Translating logic programs into conditional rewriting systems

In this paper a translation from a subclass of logic programs consisting of the simply moded logic programs into rewriting systems is defined. In these rewriting systems conditions and explicit substitutions may be present. We argue that our translation is more natural than previously studied ones and establish a result showing its correctness

On normalisation

Using a characterisation of strongly normalising $lambda$-terms, we give new and simple proofs of the following: all developments and superdevelopments are finite, a certain rewrite strategy is perpetual, a certain rewrite strategy is maximal and thus perpetual, simply typed $lambda$-calculus is strongly normalising

On normalisation

Using a characterisation of strongly normalising $lambda$-terms, we give new and simple proofs of the following: all developments and superdevelopments are finite, a certain rewrite strategy is perpetual, a certain rewrite strategy is maximal and thus perpetual, simply typed $lambda$-calculus is strongly normalising

Weak orthogonality implies confluence: the higher-order case

In this paper we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known `confluence by orthogonality' results

Weak orthogonality implies confluence : the higher-order case

In this paper we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known `confluence by orthogonality' results

Review of the Phenomenology of Noncommutative Geometry

We present a pedagogical review of particle physics models that are based on the noncommutativity of space-time, $[\hat{x}_\mu,\hat{x}_\nu]=i \theta_{\mu \nu}$, with specific attention to the phenomenology these models predict in particle experiments either in existence or under development. We summarize results obtained for high energy scattering such as would occur for example in a future $e^+e^-$ linear collider with $\sqrt{s} = 500 GeV$, as well as low energy experiments such as those pertaining to elementary electric dipole moments and other \cpviolng observables, and finally comment on the status of phenomenological work in cosmology and extra dimensions.Comment: updated, references added, corrected typo

One-loop renormalization of general noncommutative Yang-Mills field model coupled to scalar and spinor fields

We study the theory of noncommutative U(N) Yang-Mills field interacting with scalar and spinor fields in the fundamental and the adjoint representations. We include in the action both the terms describing interaction between the gauge and the matter fields and the terms which describe interaction among the matter fields only. Some of these interaction terms have not been considered previously in the context of noncommutative field theory. We find all counterterms for the theory to be finite in the one-loop approximation. It is shown that these counterterms allow to absorb all the divergencies by renormalization of the fields and the coupling constants, so the theory turns out to be multiplicatively renormalizable. In case of 1PI gauge field functions the result may easily be generalized on an arbitrary number of the matter fields. To generalize the results for the other 1PI functions it is necessary for the matter coupling constants to be adapted in the proper way. In some simple cases this generalization for a part of these 1PI functions is considered.Comment: 1+26 pages, figures using axodraw, clarifications adde