Intuitionistic Propositional Logic with Galois Negations
Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete dua...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ma, Minghui [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2022 |
|---|
| Schlagwörter: |
|---|
| Systematik: |
|
|---|
| Anmerkung: |
© Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
|---|
| Übergeordnetes Werk: |
Enthalten in: Studia logica - Springer Netherlands, 1953, 111(2022), 1 vom: 26. Sept., Seite 21-56 |
|---|---|
| Übergeordnetes Werk: |
volume:111 ; year:2022 ; number:1 ; day:26 ; month:09 ; pages:21-56 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11225-022-10014-5 |
|---|
| Katalog-ID: |
OLC2133510923 |
|---|
| LEADER | 01000naa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2133510923 | ||
| 003 | DE-627 | ||
| 005 | 20230506151318.0 | ||
| 007 | tu | ||
| 008 | 230506s2022 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s11225-022-10014-5 |2 doi | |
| 035 | |a (DE-627)OLC2133510923 | ||
| 035 | |a (DE-He213)s11225-022-10014-5-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 000 |a 100 |q VZ |
| 084 | |a 5,1 |a 17,1 |2 ssgn | ||
| 084 | |a PHILOS |q DE-12 |2 fid | ||
| 084 | |a LING |q DE-30 |2 fid | ||
| 084 | |a SA 8098 |q VZ |2 rvk | ||
| 084 | |a SA 8098 |q VZ |2 rvk | ||
| 084 | |a SA 8098 |a CA 1000 |q VZ |2 rvk | ||
| 100 | 1 | |a Ma, Minghui |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Intuitionistic Propositional Logic with Galois Negations |
| 264 | 1 | |c 2022 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. | ||
| 520 | |a Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. | ||
| 650 | 4 | |a Heyting algebra | |
| 650 | 4 | |a Galois negations | |
| 650 | 4 | |a Intuitionistic logic | |
| 650 | 4 | |a Tense logic | |
| 700 | 1 | |a Li, Guiying |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Studia logica |d Springer Netherlands, 1953 |g 111(2022), 1 vom: 26. Sept., Seite 21-56 |w (DE-627)129086916 |w (DE-600)4997-9 |w (DE-576)014421186 |x 0039-3215 |7 nnns |
| 773 | 1 | 8 | |g volume:111 |g year:2022 |g number:1 |g day:26 |g month:09 |g pages:21-56 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/s11225-022-10014-5 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a FID-PHILOS | ||
| 912 | |a FID-LING | ||
| 912 | |a SSG-OLC-PHI | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_4012 | ||
| 912 | |a GBV_ILN_4035 | ||
| 936 | r | v | |a SA 8098 |
| 936 | r | v | |a SA 8098 |
| 936 | r | v | |a SA 8098 |
| 951 | |a AR | ||
| 952 | |d 111 |j 2022 |e 1 |b 26 |c 09 |h 21-56 | ||
| author_variant |
m m mm g l gl |
|---|---|
| matchkey_str |
article:00393215:2022----::nutoitcrpstoalgcih |
| hierarchy_sort_str |
2022 |
| publishDate |
2022 |
| allfields |
10.1007/s11225-022-10014-5 doi (DE-627)OLC2133510923 (DE-He213)s11225-022-10014-5-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 Ma, Minghui verfasserin aut Intuitionistic Propositional Logic with Galois Negations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. Heyting algebra Galois negations Intuitionistic logic Tense logic Li, Guiying aut Enthalten in Studia logica Springer Netherlands, 1953 111(2022), 1 vom: 26. Sept., Seite 21-56 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:111 year:2022 number:1 day:26 month:09 pages:21-56 https://doi.org/10.1007/s11225-022-10014-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 111 2022 1 26 09 21-56 |
| spelling |
10.1007/s11225-022-10014-5 doi (DE-627)OLC2133510923 (DE-He213)s11225-022-10014-5-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 Ma, Minghui verfasserin aut Intuitionistic Propositional Logic with Galois Negations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. Heyting algebra Galois negations Intuitionistic logic Tense logic Li, Guiying aut Enthalten in Studia logica Springer Netherlands, 1953 111(2022), 1 vom: 26. Sept., Seite 21-56 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:111 year:2022 number:1 day:26 month:09 pages:21-56 https://doi.org/10.1007/s11225-022-10014-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 111 2022 1 26 09 21-56 |
| allfields_unstemmed |
10.1007/s11225-022-10014-5 doi (DE-627)OLC2133510923 (DE-He213)s11225-022-10014-5-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 Ma, Minghui verfasserin aut Intuitionistic Propositional Logic with Galois Negations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. Heyting algebra Galois negations Intuitionistic logic Tense logic Li, Guiying aut Enthalten in Studia logica Springer Netherlands, 1953 111(2022), 1 vom: 26. Sept., Seite 21-56 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:111 year:2022 number:1 day:26 month:09 pages:21-56 https://doi.org/10.1007/s11225-022-10014-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 111 2022 1 26 09 21-56 |
| allfieldsGer |
10.1007/s11225-022-10014-5 doi (DE-627)OLC2133510923 (DE-He213)s11225-022-10014-5-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 Ma, Minghui verfasserin aut Intuitionistic Propositional Logic with Galois Negations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. Heyting algebra Galois negations Intuitionistic logic Tense logic Li, Guiying aut Enthalten in Studia logica Springer Netherlands, 1953 111(2022), 1 vom: 26. Sept., Seite 21-56 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:111 year:2022 number:1 day:26 month:09 pages:21-56 https://doi.org/10.1007/s11225-022-10014-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 111 2022 1 26 09 21-56 |
| allfieldsSound |
