Here's what the bill aims to achieve, and how it crossed many hurdles en route to becoming law. The Take It Down Act was borne out of the suffering--and then activism--of a handful of teenagers. In October 2023, 14-year-old Elliston Berry of Texas and 15-year-old Francesca Mani of New Jersey each learned that classmates had used AI software to fabricate nude images of them and female classmates. The tools that had been used to humiliate them were relatively new: products of the generative AI boom in which virtually any image could be created with the click of a button. Pornographic and sometimes violent deepfake images of Taylor Swift and others soon spread across the internet.

The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification problems are known to be of limited use for understanding the meaningfulness of models or their relevance. Arguably, they are neither of patterns nor proofs. Further, there are no good measures or representations for analogous concepts in the cognition domain. In this research, the key issues are reflected upon, and a compositional knowledge representation approach in a minimalist general rough framework is proposed for the problem contexts. The latter is general enough to cover most application contexts, and may be applicable in the light of improved computational tools available.

A teacher's knowledge base consists of knowledge of mathematics content, knowledge of student epistemology, and pedagogical knowledge. It has severe implications on the understanding of student's knowledge of content, and the learning context in general. The necessity to formalize the different content knowledge in approximate senses is recognized in the education research literature. A related problem is that of coherent formalizability. Existing responsive or smart AI-based software systems do not concern themselves with meaning, and trained ones are replete with their own issues. In the present research, many issues in modeling teachers' understanding of content are identified, and a two-tier rough set-based model is proposed by the present author for the purpose of developing software that can aid the varied tasks of a teacher. The main advantage of the proposed approach is in its ability to coherently handle vagueness, granularity and multi-modality. An extended example to equational reasoning is used to demonstrate these. The paper is meant for rough set researchers intending to build logical models or develop meaning-aware AI-software to aid teachers, and education research experts.

In October last year Francesa Mani came home from school in the suburbs of New Jersey with devastating news for her mother, Dorota. Earlier in the day the 14-year-old had been called into the vice-principal's office and notified that she and a group of girls at Westfield High had been the victims of targeted abuse by a fellow student. Faked nude images of her and others had been circulating around school. They had been generated by artificial intelligence. Dorota had been tangentially aware of the power of this relatively new technology, but the ease with which the images were generated took her aback.

Francesca Mani and her mother Dorota join'The Ingraham Angle' to demand accountability for victims. Francesca Mani told "The Ingraham Angle" that the principal at Westfield High School recently notified her that she was one of multiple victims. "After that, I just felt, like, betrayed because I never thought it'd be my classmate, and when I came home, I told my mom and I said, 'We need to do something about this because it's not OK, and people are making it seem like it is.'" Mani said she never personally witnessed the explicit images, but that she felt betrayed. Mani said she believes she knows who the main culprit in the dissemination of the images is, but did not mention their name on air.

In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves initially, and interact with their environment subsequently. Examples of the concept, such as those of granular balls, though inadequately defined, algorithmically established, and insufficiently theorized in earlier works by others, are already used in applications of rough sets and soft computing. It is shown that they fit into multiple theoretical frameworks (axiomatic, adaptive, and others) of granular computing. The characterization is intended for algorithm development, application to classification problems and possible mathematical foundations of generalizations of the approach. Additionally, many open problems are posed and directions provided.

In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional meaning that go beyond structural conjunction and disjunction as in the theory of $*$-norms and associated implications over $L$-fuzzy sets. In the present research, algebraic models of acts of combining things in generalized rough sets over lattices with approximation operators (called rough convenience lattices) is invented. The investigation is strongly motivated by the desire to model skeptical or pessimistic, and optimistic or possibilistic aggregation in human reasoning, and the choice of operations is constrained by the perspective. Fundamental results on the weak negations and implications afforded by the minimal models are proved. In addition, the model is suitable for the study of discriminatory/toxic behavior in human reasoning, and of ML algorithms learning such behavior.

A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable artificial intelligence and machine learning). In this research, new concepts of rough randomness that are neither stochastic nor based on properties of strings are introduced by the present author. Her concepts are intended to capture a wide variety of rough processes (applicable to both static and dynamic data), construct related models, and explore the validity of other machine learning algorithms. The last mentioned is restricted to soft/hard clustering algorithms in this paper. Two new computationally efficient algebraically-justified algorithms for soft and hard cluster validation that involve rough random functions are additionally proposed in this research. A class of rough random functions termed large-minded reasoners have a central role in these.

Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between granularity, mereology and approximations in the context. In addition, a framework for rational approximations is introduced by her in the mentioned paper(s). Granular approximations constructed as per the procedures of variable precision rough sets (VPRS) are likely to be more rational than those constructed from a classical perspective under certain conditions. This may continue to hold for some generalizations of the former. However, a formal characterization of such conditions is not available in the previously published literature. In this research, theoretical aspects of the problem are critically examined, uniform generalizations of granular VPRS are introduced, new connections with granular graded rough sets are proved, appropriate concepts of substantial parthood are introduced, their extent of compatibility with the framework is accessed, and the framework is extended. Basic assumptions are explained in detail, and additional examples are constructed for readability. Furthermore, meta applications to cluster validation, image segmentation and dynamic sorting are invented. Extensions to direct generalizations of VPRS such as probabilistic rough sets are a natural consequence of the work.

Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas of generalized closure under up-directedness that may be read as a form of weak consequence. This yields approximation operators that satisfy cautious monotony, while pi-groupoidal approximations (that additionally involve strategic choice and algebraic operators) have nicer properties. The study is primarily motivated by possible structure of concepts in distributed cognition perspectives, real or virtual classroom learning contexts, and student-centric teaching. Rough clustering techniques for datasets that involve up-directed relations (as in the study of Sentinel project image data) are additionally proposed. This research is expected to see significant theoretical and practical applications in related domains.