Studia Logica 106 (6):1097-1122 (2018)

Authors
Philip Kremer
University of Toronto at Scarborough
Abstract
The simplest bimodal combination of unimodal logics \ and \ is their fusion, \, axiomatized by the theorems of \ for \ and of \ for \, and the rules of modus ponens, necessitation for \ and for \, and substitution. Shehtman introduced the frame product \, as the logic of the products of certain Kripke frames: these logics are two-dimensional as well as bimodal. Van Benthem, Bezhanishvili, ten Cate and Sarenac transposed Shehtman’s idea to the topological semantics and introduced the topological product \, as the logic of the products of certain topological spaces. For almost all well-studies logics, we have \, for example, \. Van Benthem et al. show, by contrast, that \. It is straightforward to define the product of a topological space and a frame: the result is a topologized frame, i.e., a set together with a topology and a binary relation. In this paper, we introduce topological-frame products \ of modal logics, providing a complete axiomatization of \, whenever \ is a Kripke complete Horn axiomatizable extension of the modal logic D: these extensions include \ and \, but not \ or \. We leave open the problem of axiomatizing \, \, and other related logics. When \, our result confirms a conjecture of van Benthem et al. concerning the logic of products of Alexandrov spaces with arbitrary topological spaces.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11225-017-9775-3
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,132
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Products of Modal Logics, Part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.

View all 17 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Dynamic Topological S5.Philip Kremer - 2009 - Annals of Pure and Applied Logic 160 (1):96-116.
Dynamic Topological Logic.Philip Kremer & Grigori Mints - 2005 - Annals of Pure and Applied Logic 131 (1-3):133-158.
Dynamic Topological Logic.Philip Kremer & Giorgi Mints - 2005 - Annals of Pure and Applied Logic 131 (1-3):133-158.
More on D-Logics of Subspaces of the Rational Numbers.Guram Bezhanishvili & Joel Lucero-Bryan - 2012 - Notre Dame Journal of Formal Logic 53 (3):319-345.

Analytics

Added to PP index
2017-12-12

Total views
14 ( #712,296 of 2,454,694 )

Recent downloads (6 months)
1 ( #449,768 of 2,454,694 )

How can I increase my downloads?

Downloads

My notes