By Michel Chein
This ebook reviews a graph-based wisdom illustration and reasoning formalism stemming from conceptual graphs, with a considerable concentrate on the computational properties.
Knowledge will be symbolically represented in lots of methods, and the authors have selected categorized graphs for his or her modeling and computational traits.
Key good points of the formalism provided will be summarized as follows:
• every kind of information (ontology, proof, ideas, constraints) are classified graphs, which offer an intuitive and simply comprehensible potential to symbolize knowledge,
• reasoning mechanisms are according to graph-theoretic operations and this enables, specifically, for linking the fundamental challenge to different basic difficulties in computing device technological know-how (e.g. constraint networks, conjunctive queries in databases),
• it's logically based, i.e. it has a logical semantics and the graph inference mechanisms are sound and complete,
• there are effective reasoning algorithms, hence knowledge-based platforms may be equipped to unravel genuine difficulties.
In a nutshell, the authors have tried to respond to, the subsequent question:
``how a ways is it attainable to move in wisdom illustration and reasoning by way of representing wisdom with graphs and reasoning with graph operations?''
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Extra resources for Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs
We will call them isolated concept nodes. But as soon as a BG contains a relation node, it contains at least one concept node, since there are no 0-ary relation symbols. Note also that, as there may be parallel edges, one has to distinguish between the number of edges incident to a relation node (this number is given by the arity of its type) and the number of its neighbors. For instance, the relation (wash) in Fig. 4 is incident to two edges but has only one neighbor. An important kind of BGs consists of BGs having a single relation node.
Then (G, ) is a lattice. Proof. The set of BGs over a given vocabulary admits a greatest element: the empty BG. Should we exclude the empty BG, there is still a greatest element, the BG restricted to one generic concept with universal type. Now let us consider G and H two (irredundant) BGs and their disjoint sum G + H. G and H subsume G + H. And every BG K which is subsumed both by G and H is also subsumed by G + H (the union of two homomorphisms from G to K and from H to K defines a homomorphism from G + H to K).
15 (Generalization operations). The five elementary generalization operations are: • Copy. Create a disjoint copy of a BG G. More precisely, given a BG G, copy(G) is a BG which is disjoint from G and isomorphic to G. • Relation duplicate. , the same neighbors in the same order. Two such relations of the same type and having exactly the same neighbors in the same order are called twin relations. • Increase. Increase the label of a node (concept or relation). More precisely, given a BG G, a node x of G, and a label L ≥ l(x) increase(G, x, L) is the BG obtained from G by increasing the label of x up to L, that is its type if x is a relation, its type and/or its marker if x is a concept.