Open Access
Translator Disclaimer
Winter 1994 Some Logics Related to von Wright's Logic of Place
Ramón Jansana
Notre Dame J. Formal Logic 35(1): 88-98 (Winter 1994). DOI: 10.1305/ndjfl/1040609296


In this paper we study some logics related to the logic of place introduced by von Wright and studied by Segerberg. For every $n \geq 1$ we study the logic of the class of frames whose accessibility relation R satisfies the following condition: if $x \neq y$ then there is $j \leq n$ such that $xR^j y$. For a fixed $n \geq 1$ the logic is the one axiomatized by K $ + [n] \phi \rightarrow [n+1]\phi+ \phi \rightarrow [n]\langle n\rangle\phi$, which we call Kn.4B, where $[n]\phi \hbox{ is } \phi \wedge \square\phi \wedge \dots\wedge \square^n\phi $. We prove that these logics are canonical and hence complete, and that they have the finite model property, being thus decidable. We also characterize their classes of frames. In the way of studying them we also study the logics ${\bf K} + [n]\phi \rightarrow [n+1]\phi $, called Kn.4, and ${\bf K} + \phi \rightarrow [n]\langle n\rangle\phi $, called Kn.B. A translation between these logics and S5 is also presented, and the relation among them all is established.


Download Citation

Ramón Jansana. "Some Logics Related to von Wright's Logic of Place." Notre Dame J. Formal Logic 35 (1) 88 - 98, Winter 1994.


Published: Winter 1994
First available in Project Euclid: 22 December 2002

zbMATH: 0801.03015
MathSciNet: MR1271700
Digital Object Identifier: 10.1305/ndjfl/1040609296

Primary: 03B45
Secondary: 03B25

Rights: Copyright © 1994 University of Notre Dame


Vol.35 • No. 1 • Winter 1994
Back to Top