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
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
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 state-based evolving systems such as transition systems or
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 Algebra|Coalgebra project aims at
Each of these research directions being characterized by a fascinating mix of
algebraic and coalgebraic aspects, characteristic about the Algebra|Coalgebra
project is that we approach with algebra and coalgebra operating in tandem.
the representation and duality theory of ordered algebras as a natural
generalization of the modal theory of notions like canonicity and
the theory of coalgebraic modal logics as uniformly designed languages and
derivation systems for describing and reasoning about behavior and related
the theory of modal fixpoint logics, these being the natural formalisms
for reasoning about ongoing behavior.
Apart from the principal investigator of the project,
Yde Venema, the
Algebra|Coalgebra project is staffed by two post-doctoral researchers and
three PhD students:
- Vincenzo Ciancia will
start working as a post-doc 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
- Raul Leal
is a PhD student doing research in coalgebraic modal logic and universal
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 Stone-type dualities.
He started in November 2006 and hopes to finish in the fall of 2010.
The A|C group runs a weekly seminar in which group members, guests, or invited
speakers present their research: the
Apart from this, the group organized a number of scientific events, of which
the most important were:
List of guests to be supplied.