A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB
A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB
Author(s): Takao InoueSubject(s): Logic
Published by: Wydawnictwo Uniwersytetu Łódzkiego
Keywords: Leśniewski's ontology; propositional ontology; translation; interpretation; modal logic; KTB; soundness; Grzegorczyk's modal logic
Summary/Abstract: In this paper, we shall show that the following translation IM from the propositional fragment L1 of Leśniewski's ontology to modal logic KTB is sound: for any formula ϕ and ψ of L1, it is defined as(M1) IM(ϕ∨ψ)=IM(ϕ)∨IM(ψ),(M2) IM(¬ϕ)=¬IM(ϕ),(M3) IM(ϵab)=◊pa⊃pa.∧.◻pa⊃◻pb.∧.◊pb⊃pa,where pa and pb 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.
Journal: Bulletin of the Section of Logic
- Issue Year: 50/2021
- Issue No: 4
- Page Range: 455-463
- Page Count: 9
- Language: English