........................................................................................xiii CHAPTER 1 CONFLUENCE ..................................................................1 1.

We show that non-collapsing orthogonal term rewriting systems do not have the transfinite Church-Rosser property in the setting of Cauchy convergence. In addition, we show that for (a transfinite version of) the Parallel Moves Lemma to hold, any definition of residual for Cauchy convergent rewriting must either part with a number of fundamental properties enjoyed by rewriting systems in the fin...

We investigate the modularity behaviour of termination and connuence properties of conditional term rewriting systems. In particular , we show how to obtain suucient conditions for the modularity of weak termination, weak innermost termination, (strong) innermost termination , (strong) termination, connuence and completeness of conditional rewrite systems.

We investigate the modularity behaviour of termination and connuence properties of (join) conditional term rewriting systems. We give counterexamples showing that the properties weak termination, weak innermost termination and (strong) innermost termination are not preserved in general under signature extensions. Then we develop suucient conditions for the preservation of these properties under...

We present here a new approach to the development of a global land cover map. We combined three existing global land cover maps (MOD12, GLC2000, and UMD) based on the principle that the majority view prevails and validated the resulting map by using information collected as part of the Degree Confluence Project (DCP). We used field survey information gathered by DCP volunteers from 4211 worldwi...

1 I n t r o d u c t i o n Equational specifications can be considered as the programs of an applicat ive programming language with rewriting being its computat ion mechanism. Semantics is assigned to such specification programs using canonical term algebras. Usually all ground germs of the given signature contribute to the construction of the carrier set. Sometimes however it is convenient to i...

We give a relatively simple coinductive proof of confluence, modulo equivalence of root-active terms, of nearly orthogonal infinitary term rewriting systems. Nearly orthogonal systems allow certain root overlaps, but no non-root overlaps. Using a slightly more complicated method we also show confluence modulo equivalence of hypercollapsing terms. The condition we impose on root overlaps is simi...

Recursive definitions can be adequately and conveniently modeled with left-linear conditional term rewriting systems, provided that non-termination, non-trivial critical pairs, and extra variables are admitted. Confluence of such systems guarantees the object-level consistency of the underlying data types. We present a novel sufficient criterion for shallow confluence, a property which is logic...

We prove the confluence and strong normalization properties for second order lambda calculus equipped with an expansive version of -reduction. Our proof technique, based on a simple abstract lemma and a labelled -calculus, can also be successfully used to simplify the proofs of confluence and normalization for first order calculi, and can be applied to various extensions of the calculus present...

iv alpine river confluences. Systematic laboratory experiments were performed in a confluence flume where the main channel is 8.5 m long and 0.50 m wide. A 4.9 m long and 0.15 m wide tributary channel is connected at an angle of 90°. Three discharge scenarios were tested for four different geometrical configurations: a reference case (without widening) and three different tributary widenings: t...