AlgebraCoalgebra Project
This page concerns the
NWO research project
`Algebra and Coalgebra: the mathematical environments of modal logic',
that is running at University of Amsterdam from September 2006  December
2011 under the supervision of
Yde Venema.
Project description
People
Activities
The theory of modal logic has gained considerable momentum in recent years, and
increasingly, tools and ideas from modal logic have found applications and
generalizations in a wider area.
These developments witness the fact that modal logic lies at a fault line of
two similar but distinct branches of mathematics: algebra and
coalgebra.
Here algebra refers to the tradition in mathematical logic of taking a universal
algebraic perspective on logic, with classes of algebras systematically
encoding certain formal systems of logic.
Coalgebra is a more recent contribution of theoretical computer science, with
universal coalgebra being proposed a general mathematical framework for
modelling statebased evolving systems such as transition systems or
finite automata.
Their interactions in the theory of modal logic are manifestations of a
wider duality between algebra and coalgebra that is both intuitively useful
and mathematically meaningful.
More specifically, the research in the AlgebraCoalgebra project aims at
(further) developing:

the representation and duality theory of ordered algebras as a natural
generalization of the modal theory of notions like canonicity and
correspondence;

the theory of coalgebraic modal logics as uniformly designed languages and
derivation systems for describing and reasoning about behavior and related
notions;

the theory of modal fixpoint logics, these being the natural formalisms
for reasoning about ongoing behavior.
Each of these research directions being characterized by a fascinating mix of
algebraic and coalgebraic aspects, characteristic about the AlgebraCoalgebra
project is that we approach with algebra and coalgebra operating in tandem.
Apart from the principal investigator of the project,
Yde Venema, the
AlgebraCoalgebra project is staffed by two postdoctoral researchers and
three PhD students:
 Vincenzo Ciancia will
start working as a postdoc on the project in January 2010.
He will work on nominal calculi, modal logic and category theory.
 Gaëlle Fontaine
is working on modal fixpoint logics.
She started as a PhD student in November 2006 and hopes to finish in the fall
of 2010.
 Raul Leal
is a PhD student doing research in coalgebraic modal logic and universal
coalgebra.
He started as a PhD student in September 2007 and hopes to finish in the
summer of 2011.
 Alessandra Palmigiano
worked as a postdoc on the project from November 2006 to June 2009. Her
field of expertise is algebraic and coalgebraic logic.
She is currently holding a VENI research grant and is working as an assistant
professor at ILLC.
 Jacob Vosmaer is
doing his PhD research on (co)algebraic logic and Stonetype dualities.
He started in November 2006 and hopes to finish in the fall of 2010.
The AC group runs a weekly seminar in which group members, guests, or invited
speakers present their research: the
AC seminar.
Apart from this, the group organized a number of scientific events, of which
the most important were:
Guests
List of guests to be supplied.