Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T01:13:52.503Z Has data issue: false hasContentIssue false
  • English
  • Français

REFLEXIVE-INSENSITIVE MODAL LOGICS

Published online by Cambridge University Press:  24 August 2015

DAVID R. GILBERT  and
GIORGIO VENTURI
DAVID R. GILBERT*
Affiliation:
State University of Campinas
GIORGIO VENTURI*
Affiliation:
State University of Campinas
*
*CENTRE FOR LOGIC EPISTEMOLOGY AND THE HISTORY OF SCIENCE STATE UNIVERSITY OF CAMPINAS 13083-859, CAMPINAS SÃO PAULO, BRAZIL E-mail:gilbert.dave.r@gmail.com, gio.venturi@gmail.com
*CENTRE FOR LOGIC EPISTEMOLOGY AND THE HISTORY OF SCIENCE STATE UNIVERSITY OF CAMPINAS 13083-859, CAMPINAS SÃO PAULO, BRAZIL E-mail:gilbert.dave.r@gmail.com, gio.venturi@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general completeness theorem on the basis of a translation between normal modal logics and their reflexive-insensitive counterparts. Lastly, we provide a sufficient semantic condition describing when a similarly general soundness result is also available.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 1 , March 2016 , pp. 167 - 180
Copyright
Copyright © Association for Symbolic Logic 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge: Cambridge University Press.Google Scholar
Goldblatt, R. (1991). The McKinsey axiom is not canonical. The Journal of Symbolic Logic, 56(2), 554–562.Google Scholar
Goldblatt, R., & Mares, E. (2006). General semantics for quantified modal logic. Advances in Modal Logic, 6, 227–246.Google Scholar
Marcos, J. (2005). Logics of essence and accident. Bulletin of the Section of Logic, 34(1), 43–56.Google Scholar
Steinsvold, C. (2008a). Completeness for various logics of essence and accident. Bulletin of the Section of Logic, 37(2), 93–101.Google Scholar
Steinsvold, C. (2008b). A note on logics of ignorance and borders. Notre Dame Journal of Formal Logic, 49(4), 385–392.Google Scholar
Steinsvold, C. (2011). Being wrong: Logics for false belief. Notre Dame Journal of Formal Logic, 52(3), 245–253.Google Scholar