10.1007/s11225-022-10014-5 doi (DE-627)OLC2133510923 (DE-He213)s11225-022-10014-5-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 Ma, Minghui verfasserin aut Intuitionistic Propositional Logic with Galois Negations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. Heyting algebra Galois negations Intuitionistic logic Tense logic Li, Guiying aut Enthalten in Studia logica Springer Netherlands, 1953 111(2022), 1 vom: 26. Sept., Seite 21-56 (DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 0039-3215 nnns volume:111 year:2022 number:1 day:26 month:09 pages:21-56 https://doi.org/10.1007/s11225-022-10014-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 SA 8098 SA 8098 SA 8098 AR 111 2022 1 26 09 21-56 |
| language |
English |
| source |
Enthalten in Studia logica 111(2022), 1 vom: 26. Sept., Seite 21-56 volume:111 year:2022 number:1 day:26 month:09 pages:21-56 |
| sourceStr |
Enthalten in Studia logica 111(2022), 1 vom: 26. Sept., Seite 21-56 volume:111 year:2022 number:1 day:26 month:09 pages:21-56 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Heyting algebra Galois negations Intuitionistic logic Tense logic |
| dewey-raw |
000 |
| isfreeaccess_bool |
false |
| container_title |
Studia logica |
| authorswithroles_txt_mv |
Ma, Minghui @@aut@@ Li, Guiying @@aut@@ |
| publishDateDaySort_date |
2022-09-26T00:00:00Z |
| hierarchy_top_id |
129086916 |
| dewey-sort |
0 |
| id |
OLC2133510923 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2133510923</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230506151318.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230506s2022 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11225-022-10014-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2133510923</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11225-022-10014-5-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">000</subfield><subfield code="a">100</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">5,1</subfield><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHILOS</subfield><subfield code="q">DE-12</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">LING</subfield><subfield code="q">DE-30</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SA 8098</subfield><subfield code="q">VZ</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SA 8098</subfield><subfield code="q">VZ</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SA 8098</subfield><subfield code="a">CA 1000</subfield><subfield code="q">VZ</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ma, Minghui</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Intuitionistic Propositional Logic with Galois Negations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Heyting algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Galois negations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Intuitionistic logic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tense logic</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Li, Guiying</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Studia logica</subfield><subfield code="d">Springer Netherlands, 1953</subfield><subfield code="g">111(2022), 1 vom: 26. Sept., Seite 21-56</subfield><subfield code="w">(DE-627)129086916</subfield><subfield code="w">(DE-600)4997-9</subfield><subfield code="w">(DE-576)014421186</subfield><subfield code="x">0039-3215</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:111</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:1</subfield><subfield code="g">day:26</subfield><subfield code="g">month:09</subfield><subfield code="g">pages:21-56</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11225-022-10014-5</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-PHILOS</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-LING</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHI</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="936" ind1="r" ind2="v"><subfield code="a">SA 8098</subfield></datafield><datafield tag="936" ind1="r" ind2="v"><subfield code="a">SA 8098</subfield></datafield><datafield tag="936" ind1="r" ind2="v"><subfield code="a">SA 8098</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">111</subfield><subfield code="j">2022</subfield><subfield code="e">1</subfield><subfield code="b">26</subfield><subfield code="c">09</subfield><subfield code="h">21-56</subfield></datafield></record></collection>
|
| author |
Ma, Minghui |
| spellingShingle |
Ma, Minghui ddc 000 ssgn 5,1 fid PHILOS fid LING rvk SA 8098 misc Heyting algebra misc Galois negations misc Intuitionistic logic misc Tense logic Intuitionistic Propositional Logic with Galois Negations |
| authorStr |
Ma, Minghui |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)129086916 |
| format |
Article |
| dewey-ones |
000 - Computer science, information & general works 100 - Philosophy & psychology |
| delete_txt_mv |
keep |
| author_role |
aut aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0039-3215 |
| topic_title |
000 100 VZ 5,1 17,1 ssgn PHILOS DE-12 fid LING DE-30 fid SA 8098 VZ rvk SA 8098 CA 1000 VZ rvk Intuitionistic Propositional Logic with Galois Negations Heyting algebra Galois negations Intuitionistic logic Tense logic |
| topic |
ddc 000 ssgn 5,1 fid PHILOS fid LING rvk SA 8098 misc Heyting algebra misc Galois negations misc Intuitionistic logic misc Tense logic |
| topic_unstemmed |
ddc 000 ssgn 5,1 fid PHILOS fid LING rvk SA 8098 misc Heyting algebra misc Galois negations misc Intuitionistic logic misc Tense logic |
| topic_browse |
ddc 000 ssgn 5,1 fid PHILOS fid LING rvk SA 8098 misc Heyting algebra misc Galois negations misc Intuitionistic logic misc Tense logic |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
Studia logica |
| hierarchy_parent_id |
129086916 |
| dewey-tens |
000 - Computer science, knowledge & systems 100 - Philosophy |
| hierarchy_top_title |
