A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB
In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf L_1\), it is defined as (M1) \(I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(...
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| Format: | Article |
| Language: | English |
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Lodz University Press
2022-03-01
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| Series: | Bulletin of the Section of Logic |
| Subjects: | |
| Online Access: | https://www.czasopisma.uni.lodz.pl/bulletin/article/view/8071 |
| _version_ | 1818204047644033024 |
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| author | Takao Inoue |
| author_facet | Takao Inoue |
| author_sort | Takao Inoue |
| collection | DOAJ |
| description | In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf L_1\), it is defined as
(M1) \(I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(\psi)\),
(M2) \(I^M(\neg \phi) = \neg I^M(\phi)\),
(M3) \(I^M(\epsilon ab) = \Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b .\wedge . \Diamond p_b \supset p_a\),
where \(p_a\) and \(p_b\) are propositional variables corresponding to the name variables \(a\) and \(b\), respectively. In the last, we shall give some comments including some open problems and my conjectures. |
| first_indexed | 2024-12-12T03:35:02Z |
| format | Article |
| id | doaj.art-df30f79b885d419e833d8830d19cceb4 |
| institution | Directory Open Access Journal |
| issn | 0138-0680 2449-836X |
| language | English |
| last_indexed | 2024-12-12T03:35:02Z |
| publishDate | 2022-03-01 |
| publisher | Lodz University Press |
| record_format | Article |
| series | Bulletin of the Section of Logic |
| spelling | doaj.art-df30f79b885d419e833d8830d19cceb42022-12-22T00:39:50ZengLodz University PressBulletin of the Section of Logic0138-06802449-836X2022-03-0150445546310.18778/0138-0680.2021.257079A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTBTakao Inoue0https://orcid.org/0000-0002-2080-7480Meiji Pharmaceutical University, Department of Medical Molecular Informatics, Tokyo, Japan; Hosei University, Graduate School of Science and Engineering Tokyo, JapanIn this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf L_1\), it is defined as (M1) \(I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(\psi)\), (M2) \(I^M(\neg \phi) = \neg I^M(\phi)\), (M3) \(I^M(\epsilon ab) = \Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b .\wedge . \Diamond p_b \supset p_a\), where \(p_a\) and \(p_b\) are propositional variables corresponding to the name variables \(a\) and \(b\), respectively. In the last, we shall give some comments including some open problems and my conjectures.https://www.czasopisma.uni.lodz.pl/bulletin/article/view/8071le´sniewski’s ontologypropositional ontologytranslationinterpretationmodal logicktbsoundnessgrzegorczyk’s modal logic |
| spellingShingle | Takao Inoue A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB Bulletin of the Section of Logic le´sniewski’s ontology propositional ontology translation interpretation modal logic ktb soundness grzegorczyk’s modal logic |
| title | A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB |
| title_full | A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB |
| title_fullStr | A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB |
| title_full_unstemmed | A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB |
| title_short | A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB |
| title_sort | sound interpretation of lesniewski s epsilon in modal logic ktb |
| topic | le´sniewski’s ontology propositional ontology translation interpretation modal logic ktb soundness grzegorczyk’s modal logic |
| url | https://www.czasopisma.uni.lodz.pl/bulletin/article/view/8071 |
| work_keys_str_mv | AT takaoinoue asoundinterpretationoflesniewskisepsiloninmodallogicktb AT takaoinoue soundinterpretationoflesniewskisepsiloninmodallogicktb |