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## Visual Multiset Rewriting: Applications to Diagram Parsing and Reasoning.

Bottoni, Paolo;
Meyer, Bernd;
Presicce, Francesco Parisi
In:
*LNCS 2235:*, pages 45-pp.
December 2001.

Abstract:
Diagrammatic notations, such as Venn diagrams, Petri-Nets and finite state
automata, are in common use in mathematics and computer science. While the
semantic domain of such systems is usually well formalized, the visual
notation itself seldom is, so that they cannot be used as valid devices of
formal reasoning. A complete formalization of such notations requires the
construction of diagram systems with rigorously defined syntax and
semantics. We discuss how diagram specification can be interpreted as
multiset rewriting and, based on this, how it can be formalized in linear
logic. We discuss the power of our approach through an illustration of its
possible extension with reflective capabilities to manage negative
conditions, and through the identification of a class of diagrammatic
transformations which can be directly expressed in our framework.

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