Mani A.

Mani A.
  • Ph.d, M.Sc, B.Sc., PGD,
  • Senior Member at International Rough Set Society

About

164
Publications
18,985
Reads
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862
Citations
Introduction
A. Mani is a leading researcher on rough sets, algebra, logic, rough sets, AIML, vagueness, mereology and FOM. Her interests include algebraic semantics, granularity, clustering, other formal approaches to vagueness, education research and gender studies. She is a research scientist at ISI, Kolkata, a senior member (elected) of the International Rough Set Society and was a visiting faculty at HBCSE, TIFR Mumbai till recently. Her homepage is at https://www.logicamani.in
Current institution
International Rough Set Society
Current position
  • Senior Member
Additional affiliations
Indian Statistical Institute
Position
  • Woman Scientist
March 2012 - present
University of Calcutta
Position
  • Researcher
January 2001 - present
Rough Sets, Algebra and Logic, Kolkata India
Position
  • Researcher

Publications

Publications (164)
Chapter
Antichain based semantics for general rough sets was introduced recently by the present author. In her paper two different semantics, one for general rough sets and another for general approximation spaces over quasi-equivalence relations, were developed. These semantics are improved and studied further from a lateral algebraic logic and an algebra...
Book
This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the boo...
Chapter
In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic sem...
Article
Full-text available
Rough sets are used in numerous knowledge representation contexts, and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalizations of graded and variable precision rough sets are investigated by the present author from the pe...
Chapter
Several types of ethnomathematics are studied in the literature, and they come with their own questions, problems of representation, and classification. Approximate reasoning or rather reasoning over vaguely defined entities (real or abstract), and uncertain information is natural to ethnomathematics, and human interactions. The main issue is one o...
Article
The collective concept of clean rough randomness (C-rough randomness), with the explicit purpose of handling meaning in vague and dynamic contexts of rough reasoning (and therefore meaningful artificial intelligence and machine learning), is recently introduced by the present author. These ideas are applied to propose validation methods for soft an...
Poster
Full-text available
Granular rough sets (GRST) from axiomatic algebraic perspective perspectives are potentially capable of solving the problem of meaning in AI (specifically generative AI) through the following specific interrelated methodologies: 1. Representations of dependence between subsets of attributes by other subsets of attributes (and a related new theory o...
Article
Anthropomorphic perspectives are frequently used to represent or misrepresent information concerning living, and non-living entities, particularly in sociology, biology, and artificial intelligence. Formal models of related approximate reasoning patterns are of natural interest, given the research trends in the last-mentioned area. In this research...
Article
Full-text available
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. Arguabl...
Presentation
Full-text available
This talk is intended to cover aspects of research on applications of mereological methods and general rough sets to problems in education research due to the present author. Specifically, her talk features a broad introduction to mereology, and applications to modeling students' and teachers' languages of discourse, and STEM. Further research dire...
Preprint
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. Arguabl...
Presentation
Full-text available
It is known that LBTQIA+ people experience much harassment, discrimination, and marginalization in the STEM ecosystem in India. This talk is about issues in policymaking and related interventions in the light of their lived experiences, and related theoretical insights. [Note: Some of the slides were used in the invited talk].
Article
Full-text available
The concept of clean rough randomness (C-rough randomness), with the explicit purpose of handling meaning in vague and dynamic contexts of rough reasoning (and therefore meaningful artificial intelligence and machine learning), is recently introduced by the present author. These ideas are applied to propose validation methods for soft and hard clus...
Presentation
Full-text available
(Full Version of my ICME-15 Slides: I used about 23 slides in my talk.) Abstract: Mereology is the study of parts, wholes, related predicates and predications. While the subject finds wide application in specialized areas, it has not been explored in matching depth in education research, and specifically in mathematics education. A recent paper, d...
Research
MR4461095 03-02 03B52 03G27 08C20 Bonzio, Stefano (I-CAGL-MI) ; Paoli, Francesco (I-CAGL-PPQ) ; Pra Baldi, Michele (E-CSIC-AI) FLogics of variable inclusion. Trends in Logic—Studia Logica Library, 59. Springer, Cham, [2022],
Article
Full-text available
Article
Full-text available
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 appr...
Conference Paper
Full-text 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...
Article
Concepts of precision are used in different contexts in various senses. While every case has re- lated structural properties associated, only some are justifiably quantifiable in terms of real num- bers. For example, an ancient Egyptian limestone sculpture may be said to be precisely sculpted with great skill using simple tools. The idea of precisi...
Conference Paper
Full-text available
A number of generalizations of stochastic and information-theoretic randomness are known in the literature. In earlier research, it is shown by the present author and others that probabilistic methods are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore meaningful AIML) [1, 2]. Based on these, new...
Article
Full-text available
Five of my recent reviews for AMS Mathematical Reviews.
Chapter
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 implic...
Chapter
