Partial Orders Based on the CS Decomposition

Partial Orders on Partial Isometries

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spac...

Partial orders in rings based on generalized inverses – unified theory

Article history: Received 20 August 2014 Accepted 3 January 2015 Available online xxxx Submitted by Y. Wei MSC: 06A06 15A09 16U99

Revising Partial Pre-Orders with Partial Pre-Orders: A Unit-Based Revision Framework

Belief revision studies strategies about how agents revise their belief states when receiving new evidence. Both in classical belief revision and in epistemic revision, a new input is either in the form of a (weighted) propositional formula or a total pre-order (where the total pre-order is considered as a whole). However, in some real-world applications, a new input can be a partial pre-order ...

Extending Partial Orders to Dense Linear Orders

Automata Theory on Trees and Partial Orders

The paper reviews recent results which aim at generalizing nite automata theory from words and trees to labelled partial orders (presented as labelled directed acyclic graphs), with an emphasis on logical aspects. As an important type of labelled partial order we consider pictures (two-dimensional words). Graph acceptors and their specialization for pictures, \tiling systems", are presented, an...