The inseparability graph of an oriented matroid is an invariant of its class of orientations. When an orientable matroid has exactly one class of orientations the inseparability graph of all its orientations is in fact determined by its non-oriented underlying matroid. From this point of view it is natural to ask if inseparability graphs can be used to characterize matroids which have exactly o...

We investigate conjunctive query inseparability of description logic knowledge bases (KBs) with respect to a given signature, a fundamental problem for KB versioning, module extraction, forgetting and knowledge exchange. We develop a game-theoretic technique for checking query inseparability of KBs expressed in fragments of Horn-ALCHI, and show a number of complexity results ranging from P to E...

We present a formal framework for (minimal) module extraction based on an abstract notion of inseparability w.r.t. a signature between ontologies. Two instances of this framework are discussed in detail for DL-Lite ontologies: concept inseparability, when ontologies imply the same complex concept inclusions over the signature, and query inseparability, when they give the same answers to existen...

The partial transposition (PT) operation is an efficient tool in detecting the inseparability of a mixed state. We give an explicit formula for the PT operation for the continuous variable states in Fock space. We then give the necessary and sufficient condition for the positivity of Gaussian operators. Based on this, a number of criteria on the inseparability and distillability for the multimo...

We develop a formal framework for comparing different versions of ontologies, and apply it to ontologies formulated in terms of DL-Lite, a family of ‘lightweight’ description logics designed for data-intensive applications. The main feature of our approach is that we take into account the vocabulary (= signature) with respect to which one wants to compare ontologies. Five variants of difference...

An inseparability criterion based on the total variance of a pair of Einstein-Podolsky-Rosen type operators is proposed for continuous variable systems. The criterion provides a sufficient condition for entanglement of any two-party continuous variable states. Furthermore, for all Gaussian states, this criterion turns out to be a necessary and sufficient condition for inseparability.