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t-Representations Of Modal Logics
by
Alexei Muravitsky
Northwestern State University
We consider the consistent logics in the lattice ExtS4 in relation to their assertoric consistent companions from the lattice ExtInt. We examine t-representations of logics in ExtS4, that is, equalities M=M*+tr(M), where M* ∈ [S4, Grz] and is called a modal component of M. We prove that all modal components of M have a special location in [S4, Grz]. Also, we show that the existence of a least modal component of M depends on whether a pseudo-difference (a modification of Rauzser's pseudo-complement) is defined in that location.
Date received: April 15, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caug-05.