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 ball...
Article
Full-text available
Mereology is the study of parts, wholes, related predicates and predications. While the subject finds wide application in specialized areas, it has not been explored in matching depth in education research, and specifically in mathematics education. A recent paper, due to the present author, explores potential areas of development for STEAM, in gen...
Article
Full-text available
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 implicat...
Article
Full-text available
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 ball...
Preprint
Full-text available
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 ball...
Preprint
Full-text available
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 implicat...
Article
Full-text available
Several methods of approximate reasoning are known, and many remain to be discovered across domains. Some are tied to reasoning with uncertainty. The developments over the last fifty years or so in the development of approximate reasoning methods, and their application across multiple STEM domains, suggest that it is necessary to introduce them ear...
Conference Paper
Full-text available
Extended abstract: Several methods of approximate reasoning are known, and many remain to be discovered across domains. Some are tied to reasoning with uncertainty. The developments over the last fifty years or so in the development of approximate reasoning methods, and their application across multiple STEM domains, suggest that it is necessary to...
Article
Full-text available
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 neit...
Preprint
Full-text available
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 neit...
Article
Rough sets are used in a number of knowledge representation contexts, and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalizations of graded and variable precision rough sets are investigated by the present author from the...
Conference Paper
Full-text available
A phenomenon is stochastically random if it has probabilistic regularity in the absence of other types of regularity [1]. On the other hand, a sequence is algorithmically random if and only if no computational agent recognizes it as possessing some rare property (that is, properties valid over a set of measure zero that could be tested in a suffici...
Chapter
The concept of rational discourse is typically determined by subjective, normative, and rule based constraints in the context under consideration. It is typically determined by related ontologies, and coherence between associated concepts employed in the discourse. Classical rough approximations, and variants of variable precision rough sets (VPRS)...
Article
Full-text available
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 appr...
Preprint
Full-text available
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 appr...
Preprint
Full-text available
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 appr...
Article
Full-text available
Rational approximations are introduced and studied in granular graded 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, parthood perspective and approximations used in the context. In addition, a framework is introduced by...
Conference Paper
Full-text available
Mereology is widely applied in STEAM and philosophy. However, serious applications tend to be restricted to specialist groups or the nature of applications is too focused. In addition, methodologies associated do not percolate to school or college-level classroom discourses in a clear way. This is worrying because mereology can be used for effectiv...
Preprint
Full-text available
Rational approximations are introduced and studied in granular graded 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, parthood perspective and approximations used in the context. In addition, a framework is introduced by...
Presentation
Full-text available
Compositionality is essential for reducing the complexity of AIML models. This is naturally related to knowledge representation and granularity. These, in turn, can be done in different ways. Also, approximate reasoning and decision-making essentially involve knowledge representation and granularity. In the talk, the following topics will be review...
Article
Full-text available
The concept of rational discourse is typically determined by subjective, normative, and rule based constraints in the context under consideration. It is typically determined by related ontologies, and coherence between associated concepts employed in the discourse. Classical rough approximations, and variants of variable precision rough sets (VPRS)...
Article
In this research, directed and parthood relations are studied in the context of general rough sets. This extends earlier work on directed approximation spaces. The relations are also specialized to representations of general parthood that are upper-directed, reflexive and anti-symmetric for a better behaved groupoidal semantics over the set of roug...
Article
Full-text available
A number of numeric measures like rough inclusion functions (RIFs) are used in general rough sets and soft computing. But these are often intrusive by definition, and amount to making unjustified assumptions about the data. The contamination problem is also about recognizing the domains of discourses involved in this, specifying errors and reducing...
Conference Paper
Full-text available
Of the many generalizations of rough sets in the literature, graded rough sets are among the most controversial. When approached from a pointwise perspective, these are closely related to graded modal logic. In this research, a few granular generalizations are proposed by the present author. Some mistakes in the literature are rectified, and defina...
Conference Paper
In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). \emph{It is well-known that...
Chapter
In this research a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). It is well-known that of the...
Preprint
Full-text available
A number of numeric measures like rough inclusion functions (RIFs) are used in general rough sets and soft computing. But these are often intrusive by definition, and amount to making unjustified assumptions about the data. The contamination problem is also about recognizing the domains of discourses involved in this, specifying errors and reducing...
