We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier $\sf Q$ in ${\rm FO}({\vec Q}_k)$ , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two ${\rm FO}({\vec Q}_1)$ -equivalent models with certain additional structure, yields a pair of ${\rm FO}({\vec Q}_k)$ -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as connectivity (...) and planarity. (shrink)

Vectorization of a class of structures is a natural notion in finite model theory. Roughly speaking, vectorizations allow tuples to be treated similarly to elements of structures. The importance of vectorizations is highlighted by the fact that if the complexity class PTIME corresponds to a logic with reasonable syntax, then it corresponds to a logic generated via vectorizations by a single generalized quantifier (Dawar in J Log Comput 5(2):213–226, 1995). It is somewhat surprising, then, that there have been few (...) systematic studies of the expressive power of vectorizations of various quantifiers. In the present paper, we consider the simplest case: the cardinality quantifiers C S. We show that, in general, the expressive power of the vectorized quantifier logic $${{\rm FO}(\{{\mathsf C}_S^{(n)}\, | \, n \in \mathbb{Z}_+\})}$$ is much greater than the expressive power of the non-vectorized logic FO(C S ). (shrink)

A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig quantifier is not definable by monadic quantifiers. The techniques rely on Ramsey theory.

Intelligent communication processing in English aims to obtain effective information from unstructured text data using various text processing techniques. Text vector representation and text similarity calculation are important fundamental tasks in the whole field of natural language processing. In response to the shortcomings of existing sentence vector representation models and the singularity of text similarity algorithms, improved models and algorithms are proposed based on a thorough study of related domain technologies. This paper presents an in-depth and comprehensive study of text (...) vectorization representation and text similarity calculation algorithms in the field of natural language processing. The existing text vectorized representation models and text similarity computation algorithms are described, and their shortcomings are summarized to provide a basis for the background and significance of this paper, as well as to provide ideas for improvement directions. It is experimentally verified that the sentence vector model proposed in this paper achieves higher accuracy than the SIF sentence vector model for text classification tasks. In the task of text similarity computation, it achieves better results in three evaluation metrics: accuracy, recall, and F1 value. The algorithm also improves the computational efficiency of the model to a certain extent by removing feature words with low feature contribution. The algorithm first improves the deficiencies of the traditional word-shift distance algorithm by defining multifeature fusion weights and realizes a text similarity calculation algorithm based on multifeature weighted fusion with better similarity calculation results. Then, a linear weighting model is constructed to further combine the similarity calculation results of the hierarchical pooled IIG-SIF sentence vectors to realize the multimodel fusion text similarity calculation algorithm. (shrink)

The highly structured mechanisms of cancers, their tendency to occur as a response to environmental stress, and the existence of oncogenes, suggest that neoplasticity may represent more than a biological disfunction. It is proposed that cancer exists as a phylogenetic mechanism serving to promote hyperevolution, albeit at the expense of the ontogeny, that is similar to a process recently discovered in bacterial mutations. Cell-surface-associated nucleic acid in tumorigenic cells and sperm cell vectorization of foreign DNA indicate the existence of (...) essential mechanisms necessary to the occurrence of cancer mediated hyperevolution. An analysis of the proposed mechanism indicates that for mutagenesis of chemical cytology, stress induced neoplasticity confers an evolutionary advantage of more than two orders of magnitude. (shrink)