The Review of Symbolic Logic

Table of Contents - June 2012 - Volume 5, Issue 02  

Research Article

COMPLETENESS RESULTS FOR SOME TWO-DIMENSIONAL LOGICS OF ACTUALITY

DAVID R. GILBERTa1 c1 and EDWIN D. MARESa1 c2

a1 Centre for logic, language and computation, Victoria University of Wellington

Abstract

We provide a Hilbert-style axiomatization of the logic of ‘actually’, as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions.

(Received August 01 2011)

Correspondence:

c1 CENTRE FOR LOGIC, LANGUAGE AND COMPUTATION, VICTORIA UNIVERSITY OF WELLINGTON, NEW ZEALAND. E-mail: david.gilbert@vuw.ac.nz

c2 CENTRE FOR LOGIC, LANGUAGE AND COMPUTATION, VICTORIA UNIVERSITY OF WELLINGTON, NEW ZEALAND. E-mail: edwin.mares@vuw.ac.nz