Tuesday 24 May 2005, 16h00, M 111 (Seminar Room)
Abstract
A type of duality - duality via truth - between classes of algebras and
classes of relational systems (frames) is presented. Both classes are
defined axiomatically, so they are presented at the same level of
abstraction. In Stone or Priestley duality theory a class of
algebras is defined in an abstract way with a set of axioms, but
dual spaces can be seen as 'concrete' objects whose definition is
explicitly given. Our approach is to view algebras and frames as
being semantic structures for formal languages. Having a semantics
we are able to define a concept of truth of formulae of a formal
language. A duality principle for establishing duality via truth
says that a given class of algebras and a class of frames provide
equivalent semantics of a formal language whose signature
coincides with the signature of the algebras in question.
Consequently, the algebras and the frames express equivalent
notions of truth. As examples of duality via truth we will consider
two ways of associating a frame with a lattice.
(Joint work with Prof Ewa Orlowska, National Institute of Telecommunications in Warsaw, funded by the NRF and SA-Poland bilateral cooperation.)
© 2005 Vasco Brattka