M. Chein and M.-L. Mugnier. Conceptual graphs are also graphs. Technical report, LIRMM, Universite Montpellier II, 1995. Rapport de Recherche 95003.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....CGs to facilitate consistency checking in our work. CGs can be mapped to and from predicate calculus and many forms of logic, such as propositional logic and modal logic [6] 21] Additionally, there have been some attempts to perform CG reasoning based on the graph models of CGs themselves [22][23] For the sake of simplicity, we apply the transformation of CGs into first order predicate logic to perform reasoning procedure in our framework. As it is not our intention to explain the notion of CGs at length and we rather intend to demonstrate how the graphs are applied in our work, ....

Chein M., and Mugnier M. L., "Conceptual Graphs are Also Graphs", LIRMM (CNRS and Universit Montpellier II), France, Report Number: RRI CHIEN 95, 1995.

....for obtaining: i) graph derivations, and (ii) a projection algorithm. Notwithstanding the logical nature of CGs, most of the research work on conceptual graphs has focused on graph theory and graph algorithms [3, 4, 5, 6] which have been considered as the core of conceptual graph theory [7]. Nevertheless, there have been some attempts to provide a sound and complete graph derivation algorithm with respect to the FOL semantics and graph derivation [8, 9, 10, 11] As for the existential fragment, our characterization is different from the previous proposals. First, we give a proper ....

....the lack of a unique characterization of CGs in their general form has led to the belief that a CG is a formalism somehow different from the logical one, or possessing some complex logical characterization. For instance, many conceptual graph operators or extra notions, such as the maximal join [7], have been introduced without background semantics or explanation. Our completeness results bring about other consequences. The logical deduction of the theorem prover automatically finds out which graph rules are needed and even their right application order in the graph derivation. Up to now ....

Chein, M. and Mugnier, M. L. (1995) Conceptual Graphs are also Graphs. Research report 95-004, LIRMM.

....standard models. In particular, this allows us to describe the infimum and supremum of concept graphs by join and intersection in the standard model. The infimum of the two equivalence classes of the concept graphs G 1 and G 2 is the equivalence class of the juxtaposition G 1 Phi G 2 (cf. [CM95]) It is not difficult to see that the standard model of this juxtaposition is exactly the standard model one obtains by joining the standard models : for (K G1 PhiG 2 ; G1 PhiG 2 ) we have I G1 PhiG 2 = I G1 [ I G2 and G1 PhiG 2 R (R) G1 R (R) G2 R (R) for all R ....

Chein, M., Mugnier, M.-L.: Conceptual Graphs are also Graphs. Rapport de Recherche 95003, LIRMM, Universit'e Montpellier II (1995)

....logic to having a formula C(a) C(a) in the document index. It is obvious that the latter is equivalent to C(a) which is its normalized form. The conceptual graphs community already agreed that the only form of graphs for which the formalism is sound and complete is the normalized form of graphs [20, 21]. Following this idea, we consider that a conceptual graph must be given in a normalized form. We call this form the standard logical form of graphs. Definition 6.1 (Standard Logical Form) A graph g of indefinite structure can be transformed into a graph h in standard logical form by joining the ....

....group(w 2 d i ) can be obtained from group(w 6 d i ) by restricting [C 11 ] to [C 11 :a] so they should be joined into one group. The reader will note that such a constraint imposed on the form of the graphs is less strong than those implied by the use of normalized graphs, such as those in [20, 21]. An interesting point arises here, and it is related to the complexity of our retrieval algorithm for graphs in standard logical form. As a joined group cannot have multiple occurrences in the same graph, we have t d = 1 in the factor t t q d in the complexity formula, so our retrieval ....

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M. Chein and M.L. Mugnier. Conceptual graphs are also graphs. Research report 95-004, LIRMM, January 1995.

....implementation of conceptual graph processors, we think that the graph grammars approach is a practible and powerful one to deal with graph reasoning. In this paper, we focuse on the canonical derivation rules, as they are the primitives of conceptual graph operations, such as the graph projection [23]. Given our algebraic model to express conceptual graphs, we have a bridge between the conceptual graph framework and the graph grammars eld, hence a way to re ne and extended the conceptual graph theory. Graph grammars principles, say the pushout vision of the rule applications, stand as a ....

M. Chein and M.L. Mugnier. Conceptual graphs are also graphs. Technical Report RRI-Chein-95, LIRMM, ftp : ==ftp:lirmm:fr=pub=LIRMM=papers=1995=RRI \Gamma Chein \Gamma 95:ps:gz, 1995.

....partial orders on types in the support S. But it is not complete, in the sense that it does not allow to compute all logical deductions (see Figure 1) Let us propose another set of rules, which ensures the desirable soundness and completeness properties (this set has originally been de ned in [CM95]; here, some operation names have been changed in order to avoid confusion with [Sow99] There are four specialization operations and four inverse operations, called generalization operations. In both cases, the rst operation produces a graph equivalent to the original graph (where equivalent ....

....is not equivalent to one of its subgraphs. Then any equivalence class for contains a unique irredundant graph (up to isomorphism) moreover this graph is the smallest graph of the equivalence class 3. The restriction of to irredundant graphs is a lattice. Proof. See [CM92] for property 2 and [CM95] for property 3. 1.4 Soundness and completeness of graph operations The semantic assigns a rst order formula (G) to each graph G [Sow84] G) is a positive, conjunctive and existentially closed formula. And to a support S is assigned a set of formulas, S) which corresponds to the ....

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M. Chein and M.L. Mugnier. Conceptual Graphs are also Graphs. Research Report 95-004, LIRMM, Jan. 1995. 17 pages.

....5. 2 The Framework 2.1 Rules By simple conceptual graphs (CGs) we mean non nested conceptual graphs, in particular without negation (as defined in [Sow84] Chapter III) But we do not impose the CGs be connected. This choice proved to be convenient for some definitions and properties [MC96] CM95] Notably, it allows to consider a set of connected CGs as one CG. It is a technical choice, without semantic implications. Both viewpoints are coherent with the following intuitive semantics: if graphs G 1 and G 2 are asserted, then the graph G 1 G 2 is asserted (where denotes the disjoint ....

M. Chein and M.L. Mugnier. Conceptual graphs are also graphs. Research Report 95-004, LIRMM, Jan. 1995. 17 pages.

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M. Chein and M.-L. Mugnier. Conceptual graphs are also graphs. Technical report, LIRMM, Universite Montpellier II, 1995. Rapport de Recherche 95003.

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