We extend the expressive power of the region connection calculus RCC-8 by allowing applications of the 8 binary relations of RCC-8 not only to atomic regions but also to Boolean combinations of them. It is shown that the statisfiability problem for the extended language in arbitrary topological spaces is still in NP; however, it becomes PSPACE-complete if only the Euclidean spaces R , n > 0, ar...

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove, that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that ...

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that t...