Algebra|Coalgebra 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

Project description

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 state-based 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 Algebra|Coalgebra 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 Algebra|Coalgebra project is that we approach with algebra and coalgebra operating in tandem.

People

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 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 Stone-type dualities. He started in November 2006 and hopes to finish in the fall of 2010.

Activities

The A|C group runs a weekly seminar in which group members, guests, or invited speakers present their research: the A|C seminar.

Apart from this, the group organized a number of scientific events, of which the most important were:

A two day workshop on Logic for Coalgebras, on May 10-11, 2007.
A three day workshop on modal fixpoint logic, from March 25-27, 2008.
The fourth International Conference on Topology, Algebra and Categories in Logic, from July 7-11, 2009.

Guests

List of guests to be supplied.