Studia logica |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)129086916 (DE-600)4997-9 (DE-576)014421186 |
| title |
Intuitionistic Propositional Logic with Galois Negations |
| ctrlnum |
(DE-627)OLC2133510923 (DE-He213)s11225-022-10014-5-p |
| title_full |
Intuitionistic Propositional Logic with Galois Negations |
| author_sort |
Ma, Minghui |
| journal |
Studia logica |
| journalStr |
Studia logica |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
000 - Computer science, information & general works 100 - Philosophy & psychology |
| recordtype |
marc |
| publishDateSort |
2022 |
| contenttype_str_mv |
txt |
| container_start_page |
21 |
| author_browse |
Ma, Minghui Li, Guiying |
| container_volume |
111 |
| class |
000 100 VZ 5,1 17,1 ssgn PHILOS DE-12 fid LING DE-30 fid SA 8098 VZ rvk SA 8098 CA 1000 VZ rvk |
| format_se |
Aufsätze |
| author-letter |
Ma, Minghui |
| doi_str_mv |
10.1007/s11225-022-10014-5 |
| dewey-full |
000 100 |
| title_sort |
intuitionistic propositional logic with galois negations |
| title_auth |
Intuitionistic Propositional Logic with Galois Negations |
| abstract |
Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$. © Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-PHILOS FID-LING SSG-OLC-PHI SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 |
| container_issue |
1 |
| title_short |
Intuitionistic Propositional Logic with Galois Negations |
| url |
https://doi.org/10.1007/s11225-022-10014-5 |
| remote_bool |
false |
| author2 |
Li, Guiying |
| author2Str |
Li, Guiying |
| ppnlink |
129086916 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s11225-022-10014-5 |
| up_date |
2024-07-03T19:53:41.144Z |
| _version_ |
1803588910346928128 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2133510923</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230506151318.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230506s2022 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11225-022-10014-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2133510923</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11225-022-10014-5-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">000</subfield><subfield code="a">100</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">5,1</subfield><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHILOS</subfield><subfield code="q">DE-12</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">LING</subfield><subfield code="q">DE-30</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SA 8098</subfield><subfield code="q">VZ</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SA 8098</subfield><subfield code="q">VZ</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SA 8098</subfield><subfield code="a">CA 1000</subfield><subfield code="q">VZ</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ma, Minghui</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Intuitionistic Propositional Logic with Galois Negations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Nature B.V. 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Intuitionistic propositional logic with Galois negations ($$\mathsf {IGN}$$) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair $$(\lnot ,{\sim })$$ and dual Galois pair $$(\dot{\lnot },\dot{\sim })$$ of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for $$\mathsf {IGN}$$ are developed. A Hilbert-style axiomatic system $$\mathsf {HN}$$ is given for $$\mathsf {IGN}$$, and Galois negation logics are defined as extensions of $$\mathsf {IGN}$$. We give the bi-tense logic $$\mathsf {S4N}_t$$ which is obtained from the minimal tense extension of the modal logic $$\mathsf {S4}$$ by adding tense operators. We give a new extended Gödel translation $$\tau $$ and prove that $$\mathsf {IGN}$$ is embedded into $$\mathsf {S4N}_t$$ by $$\tau $$. Moreover, every Kripke-complete Galois negation logic L is embedded into its tense companion $$\tau (L)$$.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Heyting algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Galois negations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Intuitionistic logic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tense logic</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Li, Guiying</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Studia logica</subfield><subfield code="d">Springer Netherlands, 1953</subfield><subfield code="g">111(2022), 1 vom: 26. Sept., Seite 21-56</subfield><subfield code="w">(DE-627)129086916</subfield><subfield code="w">(DE-600)4997-9</subfield><subfield code="w">(DE-576)014421186</subfield><subfield code="x">0039-3215</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:111</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:1</subfield><subfield code="g">day:26</subfield><subfield code="g">month:09</subfield><subfield code="g">pages:21-56</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11225-022-10014-5</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-PHILOS</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-LING</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHI</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="936" ind1="r" ind2="v"><subfield code="a">SA 8098</subfield></datafield><datafield tag="936" ind1="r" ind2="v"><subfield code="a">SA 8098</subfield></datafield><datafield tag="936" ind1="r" ind2="v"><subfield code="a">SA 8098</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">111</subfield><subfield code="j">2022</subfield><subfield code="e">1</subfield><subfield code="b">26</subfield><subfield code="c">09</subfield><subfield code="h">21-56</subfield></datafield></record></collection>
|
| score |
7.4007845 |