Agi Kurucz:
Many-dimensional modal logics
Abstract
It is now well-known that the Kripke (or relational) semantics for modal
logic was anticipated by Jonsson and Tarski's work on Boolean algebras
with operators. As a particular case of this connection, various
classes of cylindric set algebras correspond to multimodal logics
characterised by classes of `many-dimensional' frames: the worlds of
these frames are n-tuples, and two such n-tuples are i-related iff
they differ at most in their i-th coordinates.
The accessibility relations resulting this way are equivalence relations.
A natural generalisation of this kind of frames are those relational
structures where
- the worlds are still n-tuples
- the relations between them * still `act coordinate-wise'
* but not necessarily equivalence relations.
Various restrictions on these accessibility relations give rise to
different many-dimensional modal logics. I will give an overview of
axiomatisability and decidability results in this area, and describe
some of the ideas behind the used methods.