New PDF release: Graph theory and Feynman integrals

By Nakanishi N.

ISBN-10: 0677029500

ISBN-13: 9780677029504

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While unification has been studied for a long time, many divergent techniques exist for accomplishing unification in different domains. Generalization, or anti-unification, is the dual function to unification. The Most General Unifier of two Conceptual Graphs is the most general graph which is more specific than the two graphs under consideration. In Chapter Five, it will be shown that a complete set of tools for Conceptual Graphs will include not only unification and Most General Unifier, but also constraint satisfaction, generalization and all of the canonical formation rules.

The external join rule can be used to "glue together" two graphs in Willems' sense, in that a few compatible concepts and relations can be joined together from two graphs to make a larger, joined graph. Willems then attempts to create a truly unified graph by finding the least upper bound of the two graphs that will validate this newly joined graph [Willems 1995]. As discussed in Chapter One, in the true sense of unification simply joining a few concepts and relations does not guarantee the conjunction of the knowledge contained in the graphs.

Biirckert describes a framework for general constraint resolution theorem proving [Biirckert 1991]. ). His work with constraints proposed a method to handle clauses whose variables are bound by restricted quantifiers. In Eisinger and Ohlbach's discussion of intelligent behavior in deduction systems based on resolution [Eisinger and Ohlbach 1993], the importance of defining a resolution technique is made clear. They describe the logic of a system as the syntax and semantics of a deduction system, which includes the ideas of entailment and the formalization of 42 Reasoning and Unification over Conceptual Graphs the intuitive relationship between statements.

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Graph theory and Feynman integrals by Nakanishi N.

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