Conceptual Graph Projection
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A Conceptual Graph Projection is a graph projection performed on a conceptual graph.
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- Counter-Example(s):
- See: Labelled Graph Homomorphism, Graph, Bipartite Graph, Projection Algorithm.
References
2008
- (Corbett, 2008) ⇒ Dan R. Corbett. (2008). “Graph-based Representation and Reasoning for Ontologies.” In: Studies in Computational Intelligence, Springer.
- QUOTE: A canonical graph is a conceptual graph which is in the closure of the conceptual graphs in its canonical basis under the following operations, called the canonical formation rules.
- 1. External join. Given two CGs G=(C,R, type, referent, arg1, ..., argm) and G'=(C',R', type', referent', arg'1, ..., arg'm) ...
- 2. Internal join. Given a CG G=(C,R, type, referent, arg1, ..., argm) ...
- 3. Restrict type. Given a CG G=(C,R, type, referent, arg1, ..., argm) ...
- 4. Restrict referent. Given a CG G=(C,R, type, referent, arg1, ..., argm) ...
- G=(C,R, type, referent, arg1, ..., argm) is said to have a projection into G'=(C',R', type', referent', arg'1, ..., arg'm). “G ≥ G, if and only if there is a pair of functions hC : C → C' and hR : R → R', called morphisms, such that:
- ∀c ∈ [math]\displaystyle{ C }[/math] and ∀c ∈ C, hC(c) = c only if type(c) ≥ type'(c), and referent(c) = ∗ or referent(c) = referent(c)
- ∀r ∈ [math]\displaystyle{ R }[/math] and ∀r ∈ R, hR(r) = r only if type(r) ≥ type'(r)
- ∀r ∈ [math]\displaystyle{ R }[/math], arg'i (hR(r)) = hC(argi(r))
- QUOTE: A canonical graph is a conceptual graph which is in the closure of the conceptual graphs in its canonical basis under the following operations, called the canonical formation rules.
2005
- (Croitoru & Compatanglo, 2005) Croitoru, M., & Compatangelo, E. (2005). A combinatorial approach to conceptual graph projection checking. In Research and Development in Intelligent Systems XXI (pp. 130-143). Springer London.
- (...). Reasoning with and about conceptual graphs, which is logically sound and complete, 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 general than a structure H (denoted as G ≥ H) if there is a projection from G to H. The “≥” symbol is interpreted as “greater than” in the sense that a “human” is more generic (i.e. broader) than a “student”. The algorithms devised for computing projection in CGs are either based on logic or on graph theory.