Rewrite, rewrite, rewrite, rewrite, rewrite, …

We study properties of rewrite systems that are not necessarily terminating, but allow instead for transfinite derivations that have a limit. In particular, we give conditions for the existence of a limit and for its uniqueness and relate the operational and algebraic semantics of infinitary theories. We also consider sufficient completeness of hierarchical systems

A Multi-Layered Architecture for Collaborative and Decentralized Consequence Finding

The consequence finding problem consists in producing all the consequences of a logical theory or, depending on the application context, in a restricted subset of these consequences. When the available knowledge is naturally scattered among different sources of information, computing such consequences with respect to the global theory in a decentralized way is a challenging problem. This paper presents Somewhere2, a multilayered architecture that may be used to solve such consequence finding problems in peer-to-peer networks of collaborating entities, that may evolve over time. The general layout of this architecture is described as well as the roles of its main components. Thanks to a careful and modular design, the resulting framework is very generic. This facilitates alternative implementations of specific components as well as its extension with additional features. First experimental results are presented, illustrating the scalability and robustness of this architecture. This framework may be used as a robust building block for more advanced distributed applications, such as Peer Data Management Systems

Divergence function of the braided Thompson group

We prove that the braided Thompson group $BV$ has a linear divergence function. By the work of Dru\c{t}u, Mozes, and Sapir, this leads none of asymptotic cones of $BV$ has a cut-point.Comment: 35 pages, 25 figure

Equational term graph rewriting

We present an equational framework for term graph rewriting with cycles. The usual notion of homomorphism is phrased in terms of the notion of bisimulation, which is well-known in process algebra and concurrency theory. Specifically, a homomorphism is a functional bisimulation. We prove that the bisimilarity class of a term graph, partially ordered by functional bisimulation, is a complete lattice. It is shown how Equational Logic induces a notion of copying and substitution on term graphs, or systems of recursion equations, and also suggests the introduction of hidden or nameless nodes in a term graph. Hidden nodes can be used only once. The general framework of term graphs with copying is compared with the more restricted copying facilities embodied in the $mu$-rule, and translations are given between term graphs and $mu$-expressions. Using these, a proo

The Anglo-Scottish Ballad and its Imaginary Contexts

This is the first book to combine contemporary debates in ballad studies with the insights of modern textual scholarship. Just like canonical literature and music, the ballad should not be seen as a uniquely authentic item inextricably tied to a documented source, but rather as an unstable structure subject to the vagaries of production, reception, and editing. Among the matters addressed are topics central to the subject, including ballad origins, oral and printed transmission, sound and writing, agency and editing, and textual and melodic indeterminacy and instability. While drawing on the time-honoured materials of ballad studies, the book offers a theoretical framework for the discipline to complement the largely ethnographic approach that has dominated in recent decades. Primarily directed at the community of ballad and folk song scholars, the book will be of interest to researchers in several adjacent fields, including folklore, oral literature, ethnomusicology, and textual scholarship