Conference Paper
Full-text available
Diversity-friendly and inclusive practices, in the Indian context, are hindered by a spectrum of issues ranging from machinations of the patriarchy sustained by systems of microaggressions, policies disconnected from stakeholders, missing support systems, unscientific colonial mindset of people, hubris of societal norms, and ineffective policies am...
Article
This is the much extended version of my IFSA-EUSFLAT'2021 paper.
Conference Paper
Full-text available
It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the present research, a proposal based on mereological principles is advanced towards solving aspects of the problem by...
Article
It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the present research, a proposal based on mereological principles is advanced towards solving aspects of the problem by...
Preprint
Full-text available
In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). \emph{It is well-known that...
Chapter
Full-text available
Tabular representation of information can be traced to ancient times. They were and are used in a wide variety of ways. While every table is essentially a list, their interpretation varies from the simpler to the very complex. This aspect is explored in some detail by the present author. Based on the considerations, she suggests a number of ways of...
Conference Paper
Full-text available
Concepts of granules and granular computing have evolved from a number of perspectives over the last few decades. In this short expository paper, the present author discusses aspects of Zadeh’s contributions to a specific form of granular computing especially in the contexts of fuzzy sets, computing with words, and AI. Further she mentions new area...
Conference Paper
Full-text available
Education research is a relatively young field with a history that goes back to about 100 years or so. Work done in various parts of the world has contributed to a better understanding of the complexity of associated problems, and their related social context. But most teachers and academics are not aware of methodologies and issues in teaching, an...
Poster
Full-text available
It is well-known that concepts of cluster validity and associated rationale are far from being satisfactory from multiple perspectives. Indices are usually controversial. The scope of a model based approach from a statistical, mereo-topological, graph-theoretical, neural network or soft perspective, for example, is apparently limited by methodologi...
Article
In this research a general theoretical framework for abstract clustering is proposed from a philosophical perspective of increasing semantic assumptions over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realize...
Research
Full-text available
Post publication review of the following papers: 1. MR3958325 03G27 03C05 03D15 08B05 Moraschini, Tommaso (CZ-AOS-IC) On the complexity of the Leibniz hierarchy. (English summary) Ann. Pure Appl. Logic 170 (2019), no. 7, 805–824. 2. MR4027123 03E72 Wu, Hsien-Chung (RC-NKNU-M) Generalized extension principle for non-normal fuzzy sets. (English summ...
Book
The book is intended to introduce general rough methods from a relatively philosophical perspective to researchers in the field of education.
Book
The purpose of this book is to serve as an advanced introduction to issues of gender diversity in STEM education, pedagogical practices, and related research areas.
Chapter
In the context of education research, a concept inventory is an instrument (that consists of a number of multiple-choice questions) designed to test the understanding of concepts (and possibly the reasons for failure to understand) by learners. Subject to a few caveats they are known to be somewhat effective in non student centric learning environm...
Chapter
A number of low and high-level models of general rough sets can be used to represent knowledge. Often binary relations between attributes or collections thereof have deeper properties related to decisions, inference or vision that can be expressed in ternary functional relationships (or groupoid operations) – this is investigated from a minimalist...
Chapter
A number of nonequivalent perspectives on granular computing are known in the literature, and many are in states of continuous development. Further, related concepts of granules and granulations may be incompatible in many senses. This expository paper is intended to explain basic aspects of these from a critical perspective, their range of applica...
Preprint
Full-text available
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general parthood that are upper-directed, reflexive and antisymmetric for a better behaved groupoidal semantics over...
Conference Paper
Full-text available
A number of low and high-level models of general rough sets can be used to represent knowledge. Often binary relations between attributes or collections thereof have deeper properties related to decisions, inference or vision that can be expressed in ternary functional relationships (or groupoid operations)-- this is investigated from a minimalist...
Conference Paper
Full-text available
In the context of education research, a concept inventory is an instrument (that consists of a number of multiple-choice questions) designed to test the understanding of concepts (and possibly the reasons for failure to understand) by learners. Subject to a few caveats they are known to be somewhat effective in non student centric learning environm...
Presentation
Full-text available
Microaggressions are small, subtle, often subconscious actions that marginalize people in oppressed groups including women. Sue (1973) defined it as brief and commonplace daily verbal, behavioral, or environmental indignities, whether intentional or unintentional, that communicate hostile, derogatory, or negative racial slights and insults. It can...
Poster
Full-text available
Presentation
Full-text available
It is well-known that the participation of women in STEM disciplines at higher levels has been relatively bad across multiple demographics. The situation is due to systemic discrimination that has been and is couched in different ways in and outside the academia. The proof of systemic discrimination is in actualizations that span cultural practices...
