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

Abstract

On March 8, 1995, was found the following nontrivial single axiomschema characteristic of Leśniewski-Ishimoto's propositional ontologyIn this paper, we shall present the progress about the above axiomschema from 1995 and conjectures about it. Here we shall give two criteria nontiriviality and quasi-nontriviality in order to distinguish two axiom-schemata.

A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB

“…where p a and p b are propositional variables corresponding to the name variables a and b, respectively. Inoué [11] extended Blass's faithfulness result for many normal modal logics, provability logic and von Wright-type deontic logics including K4, KD, KB, KD4, etc, GL and ten Smiley-Hanson systems of monadic deontic logic, using model constructions based on Hintikka formula (cf. Kobayashi and Ishimoto [13]).…”

“…Blass [2] gave a modification of the interpretation and showed that his interpretation T is faithful, using Kripke models. Inoué [11] called the translation Blass translation (for short, B-translation) or Blass interpretation (for short, B-interpretation). The translation B from L 1 to K is defined as follows: for any formula φ and ψ of L 1 ,…”