Visual multiset rewriting: applications to diagram parsing and reasoning

Paolo Bottoni; Bernd Meyer; Francesco Parisi Presicce

doi:10.1007/3-540-45523-X_3

Visual multiset rewriting: applications to diagram parsing and reasoning

Paolo Bottoni, Bernd Meyer, Francesco Parisi Presicce

Research output: Chapter in Book/Report/Conference proceeding › Chapter (Book) › Research › peer-review

2 Citations (Scopus)

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.

Original language	English
Title of host publication	Multiset Processing
Subtitle of host publication	Mathematical, Computer Science, and Molecular Computing Points of View
Editors	Cristian S. Calude, Gheorghe Paun, Grzegorz Rozenberg, Arto Salomaa
Place of Publication	Berlin Germany
Publisher	Springer
Pages	45-67
Number of pages	23
ISBN (Print)	3540430636
DOIs	https://doi.org/10.1007/3-540-45523-X_3
Publication status	Published - 2001

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	2235
ISSN (Print)	0302-9743

Access to Document

10.1007/3-540-45523-X_3

Cite this

Bottoni, P., Meyer, B., & Presicce, F. P. (2001). Visual multiset rewriting: applications to diagram parsing and reasoning. In C. S. Calude, G. Paun, G. Rozenberg, & A. Salomaa (Eds.), Multiset Processing: Mathematical, Computer Science, and Molecular Computing Points of View (pp. 45-67). (Lecture Notes in Computer Science; Vol. 2235). Springer. https://doi.org/10.1007/3-540-45523-X_3

Bottoni, Paolo ; Meyer, Bernd ; Presicce, Francesco Parisi. / Visual multiset rewriting: applications to diagram parsing and reasoning. Multiset Processing: Mathematical, Computer Science, and Molecular Computing Points of View. editor / Cristian S. Calude ; Gheorghe Paun ; Grzegorz Rozenberg ; Arto Salomaa. Berlin Germany : Springer, 2001. pp. 45-67 (Lecture Notes in Computer Science).

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title = "Visual multiset rewriting: applications to diagram parsing and reasoning",

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.",

author = "Paolo Bottoni and Bernd Meyer and Presicce, {Francesco Parisi}",

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language = "English",

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series = "Lecture Notes in Computer Science",

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booktitle = "Multiset Processing",

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Bottoni, P, Meyer, B & Presicce, FP 2001, Visual multiset rewriting: applications to diagram parsing and reasoning. in CS Calude, G Paun, G Rozenberg & A Salomaa (eds), Multiset Processing: Mathematical, Computer Science, and Molecular Computing Points of View. Lecture Notes in Computer Science, vol. 2235, Springer, Berlin Germany, pp. 45-67. https://doi.org/10.1007/3-540-45523-X_3

Visual multiset rewriting: applications to diagram parsing and reasoning. / Bottoni, Paolo; Meyer, Bernd; Presicce, Francesco Parisi.

Multiset Processing: Mathematical, Computer Science, and Molecular Computing Points of View. ed. / Cristian S. Calude; Gheorghe Paun; Grzegorz Rozenberg; Arto Salomaa. Berlin Germany : Springer, 2001. p. 45-67 (Lecture Notes in Computer Science; Vol. 2235).

Research output: Chapter in Book/Report/Conference proceeding › Chapter (Book) › Research › peer-review

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AB - 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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Bottoni P, Meyer B, Presicce FP. Visual multiset rewriting: applications to diagram parsing and reasoning. In Calude CS, Paun G, Rozenberg G, Salomaa A, editors, Multiset Processing: Mathematical, Computer Science, and Molecular Computing Points of View. Berlin Germany: Springer. 2001. p. 45-67. (Lecture Notes in Computer Science). https://doi.org/10.1007/3-540-45523-X_3