Poster
Full-text available
Call for Participation https://www.fedcsis.org/2020/fvrm
Preprint
Full-text available
It is well-known that lesbians, trans and queer women face considerable discrimination, exclusion, stigmatization, and abuse in India. That is over and above the misogyny and discrimination faced by women in the patriarchal country. LGBTQIA people were also criminalized by law till recently. In spite of all the oppression and discrimination, lesbia...
Article
This is an extended version of https://www.researchgate.net/publication/329043829_Granularity_and_Generalized_Inclusion_Functions_-_Their_Variants_and_Contamination
Article
Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this research, the semantics of rough contact relations are studied in detail. Rough mereologies are also situated in re...
Article
Full-text available
[See ArXiv for newer version http://arxiv.org/abs/1811.06560 ] Granular operator spaces and variants had been introduced and used in theoretical investigations on the foundations of general rough sets by the present author over the last few years. In this research, higher order versions of these are presented uniformly as partial algebraic systems....
Preprint
Full-text available
Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this research, concepts of rough contact relations are introduced and rough mereologies are situated in relation to gene...
Article
It is well-known that lesbians, trans and queer women face considerable discrimination, exclusion, stigmatization, and abuse in India. That is over and above the misogyny and discrimination faced by women in the patriarchal country. LGBTQIA people were also criminalized by law till recently. In spite of all the oppression and discrimination, lesbia...
Conference Paper
Full-text available
Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this research, concepts of rough contact relations are introduced and rough mereologies are situated in relation to gene...
Conference Paper
Full-text available
Exclusion definitely affects a women’s mathematics. Some classification of the factors that shape the unique features associated can definitely be specified. On the basis of these considerations I propose a new partial theoretical model for accessing the connection between a woman's attitude towards and practice of research in mathematics, and the...
Poster
Full-text available
Special Session cum Workshop on "Generalized Rough Inclusion, Graded Inclusion, Granularity and Related Topics" at IJCRS'2019, Debrecen, Hungary
Article
Study of concepts of dependence in general rough sets had been initiated by the present author in some of her recent papers. These have been compared with possible concepts of dependence in generalized probability theory and a new deviant probability framework has also been the result of such an approach. In this research, the mereological content...
Article
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of translating between the methodologies and possibilities in the identification of concepts. Comparison of ideas...
Chapter
Full-text available
In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic sem...
Preprint
Full-text available
Granular operator spaces and variants had been introduced and used in theoretical investigations on the foundations of general rough sets by the present author over the last few years. In this research, higher order versions of these are presented uniformly as partial algebraic systems. They are also adapted for practical applications when the data...
Preprint
Full-text available
Rough inclusion functions (RIFs) are known by many other names in formal approaches to vagueness, belief, and uncertainty. Their use is often poorly grounded in factual knowledge or involve wild statistical assumptions. The concept of contamination introduced and studied by the present author across a number of her papers, concerns mixing up of inf...
Article
Full-text available
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of translating between the methodologies and possibilities in the identification of concepts. Comparison of ideas...
Chapter
Granules are the building blocks of concepts of different types in soft computing and rough sets in particular. These granules can be defined in ways that are related to computing or reasoning strategies associated. In this broad perspective, at least three concepts of granular computing have been studied in the literature. The axiomatic approach i...
Chapter
In this research chapter, dualities and representations of various kinds associated with the semantics of rough sets are explained, critically reviewed, new proofs have been proposed, open problems are specified and new directions are suggested. Some recent duality results in the literature are also adapted for use in rough contexts. New results ar...
Article
The problem of formalizing rationality of reasoning in AI is mostly handled from the perspective of formal epistemology and modal logics associated with multi agent systems that refer concepts of common knowledge. These differ significantly from ideas of instrumental rationality that is concerned with rationality for a purpose. Many approaches in A...
Article
Full-text available
Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the inverse problem. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present aut...
Conference Paper
Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the inverse problem. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present aut...
Presentation
Full-text available
Beamer Slides of my paper in Special Session on Foundations of Rough Sets, Vagueness and Mereology at IJCRS’2017

Questions

Questions (6)
Question
Why is the project title so generic and non specific?
Question
Recently it has been observed that people without 90% of their brain can still be conscious and pretty normal.
This suggests the brain is continually learning to update itself about its own activities even when neurons are being lost
Question
Am more interested in answers relating to general topology.

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