An ordered pair X (R) = (X, R ) consisting of a nonvoid set X and a nonvoid family R of binary relations on X is called a relator space. Relator spaces are straightforward generalizations not only of uniform spaces, but also of ordered sets. Therefore, in a relator space we can naturally define not only some topological notions, but also some order theoretic ones. It turns out that these two, a...

Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown that the orbit generated by successive Local Complementations on a graph can be found within the transform spectra under investigation. The flat spectra of ...

Under the term grammaticalized alternations, we understand changes in valency frames of verbs corresponding to different surface syntactic structures of the same lexical unit of a verb. Czech grammaticalized alternations are expressed either (i) by morphological means (diatheses), or (ii) by syntactic means (reciprocity). These changes are limited to changes in morphemic form(s) of valency comp...

We introduce a project to enhance a valency lexicon of Czech verbs with semantic roles. For this purpose, we make use of FrameNet. At the present stage, frame elements from FrameNet have been mapped to valency complementations of verbs of communication and verbs of exchange. The feasibility of this task has been proven by the achieved inter-annotator agreement – 95.6% for the verbs of communica...

Let v be a vertex of a graph G. By the local complementation of G at v we mean to complement the subgraph induced by the neighbors of v. This operator can be generalized as follows. Assume that, each edge of G has a label in the finite field Fq. Let (gij) be set of labels (gij is the label of edge ij). We define two types of operators. For the first one, let v be a vertex of G and a ∈ Fq, and o...

A generalized DeMorgan's theorem is presented that can be applied to Boolean equations with any number of complementations. The known form of the DeMorgan's theorem is a special case of the generalized theorem with one inversion. This new theorem simplifies and generalizes the transformation of Boolean functions to their equivalent sum of product forms. Two theorems are presented that simplify ...

Complex predicates with light verbs have proven to be very challenging for syntactic theories, particularly due to the tricky distribution of valency complementations of light verbs and predicative nouns (or other predicative units) in their syntactic structure. We propose a theoretically adequate and economical representation of complex predicates with Czech light verbs based on a division of ...

We study the interplay between principal pivot transform (pivot) and loop complementation for graphs. This is done by generalizing loop complementation (in addition to pivot) to set systems. We show that the operations together, when restricted to single vertices, form the permutation group S3. This leads, e.g., to a normal form for sequences of pivots and loop complementation on graphs. The re...

The dichotomy of topic and focus, based, in the Praguean Functional Generative Description, on the scale of communicative dynamism, is relevant not only for a possible placement of the sentence in a context, but also for its semantic interpretation. An automatic identification of topic and focus may use the input information on word order, on the systemic ordering of kinds of complementations (...

A graph H is a vertex-minor of G if it can be reached from by the successive application local complementations and vertex deletions. Vertex-minors have been subject intense study in theory over last decades found applications other fields such as quantum information theory. Therefore natural to consider computational complexity deciding whether given has isomorphic another . Here we prove that...