In this work we present a new unsupervised and language-independent methodology to detect relations of textual generality, for this, we introduce a particular case of textual entailment (TE), namely Textual Entailment by Generality (TEG). TE aims to capture primary semantic inference needs across applications in Natural Language Processing (NLP). Since 2005, in the TE recognition (RTE) task, systems are asked to automatically judge whether the meaning of a portion of the text, the Text - T, entails the meaning of another text, the Hypothesis - H. Several novel approaches and improvements in TE technologies demonstrated in RTE Challenges are signalling of renewed interest towards a more in-depth and better understanding of the core phenomena involved in TE. In line with this direction, in this work, we focus on a particular case of entailment, entailment by generality, to detect relations of textual generality. In-text, there are different kinds of entailment, yielded from different types of implicative reasoning (lexical, syntactical, common sense based), but here we focus just on TEG, which can be defined as an entailment from a specific statement towards a relatively more general one. Therefore, we have T→GH whenever the premise T entails the hypothesis H, being it also more general than the premise. We propose an unsupervised and language-independent method to recognize TEGs, from a pair 〈T,H〉 having an entailment relation. To this end, we introduce an Informative Asymmetric Measure (IAM) called Simplified Asymmetric InfoSimba (AISs), which we combine with different Asymmetric Association Measures (AAM). In this work, we hypothesize the existence of a particular mode of TE, namely TEG. Thus, the main contribution of our study is to highlight the importance of this inference mechanism. Consequently, the new annotation data seems to be a valuable resource for the community.