Correspondence Between Kripke Frames and Projective Geometries
Abstract In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using...
Ausführliche Beschreibung
Autor*in: |
Zhong, Shengyang [verfasserIn] |
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Artikel |
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Sprache: |
Englisch |
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2017 |
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Anmerkung: |
© Springer Science+Business Media Dordrecht 2017 |
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Übergeordnetes Werk: |
Enthalten in: Studia logica - Springer Netherlands, 1953, 106(2017), 1 vom: 03. Juni, Seite 167-189 |
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Übergeordnetes Werk: |
volume:106 ; year:2017 ; number:1 ; day:03 ; month:06 ; pages:167-189 |
Links: |
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DOI / URN: |
10.1007/s11225-017-9733-0 |
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Katalog-ID: |
OLC2033924572 |
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10.1007/s11225-017-9733-0 doi (DE-627)OLC2033924572 (DE-He213)s11225-017-9733-0-p DE-627 ger DE-627 rakwb eng 000 100 VZ 5,1 17,1 ssgn PHILOS DE-12 fid LING DE-30 fid SA 8098 VZ rvk SA 8098 VZ rvk SA 8098 CA 1000 VZ rvk Zhong, Shengyang verfasserin (orcid)0000-0001-5538-0002 aut Correspondence Between Kripke Frames and Projective Geometries 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to pure orthogeometries (or, equivalently, projective geometries with pure polarities), irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. Kripke frame Projective geometry Quantum logic Spatial logic Modal logic Enthalten in Studia logica Springer Netherlands, 1953 106(2017), 1 vom: 03. Juni, Seite 167-189 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:106 year:2017 number:1 day:03 month:06 pages:167-189 https://doi.org/10.1007/s11225-017-9733-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_2088 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 106 2017 1 03 06 167-189 |
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10.1007/s11225-017-9733-0 doi (DE-627)OLC2033924572 (DE-He213)s11225-017-9733-0-p DE-627 ger DE-627 rakwb eng 000 100 VZ 5,1 17,1 ssgn PHILOS DE-12 fid LING DE-30 fid SA 8098 VZ rvk SA 8098 VZ rvk SA 8098 CA 1000 VZ rvk Zhong, Shengyang verfasserin (orcid)0000-0001-5538-0002 aut Correspondence Between Kripke Frames and Projective Geometries 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to pure orthogeometries (or, equivalently, projective geometries with pure polarities), irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. Kripke frame Projective geometry Quantum logic Spatial logic Modal logic Enthalten in Studia logica Springer Netherlands, 1953 106(2017), 1 vom: 03. Juni, Seite 167-189 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:106 year:2017 number:1 day:03 month:06 pages:167-189 https://doi.org/10.1007/s11225-017-9733-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_2088 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 106 2017 1 03 06 167-189 |
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10.1007/s11225-017-9733-0 doi (DE-627)OLC2033924572 (DE-He213)s11225-017-9733-0-p DE-627 ger DE-627 rakwb eng 000 100 VZ 5,1 17,1 ssgn PHILOS DE-12 fid LING DE-30 fid SA 8098 VZ rvk SA 8098 VZ rvk SA 8098 CA 1000 VZ rvk Zhong, Shengyang verfasserin (orcid)0000-0001-5538-0002 aut Correspondence Between Kripke Frames and Projective Geometries 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to pure orthogeometries (or, equivalently, projective geometries with pure polarities), irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. Kripke frame Projective geometry Quantum logic Spatial logic Modal logic Enthalten in Studia logica Springer Netherlands, 1953 106(2017), 1 vom: 03. Juni, Seite 167-189 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:106 year:2017 number:1 day:03 month:06 pages:167-189 https://doi.org/10.1007/s11225-017-9733-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_2088 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 106 2017 1 03 06 167-189 |
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10.1007/s11225-017-9733-0 doi (DE-627)OLC2033924572 (DE-He213)s11225-017-9733-0-p DE-627 ger DE-627 rakwb eng 000 100 VZ 5,1 17,1 ssgn PHILOS DE-12 fid LING DE-30 fid SA 8098 VZ rvk SA 8098 VZ rvk SA 8098 CA 1000 VZ rvk Zhong, Shengyang verfasserin (orcid)0000-0001-5538-0002 aut Correspondence Between Kripke Frames and Projective Geometries 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to pure orthogeometries (or, equivalently, projective geometries with pure polarities), irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. Kripke frame Projective geometry Quantum logic Spatial logic Modal logic Enthalten in Studia logica Springer Netherlands, 1953 106(2017), 1 vom: 03. Juni, Seite 167-189 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:106 year:2017 number:1 day:03 month:06 pages:167-189 https://doi.org/10.1007/s11225-017-9733-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_2088 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 106 2017 1 03 06 167-189 |
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Correspondence Between Kripke Frames and Projective Geometries |
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Abstract In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to pure orthogeometries (or, equivalently, projective geometries with pure polarities), irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. © Springer Science+Business Media Dordrecht 2017 |
abstractGer |
Abstract In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to pure orthogeometries (or, equivalently, projective geometries with pure polarities), irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. © Springer Science+Business Media Dordrecht 2017 |
abstract_unstemmed |
Abstract In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to pure orthogeometries (or, equivalently, projective geometries with pure polarities), irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. © Springer Science+Business Media Dordrecht 2017 |
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container_issue |
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title_short |
Correspondence Between Kripke Frames and Projective Geometries |
url |
https://doi.org/10.1007/s11225-017-9733-0 |
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doi_str |
10.1007/s11225-017-9733-0 |
up_date |
2024-07-03T18:55:23.084Z |
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