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On Modal Logics Defining Jaśkowski’s D2-Consequence

  • Marek Nasieniewski
  • Andrzej Pietruszczak
Chapter
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 26)

Abstract

Jaśkowski’s logic D 2 (as a set of formulae) was formulated with the help of the modal logic S5 (see Jaśkowski, Stud Soc Sci Torun I(5):57–77, 1948; Stud Soc Sci Torun I(8):171–172, 1949). In Furmanowski (Stud Log 34:39–43, 1975), Perzanowski (Rep Math Log 5:63–72, 1975), Nasieniewski and Pietruszczak (Bull Sect Logic 37(3–4):197–210, 2008) it was shown that to define D 2 one can use normal and regular logics weaker than S5. In his paper Jaśkowski used a deducibility relation which we will denote by⊢ D 2 and which fulfilled the following condition: A 1,,A n ⊢; D 2 B iff \(\ulcorner \lozenge {A}_{1}^{\bullet }\rightarrow (\ldots \rightarrow (\lozenge {A}_{n}^{\bullet }\rightarrow \lozenge {B}^{\bullet })\ldots \,)\urcorner \in \mathbf{S5}\), where (−) is a translation of discussive formulae into the modal language. We indicate the weakest normal and the weakest regular modal logic which define D 2 -consequence.

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Copyright information

© Springer Science+Business Media Dordrecht. 2013

Authors and Affiliations

  1. 1.Department of LogicNicolaus Copernicus UniversityToruńPoland

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