Normatively Determined Propositions

Matteo Pascucci; Claudio E.A. Pizzi

doi:10.1007/978-3-031-15146-0_6

Normatively Determined Propositions

Matteo Pascucci^*, Claudio E.A. Pizzi

^*Corresponding author for this work

Research output: Contribution to Book/Report types › Conference contribution › peer-review

Abstract (may include machine translation)

In the present work we provide a logical analysis of normatively determined and non-determined propositions. The normative status of these propositions depends on their relation with another proposition, here named reference proposition. Using a formal language that includes a monadic operator of obligation, we define eight dyadic operators that represent various notions of “being normatively (non-)determined”; then, we group them into two families, each forming an Aristotelian square of opposition. Finally, we show how the two resulting squares can be combined to form an Aristotelian cube of opposition.

Original language	English
Title of host publication	Diagrammatic Representation and Inference - 13th International Conference, Diagrams 2022, Proceedings
Editors	Valeria Giardino, Sven Linker, Richard Burns, Francesco Bellucci, Jean-Michel Boucheix, Petrucio Viana
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	78-85
Number of pages	8
ISBN (Print)	9783031151453
DOIs	https://doi.org/10.1007/978-3-031-15146-0_6
State	Published - 2022
Externally published	Yes
Event	13th International Conference on Theory and Application of Diagrams, Diagrams 2022, co-located with the IEEE Symposium on Visual Languages and Human-Centric Computing, VL/HCC 2022 - Rome, Italy Duration: 13 Sep 2022 → 17 Sep 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13462 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Conference on Theory and Application of Diagrams, Diagrams 2022, co-located with the IEEE Symposium on Visual Languages and Human-Centric Computing, VL/HCC 2022
Country/Territory	Italy
City	Rome
Period	13/09/22 → 17/09/22

Keywords

Aristotelian cubes
Aristotelian squares
Deontic logic
Modal logic
Normatively determined propositions

Access to Document

10.1007/978-3-031-15146-0_6

Cite this

Pascucci, M., & Pizzi, C. E. A. (2022). Normatively Determined Propositions. In V. Giardino, S. Linker, R. Burns, F. Bellucci, J.-M. Boucheix, & P. Viana (Eds.), Diagrammatic Representation and Inference - 13th International Conference, Diagrams 2022, Proceedings (pp. 78-85). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13462 LNAI). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-15146-0_6

Pascucci, Matteo ; Pizzi, Claudio E.A. / Normatively Determined Propositions. Diagrammatic Representation and Inference - 13th International Conference, Diagrams 2022, Proceedings. editor / Valeria Giardino ; Sven Linker ; Richard Burns ; Francesco Bellucci ; Jean-Michel Boucheix ; Petrucio Viana. Springer Science and Business Media Deutschland GmbH, 2022. pp. 78-85 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In the present work we provide a logical analysis of normatively determined and non-determined propositions. The normative status of these propositions depends on their relation with another proposition, here named reference proposition. Using a formal language that includes a monadic operator of obligation, we define eight dyadic operators that represent various notions of “being normatively (non-)determined”; then, we group them into two families, each forming an Aristotelian square of opposition. Finally, we show how the two resulting squares can be combined to form an Aristotelian cube of opposition.",

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doi = "10.1007/978-3-031-15146-0_6",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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editor = "Valeria Giardino and Sven Linker and Richard Burns and Francesco Bellucci and Jean-Michel Boucheix and Petrucio Viana",

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Pascucci, M & Pizzi, CEA 2022, Normatively Determined Propositions. in V Giardino, S Linker, R Burns, F Bellucci, J-M Boucheix & P Viana (eds), Diagrammatic Representation and Inference - 13th International Conference, Diagrams 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13462 LNAI, Springer Science and Business Media Deutschland GmbH, pp. 78-85, 13th International Conference on Theory and Application of Diagrams, Diagrams 2022, co-located with the IEEE Symposium on Visual Languages and Human-Centric Computing, VL/HCC 2022, Rome, Italy, 13/09/22. https://doi.org/10.1007/978-3-031-15146-0_6

Normatively Determined Propositions. / Pascucci, Matteo; Pizzi, Claudio E.A.
Diagrammatic Representation and Inference - 13th International Conference, Diagrams 2022, Proceedings. ed. / Valeria Giardino; Sven Linker; Richard Burns; Francesco Bellucci; Jean-Michel Boucheix; Petrucio Viana. Springer Science and Business Media Deutschland GmbH, 2022. p. 78-85 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13462 LNAI).

Research output: Contribution to Book/Report types › Conference contribution › peer-review

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AB - In the present work we provide a logical analysis of normatively determined and non-determined propositions. The normative status of these propositions depends on their relation with another proposition, here named reference proposition. Using a formal language that includes a monadic operator of obligation, we define eight dyadic operators that represent various notions of “being normatively (non-)determined”; then, we group them into two families, each forming an Aristotelian square of opposition. Finally, we show how the two resulting squares can be combined to form an Aristotelian cube of opposition.

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KW - Aristotelian squares

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KW - Modal logic

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ER -

Pascucci M, Pizzi CEA. Normatively Determined Propositions. In Giardino V, Linker S, Burns R, Bellucci F, Boucheix JM, Viana P, editors, Diagrammatic Representation and Inference - 13th International Conference, Diagrams 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 78-85. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-15146-0_6

Normatively Determined Propositions

Abstract (may include machine translation)

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Conference

Keywords

Access to Document

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