Beta Assertive Graphs

Francesco Bellucci; Daniele Chiffi; Ahti Veikko Pietarinen

doi:10.1007/978-3-030-54249-8_49

Beta Assertive Graphs

Francesco Bellucci, Daniele Chiffi, Ahti Veikko Pietarinen^*

^*Corresponding author for this work

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

Abstract

Assertive graphs (AGs) modify Peirce’s Alpha part of Existential Graphs (EGs) and are used to reason about assertions without any ad hoc sign of assertion. This paper presents an extension of propositional AGs to Beta by lines. Absence of polarities necessitate Beta-AGs to resort to two kinds of lines: standard lines (a certain method of asserting), and barbed lines (a general method of asserting). A new set of rules of transformations for Beta-AGs is presented that derive theorems of quantificational intuitionistic logic. Beta-AGs offer a new system to analyse assertions through quantificational diagrams.

Original language	English
Title of host publication	Diagrammatic Representation and Inference
Subtitle of host publication	11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings
Editors	Ahti-Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter, Sven Linker
Publisher	Springer Cham
Pages	525-529
Number of pages	5
Edition	1st
ISBN (Electronic)	9783030542498
ISBN (Print)	9783030542481
DOIs	https://doi.org/10.1007/978-3-030-54249-8_49
Publication status	Published - 29 Jul 2020
Event	11th International Conference on the Theory and Application of Diagrams, Diagrams 2020 - Tallinn, Estonia Duration: 24 Aug 2020 → 28 Aug 2020 https://link.springer.com/book/10.1007/978-3-030-54249-8

Publication series

Name	Lecture Notes in Computer Science
Volume	12169
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	11th International Conference on the Theory and Application of Diagrams, Diagrams 2020
Country/Territory	Estonia
City	Tallinn
Period	24/08/20 → 28/08/20
Internet address	https://link.springer.com/book/10.1007/978-3-030-54249-8

Scopus Subject Areas

Theoretical Computer Science
General Computer Science

User-Defined Keywords

Existential/Assertive graphs
Intuitionistic logic
Quantifier

Access to Document

10.1007/978-3-030-54249-8_49

Cite this

Bellucci, F., Chiffi, D., & Pietarinen, A. V. (2020). Beta Assertive Graphs. In A.-V. Pietarinen, P. Chapman, L. Bosveld-de Smet, V. Giardino, J. Corter, & S. Linker (Eds.), Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings (1st ed., pp. 525-529). (Lecture Notes in Computer Science; Vol. 12169), (Lecture Notes in Artificial Intelligence), (Diagrams: International Conference on Theory and Application of Diagrams). Springer Cham. https://doi.org/10.1007/978-3-030-54249-8_49

Bellucci, Francesco ; Chiffi, Daniele ; Pietarinen, Ahti Veikko. / Beta Assertive Graphs. Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. editor / Ahti-Veikko Pietarinen ; Peter Chapman ; Leonie Bosveld-de Smet ; Valeria Giardino ; James Corter ; Sven Linker. 1st. ed. Springer Cham, 2020. pp. 525-529 (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams).

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title = "Beta Assertive Graphs",

abstract = "Assertive graphs (AGs) modify Peirce{\textquoteright}s Alpha part of Existential Graphs (EGs) and are used to reason about assertions without any ad hoc sign of assertion. This paper presents an extension of propositional AGs to Beta by lines. Absence of polarities necessitate Beta-AGs to resort to two kinds of lines: standard lines (a certain method of asserting), and barbed lines (a general method of asserting). A new set of rules of transformations for Beta-AGs is presented that derive theorems of quantificational intuitionistic logic. Beta-AGs offer a new system to analyse assertions through quantificational diagrams.",

keywords = "Existential/Assertive graphs, Intuitionistic logic, Quantifier",

author = "Francesco Bellucci and Daniele Chiffi and Pietarinen, {Ahti Veikko}",

note = "Funding Information: The paper was prepared within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project {\textquoteleft}5–100{\textquoteright}. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020 ; Conference date: 24-08-2020 Through 28-08-2020",

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Bellucci, F, Chiffi, D & Pietarinen, AV 2020, Beta Assertive Graphs. in A-V Pietarinen, P Chapman, L Bosveld-de Smet, V Giardino, J Corter & S Linker (eds), Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. 1st edn, Lecture Notes in Computer Science, vol. 12169, Lecture Notes in Artificial Intelligence, Diagrams: International Conference on Theory and Application of Diagrams, Springer Cham, pp. 525-529, 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020, Tallinn, Estonia, 24/08/20. https://doi.org/10.1007/978-3-030-54249-8_49

Beta Assertive Graphs. / Bellucci, Francesco; Chiffi, Daniele; Pietarinen, Ahti Veikko.
Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. ed. / Ahti-Veikko Pietarinen; Peter Chapman; Leonie Bosveld-de Smet; Valeria Giardino; James Corter; Sven Linker. 1st. ed. Springer Cham, 2020. p. 525-529 (Lecture Notes in Computer Science; Vol. 12169), (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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T1 - Beta Assertive Graphs

AU - Bellucci, Francesco

AU - Chiffi, Daniele

AU - Pietarinen, Ahti Veikko

N1 - Funding Information: The paper was prepared within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project ‘5–100’. Publisher Copyright: © 2020, Springer Nature Switzerland AG.

PY - 2020/7/29

Y1 - 2020/7/29

N2 - Assertive graphs (AGs) modify Peirce’s Alpha part of Existential Graphs (EGs) and are used to reason about assertions without any ad hoc sign of assertion. This paper presents an extension of propositional AGs to Beta by lines. Absence of polarities necessitate Beta-AGs to resort to two kinds of lines: standard lines (a certain method of asserting), and barbed lines (a general method of asserting). A new set of rules of transformations for Beta-AGs is presented that derive theorems of quantificational intuitionistic logic. Beta-AGs offer a new system to analyse assertions through quantificational diagrams.

AB - Assertive graphs (AGs) modify Peirce’s Alpha part of Existential Graphs (EGs) and are used to reason about assertions without any ad hoc sign of assertion. This paper presents an extension of propositional AGs to Beta by lines. Absence of polarities necessitate Beta-AGs to resort to two kinds of lines: standard lines (a certain method of asserting), and barbed lines (a general method of asserting). A new set of rules of transformations for Beta-AGs is presented that derive theorems of quantificational intuitionistic logic. Beta-AGs offer a new system to analyse assertions through quantificational diagrams.

KW - Existential/Assertive graphs

KW - Intuitionistic logic

KW - Quantifier

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SN - 9783030542481

T3 - Lecture Notes in Computer Science

SP - 525

EP - 529

BT - Diagrammatic Representation and Inference

A2 - Pietarinen, Ahti-Veikko

A2 - Chapman, Peter

A2 - Bosveld-de Smet, Leonie

A2 - Giardino, Valeria

A2 - Corter, James

A2 - Linker, Sven

PB - Springer Cham

T2 - 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020

Y2 - 24 August 2020 through 28 August 2020

ER -

Bellucci F, Chiffi D, Pietarinen AV. Beta Assertive Graphs. In Pietarinen AV, Chapman P, Bosveld-de Smet L, Giardino V, Corter J, Linker S, editors, Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. 1st ed. Springer Cham. 2020. p. 525-529. (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams). doi: 10.1007/978-3-030-54249-8_49

Beta Assertive Graphs

Abstract

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Scopus Subject Areas

User-Defined Keywords

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