Coalgebraic Geometric Logic: Basic Theory

Coalgebraic Automata Theory: Basic Results

We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of the theory of coalgebra automata. In particular, we prove the following results for any functor F that preserves weak pullbacks. We show that the class of recognizable languages of F-coalgebras is closed under taking unions, intersections, and projections. We a...

Basic geometric invariant theory

Coalgebraic Logic

We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that innnitary modal logic contains characterizing formulas. That is, every model-world pair is characterized up to bisimulation by an innnitary formula. The point of our generalization is to understand this on a deeper level. We do this by studying a frangm...

Quantum Field Theory and Coalgebraic Logic in Theoretical Computer Science

We suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical dual equivalence between the category of the q-deformed Hopf Coalgebras and the category of the q-deformed Hopf Algebras in quantum field theory (QFT), interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes a QFT system and its mirroring thermal bath, resp...

Coalgebraic Hybrid Logic

We introduce a generic framework for hybrid logics, i.e. modal logics additionally featuring nominals and satisfaction operators, thus providing the necessary facilities for reasoning about individual states in a model. This framework, coalgebraic hybrid logic, works at the same level of generality as coalgebraic modal logic, and in particular subsumes, besides normal hybrid logics such as hybr...