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

Studia Logica 110 (1):265-289 (2021)
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Abstract

In this paper, we shall give another proof of the faithfulness of Blass translation of the propositional fragment \ of Leśniewski’s ontology in the modal logic \ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, B-translation is faithful for the provability logic \ ), that is, \ \ \ \supset \Box \phi \). The faithfulness also holds for normal modal logics, e.g., \, \, \, \. We shall conclude this paper with the section of some open problems and conjectures.

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Citations of this work

A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB.Takao Inoue - 2021 - Bulletin of the Section of Logic 50 (4):455-463.

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References found in this work

S. Leśniewski's Calculus of Names.Jerzy Słupecki - 1984 - In Jan T. J. Srzednicki, V. F. Rickey & J. Czelakowski (eds.), Studia Logica. Distributors for the United States and Canada, Kluwer Boston. pp. 59--122.
S. leśniewski's calculus of names.Jerzy Słupecki - 1955 - Studia Logica 3 (1):7-72.
Reduction of second‐order logic to modal logic.S. K. Thomason - 1975 - Mathematical Logic Quarterly 21 (1):107-114.
Reduction of tense logic to modal logic. I.S. K. Thomason - 1974 - Journal of Symbolic Logic 39 (3):549-551.

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