A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the substitution rule has to be modi ed. It is developed here in its minimal form, with equality and conjunction, as partial Horn logic . Various kinds of logical theory are equivalent: partial Horn theories, quasi-equational ...

Cartesian routing is a novel packet routing methodology in which a packet's route is determined by the position of the router relative to that of the destination. Cartesian routing di€ers from existing provider-based unicast routing in that routing tables are unnecessary since communications are topologically dependent, thereby potentially reducing router and network overheads. For example, rou...

The notion of a fractional Cartesian product and a subsequent notion of combinatorial dimension appeared first in a harmonic-analytic context in the course of filling ”analytic” gaps between successive (ordinary) Cartesian products of spectral sets [1, 2]. (Detailed accounts of this, and much more, appear in [4].) Combinatorial dimension is an index of interdependence: attached to a subset of a...

Graph bundles generalize the notion of covering graphs and graph products. In [8], authors constructed an algorithm that ÿnds a presentation as a nontrivial Cartesian graph bundle for all graphs that are Cartesian graph bundles over triangle-free simple base. In [21], the unique square property is deÿned and it is shown that any equivalence relation possessing the unique square property determi...