There is a natural partial ordering of defaults in inheritance systems that resolves ambiguities in an intuitive way. This is not the shortest-path ordering used by most existing inheritance reasoners. The flaws of the shortest-path ordering become apparent when we consider multiple inheritance. We define the correct partial ordering to use in inheritance and show how it applies to semantic net...

LexLeader, a state of the art static symmetry breaking method, adds a lex ordering constraint for each variable symmetry of the problem to select the lexicographically least solution. In practice, the same method can also be used for partial symmetry breaking by breaking only a given subset of symmetries. We propose a new total ordering, reflex, as basis of a new symmetry breaking constraint th...

Stȩpniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner partial order of nonnegative definite matrices and the Löwner partial order of squares of those matrices. The paper was an important starting point for investigations of the problem of how an order between two matrices A and B from different sets of matrices can be preserved for the squares of the cor...

We take another look at two compounds which have been discussed as possible realizations of “spin ice”, namely holmium titanate and dysprosium titanate. As we have earlier observed, holmium titanate does not display icelike behaviour at low temperatures because the long ranged dipolar interactions between spins are strong compared to the nearest neighbour interactions. We show, analytically, th...

We elaborate Weiermann-style phase transitions for Gordeev well-quasi-ordering (called well-partial-ordering below, abbr.: wpo) results with respect to nested finite sequences and nested finite trees under the homeomorphic embedding with symmetrical gap condition. For every nested partial ordering in question, E, we fix a natural extension of Peano Arithmetic, T, that proves the corresponding 2...

We present partial-tree linearization, a generalized word ordering (i.e. ordering a set of input words into a grammatical and fluent sentence) task for text-to-text applications. Recent studies of word ordering can be categorized into either abstract word ordering (no input syntax except for POS) or tree linearization (input words are associated with a full unordered syntax tree). Partial-tree ...

IV. Two-Site Electron Transfer Generalized Master Equation I: Chronological Ordering Prescription Generalized Master Equation 11: Partial Ordering Prescription Second-Order Rate Kernel: Partial Ordering Prescription 1. 2. Transition from Nonadiabatic to Adiabatic Rate Kernel 1. 2. Frequency-Dependent Transmission Coefficient Time-Dependence of the Rate Kernel Energy Gap Dependence of the Rate K...