, which is the fundamental notion for any structure, is at the core of our theory. We define two ... |

2 |
Computational Situation Theory in the Conceptual Graph Language
- Ghosh, Wuwongse
- 1996
(Show Context)
Citation Context ...r(e; \Phi(D)), where e is the term associated with c. This logical semantics is similar to the logical semantics of context of [McC93], [Guh91], with descr playing the same role as the ist predicate. =-=[GW96]-=- defines nested conceptual graphs where concept labels have three fields like ours. But these kinds of nested graphs include neither non-trivial graph-theoretic operations (such as projection) for rea... |

1 |
Une autre s'emantique logique pour les graphes emboit'es
- Simonet
- 1996
(Show Context)
Citation Context ... A(G) into K. Projection is sound and complete with respect to \Psi. Theorem 3 Let G and H be two NG ref s. G subsumes H iff \Psi(S); \Psi(H) j= \Psi(G). Sketch of proof: A detailed proof is given in =-=[Sim96a]-=-, similar to that of Theorem 2 concerning \Phi. A more intuitive one is given here, which would not be available for \Phi, as the SG ref Simple(H) defined below is not in normal form. Let S 0 be the s... |

1 |
Une s'emantique logique pour les graphes emboit'es
- Simonet
- 1996
(Show Context)
Citation Context ... 1 , 'K is a projection from K to ' 0 (K), 3. 8(J; c)K 2 U 1 , (' 0 (J); ' J (c))' 0 (K) 2 U 2 . For all NGs G and H , there is a projection from G to H iff there is an A-projection from A(G) to A(H) =-=[Sim96b]-=-. As in SGs, several individual concept nodes with the same marker may appear in a NG, and it may be useful to express that several generic concept nodes represent the same entity. Note that such node... |

1 |
Modal Logics for Conceptual Graphs III
- Berg
- 1994
(Show Context)
Citation Context ...one or the other leads to different research lines. The former, a continuation of Peirce's work on existential graphs [Rob92], investigates CGs as a diagrammaticssystem of logic (for instance [Sow94] =-=[vdB94]). The later de-=-velops CG as a graphical knowledge representation model, where "graphical" is used in the sense of [Sch91], i.e. a model that "uses graph-theoretic notions in an essential and nontrivia... |

1 | The COnceptual Graphs at LIRMM Project - Carbonneill, Chein, et al. - 1997 |