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

Abstract

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), 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.

On Blass Translation for Leśniewski’s Propositional Ontology and Modal Logics

“…For the other topics for L 1 , e.g. the interpretation of Leśniewski's ǫ, axiomatic rejection, model theory, tableau systems and the modal interpretation of L 1 , some applications to linguistics and related studies, the reader will be recommended to refer to Blass [1], Inoué [3,5,6,7,8], Inoué-Ishimoto-Kobayashi [9], Ishimoto [12,13], Kobayashi-Ishimoto [16], Ozawa-Waragai [20], Pietruszczak [22], Smirnov [25], Stachniak [27], Takano [29] and so on.…”

Axiomatic Rejection for the Propositional Fragment of Leśniewski's Ontology

“…As easily seen, there are many formulas of predicate logic which are not a T -transform of a formula of L 1 . For other translation and embedding of L 1 , refer to Blass [1], Inoué [16,17,18], Smirnov [67,69] and Takano [78].…”