Peirce's diagrammatic logic in IF perspective

Ahti Veikko Pietarinen

doi:10.1007/978-3-540-25931-2_11

Peirce's diagrammatic logic in IF perspective

Ahti Veikko Pietarinen^*

^*Corresponding author for this work

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

9 Citations (Scopus)

Abstract

This paper presents a topological and game-theoretic extension of the system of Existential Graphs (EG). EGs were Charles S. Peirce's diagrammatic and iconic approach to logic. By scribing the graphs on assertion spaces of higher dimensions, this extension provides the precise iconic counterpart to the Independence-Friendly (IF) restatement of first-order logic suggested by Hintikka. Consequently, the IF extension completes the project that Peirce initiated: it breaks off from the linear confines of language by diagrams that extend to three dimensions, which Peirce predicted to be necessary and sufficient for the expression of all assertions. Apart from improved ways of performing conceptual modelling on natural-language expressions, this extension reveals the true proportions of Peirce's sign- and model-theoretic thinking in plunging into the notions of identity, negation, continuity and quantification.

Original language	English
Title of host publication	Diagrammatic Representation and Inference
Subtitle of host publication	Third International Conference, Diagrams 2004, Cambridge, UK, March 22-24, 2004, Proceedings
Editors	Alan F. Blackwell, Kim Marriott, Atsushi Shimojima
Publisher	Springer Berlin Heidelberg
Pages	97-111
Number of pages	15
Edition	1st
ISBN (Electronic)	9783540259312
ISBN (Print)	354021268X, 9783540212683
DOIs	https://doi.org/10.1007/978-3-540-25931-2_11
Publication status	Published - 12 Mar 2004
Event	3rd International Conference on Diagrammatic Representation and Inference, Diagrams 2004 - Cambridge, United Kingdom Duration: 22 Mar 2004 → 24 Mar 2004 https://link.springer.com/book/10.1007/b95854

Publication series

Name	Lecture Notes in Computer Science
Volume	2980
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Name	Lecture Notes in Artificial Intelligence

Name	Diagrams: International Conference on Theory and Application of Diagrams

Conference

Conference	3rd International Conference on Diagrammatic Representation and Inference, Diagrams 2004
Country/Territory	United Kingdom
City	Cambridge
Period	22/03/04 → 24/03/04
Internet address	https://link.springer.com/book/10.1007/b95854

Scopus Subject Areas

Theoretical Computer Science
General Computer Science

User-Defined Keywords

Imperfect Information
Semantic Game
Predicate Term
Donkey Anaphora
Atomic Graph

Access to Document

10.1007/978-3-540-25931-2_11

Cite this

Pietarinen, A. V. (2004). Peirce's diagrammatic logic in IF perspective. In A. F. Blackwell, K. Marriott, & A. Shimojima (Eds.), Diagrammatic Representation and Inference: Third International Conference, Diagrams 2004, Cambridge, UK, March 22-24, 2004, Proceedings (1st ed., pp. 97-111). (Lecture Notes in Computer Science; Vol. 2980), (Lecture Notes in Artificial Intelligence), (Diagrams: International Conference on Theory and Application of Diagrams). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-25931-2_11

Pietarinen, Ahti Veikko. / Peirce's diagrammatic logic in IF perspective. Diagrammatic Representation and Inference: Third International Conference, Diagrams 2004, Cambridge, UK, March 22-24, 2004, Proceedings. editor / Alan F. Blackwell ; Kim Marriott ; Atsushi Shimojima. 1st. ed. Springer Berlin Heidelberg, 2004. pp. 97-111 (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams).

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abstract = "This paper presents a topological and game-theoretic extension of the system of Existential Graphs (EG). EGs were Charles S. Peirce's diagrammatic and iconic approach to logic. By scribing the graphs on assertion spaces of higher dimensions, this extension provides the precise iconic counterpart to the Independence-Friendly (IF) restatement of first-order logic suggested by Hintikka. Consequently, the IF extension completes the project that Peirce initiated: it breaks off from the linear confines of language by diagrams that extend to three dimensions, which Peirce predicted to be necessary and sufficient for the expression of all assertions. Apart from improved ways of performing conceptual modelling on natural-language expressions, this extension reveals the true proportions of Peirce's sign- and model-theoretic thinking in plunging into the notions of identity, negation, continuity and quantification.",

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Pietarinen, AV 2004, Peirce's diagrammatic logic in IF perspective. in AF Blackwell, K Marriott & A Shimojima (eds), Diagrammatic Representation and Inference: Third International Conference, Diagrams 2004, Cambridge, UK, March 22-24, 2004, Proceedings. 1st edn, Lecture Notes in Computer Science, vol. 2980, Lecture Notes in Artificial Intelligence, Diagrams: International Conference on Theory and Application of Diagrams, Springer Berlin Heidelberg, pp. 97-111, 3rd International Conference on Diagrammatic Representation and Inference, Diagrams 2004, Cambridge, United Kingdom, 22/03/04. https://doi.org/10.1007/978-3-540-25931-2_11

Peirce's diagrammatic logic in IF perspective. / Pietarinen, Ahti Veikko.
Diagrammatic Representation and Inference: Third International Conference, Diagrams 2004, Cambridge, UK, March 22-24, 2004, Proceedings. ed. / Alan F. Blackwell; Kim Marriott; Atsushi Shimojima. 1st. ed. Springer Berlin Heidelberg, 2004. p. 97-111 (Lecture Notes in Computer Science; Vol. 2980), (Lecture Notes in Artificial Intelligence), (Diagrams: International Conference on Theory and Application of Diagrams).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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AB - This paper presents a topological and game-theoretic extension of the system of Existential Graphs (EG). EGs were Charles S. Peirce's diagrammatic and iconic approach to logic. By scribing the graphs on assertion spaces of higher dimensions, this extension provides the precise iconic counterpart to the Independence-Friendly (IF) restatement of first-order logic suggested by Hintikka. Consequently, the IF extension completes the project that Peirce initiated: it breaks off from the linear confines of language by diagrams that extend to three dimensions, which Peirce predicted to be necessary and sufficient for the expression of all assertions. Apart from improved ways of performing conceptual modelling on natural-language expressions, this extension reveals the true proportions of Peirce's sign- and model-theoretic thinking in plunging into the notions of identity, negation, continuity and quantification.

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Pietarinen AV. Peirce's diagrammatic logic in IF perspective. In Blackwell AF, Marriott K, Shimojima A, editors, Diagrammatic Representation and Inference: Third International Conference, Diagrams 2004, Cambridge, UK, March 22-24, 2004, Proceedings. 1st ed. Springer Berlin Heidelberg. 2004. p. 97-111. (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams). doi: 10.1007/978-3-540-25931-2_11

Peirce's diagrammatic logic in IF perspective

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