@ARTICLE{arec:char13,
author = {Areces, C. and Carreiro, F. and Figueira, S.},
title = {Characterization, Definability and Separation via Saturated Models},
journal = {Theoretical Computer Science},
year = {2014},
volume = {537},
pages = {72-86},
abstract = {Three important results about the expressivity of a modal logic L
are the Characterization Theorem (that identifies a modal logic L
as a fragment of a better known logic), the Definability theorem
(that provides conditions under which a class of L-models can be
defined by a formula or a set of formulas of L), and the Separation
Theorem (that provides conditions under which two disjoint classes
of L-models can be separated by a class definable in L).
In this article we provide general conditions under which these results
can be established for a given choice of model class and modal language
whose expressivity is below first order logic. Besides some basic
constrains that most modal logics easily satisfy, the fundamental
condition that we require is that the class of omega-saturated models
in question has the Hennessy-Milner property with respect to the
notion of observational equivalence under consideration.
As the Characterization, Definability and Separation theorems are
among the cornerstones in the model theory of L, this property can
be seen as a test that identifies the adequate notion of observational
equivalence for a particular modal logic.},
owner = {areces},
timestamp = {2013.04.11}
}