An introduction to abstract mathematical systems by David M. Burton

By David M. Burton

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Short Introduction to Conceptual Graphs . . . . . . . . . . . . . . . Conceptual Graphs from a Formal Point of View . . . . . . . . . . . The General Approach for Formal Logic with CGs . . . . . . . . . . Different Forms of Conceptual Graphs . . . . . . . . . . . . . . . . . Further Literature . . . . . . . . . . . . . . . . . . . . . . . .

For example, if the following graph on the left is a well-formed CG (which is not clear from the definition of CGs), it should be provably equivalent to the CG on the right: DOG: * DOG: * As identity is a transitive relation, the next two graphs should be provably equivalent, too: DOG: * : Snoopy PET: * and DOG: * : Snoopy Finally, given the graph BIG_THING:morning star BIG_THING:evening star PLANET: morning star PLANET: evening star visible in the morning visible in the evening it should be possible to derive PLANET: morning star visible in the evening PET: * 28 Conceptual Structures in Practice It is difficult to decide from Sowa’s definition of the calculus whether these derivations are possible.

6 The next question of the algorithm is whether the implication {Ontology} → {OWL,RDF,Pellet,Racer,KAON2} is valid. ” After adding a few more papers with various combinations of keywords, the questions of the algorithm quickly become more targeted, and implications such as {Pellet} → {OWL} are found valid. This rules out further questions, and after adding 17 objects the exploration is finished. Note that the number of necessary exploration steps is influenced by the counterexamples that are chosen.

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