All generalisations within logic involve inverting implication. Yet, ever since Plotkin's work in the early 1970's methods of generalising rst-order clauses have involved inverting the clausal subsumption relationship. However , even Plotkin realised that this approach was incomplete. Since inversion of subsumption is central to many Inductive Logic Programming approaches, this form of incomple...

In the current article we present a fast and reliable algorithm for evaluating nth order pentadiagonal determinants in linear time. It is a natural generalization of the DETGTRI algorithm [M. El-Mikkawy, A fast algorithm for evaluating nth order tri-diagonal determinants, J. Comput. Appl. Math. 166 (2004) 581–584]. The algorithm is suited for implementation using computer algebra systems (CAS) ...

Let M be a compact, connected surface, possibly with a finite set of points removed from its interior. Let d, n P N, and let € M be a d-fold covering space of M. We show that the covering map induces an embedding of the nth braid group BnpMq of M in the dnth braid group Bdnp€ Mq of € M, and give several applications of this result. First, we classify the finite subgroups of the nth braid group ...

converges uniformly on compact subsets of the upper half-plane C+ := {z ∈ C : Im z > 0} to a function analytic in C+. Let l(μ) := inf suppμ denote the left boundary of the support of μ, and μn∗ the nth convolution power of μ. The following uniqueness property of nth convolutions of measures from M∞ was discovered in connection with some probabilistic results (see for example [1], [7], [8], [9],...