- Tytuł:
- A Sound Interpretation of Leśniewskis Epsilon in Modal Logic KTB
- Autorzy:
- Inoue, Takao
- Powiązania:
- https://bibliotekanauki.pl/articles/2033852.pdf
- Data publikacji:
- 2021-11-09
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
Le´sniewski’s ontology
propositional ontology
translation
interpretation
modal logic
KTB
soundness
Grzegorczyk’s modal logic - Opis:
- 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.
- Źródło:
-
Bulletin of the Section of Logic; 2021, 50, 4; 455-463
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł