A sound interpretation of Leśniewski's epsilon in modal logic KTB

07/22/2020

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by   Takao Inoué, et al.

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In this paper, we shall show that the following translation I^M from the propositional fragment L_1 of Leśniewski's ontology to modal logic KTB is sound: for any formula ϕ and ψ of L_1, it is defined as (M1) I^M(ϕ∨ψ) = I^M(ϕ) ∨ I^M(ψ), (M2) I^M(ϕ) = I^M(ϕ), (M3) I^M(ϵ ab) = p_a ⊃ p_a . ∧ . p_a ⊃ p_b . ∧ . p_b ⊃ p_a, where p_a and p_b are propositional variables corresponding to the name variables a and b, respectively. We shall give some comments including some open problems and my conjectures.