Search

Your search keyword '"BANERJEE, MOHUA"' showing total 321 results
Start Over Author "BANERJEE, MOHUA"

Refine your results

321 results on '"BANERJEE, MOHUA"'

1. A non-distributive logic for semiconcepts of a context and its modal extension with semantics based on Kripke contexts

Author

Howlader, Prosenjit and Banerjee, Mohua

Subjects
Mathematics - Logic, 06E25, 03G10, 03B45, 03B47
Abstract

A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational semantics for \textbf{PDBL} is next proposed, where any formula is interpreted as a semiconcept of a context. For \textbf{MPDBL}, the relational semantics is based on Kripke contexts, and a formula is interpreted as a semiconcept of the underlying context. The systems are shown to be sound and complete with respect to the relational semantics. Adding appropriate sequents to \textbf{MPDBL} results in logics with semantics based on reflexive, symmetric or transitive Kripke contexts. One of these systems is a logic for topological pure double Boolean algebras. It is demonstrated that, using \textbf{PDBL}, the basic notions and relations of conceptual knowledge can be expressed and inferences involving negations can be obtained. Further, drawing a connection with rough set theory, lower and upper approximations of semiconcepts of a context are defined. It is then shown that, using the formulae and sequents involving modal operators in \textbf{MPDBL}, these approximation operators and their properties can be captured.

Published
2022

2. Kripke Contexts, Double Boolean Algebras with Operators and Corresponding Modal Systems

Author

Howlader, Prosenjit and Banerjee, Mohua

Subjects
Mathematics - Logic, 06E25, 03Gxx, 03G05, 03B60, 03B45
Abstract

The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M,I), a relation on the set G of objects and a relation on the set M of properties are included, giving a structure of the form ((G,R), (M,S), I). A Kripke context gives rise to complex algebras based on the collections of protoconcepts and semiconcepts of the underlying context. On abstraction, double Boolean algebras (dBas) with operators and topological dBas are defined. Representation results for these algebras are established in terms of the complex algebras of an appropriate Kripke context. As a natural next step, logics corresponding to classes of these algebras are formulated. A sequent calculus is proposed for contextual dBas, modal extensions of which give logics for contextual dBas with operators and topological contextual dBas. The representation theorems for the algebras result in a protoconcept-based semantics for these logics., Comment: To appear in Journal of Logic Language and Information

Published
2022

3. Topological Representation of Double Boolean Algebras

Author

Howlader, Prosenjit and Banerjee, Mohua

Subjects
Mathematics - Logic, Mathematics - Rings and Algebras, 06B15, 06D50, 06E15, 06E75
Abstract

In formal concept analysis, the collection of protoconcepts of any context forms a double Boolean algebra (dBa) which is fully contextual. Semiconcepts of a context form a pure dBa. The present article is a study on topological representation results for dBas, and in particular, those for fully contextual and pure dBas. In this work, a context on topological spaces (CTS) is considered, and the focus is on a special kind of CTS in which the relation defining the context as well as the converse of the relation are continuous with respect to the topologies. Such CTS are denoted as CTSCR. It is observed that clopen object oriented protoconcepts of a CTSCR form a fully contextual dBa, while clopen object oriented semiconcepts form a pure dBa. Every dBa is shown to be quasi-embeddable into the dBa of clopen object oriented protoconcepts of a particular CTSCR. The quasi-embedding turns into an embedding in case of a contextual dBa, and into an isomorphism, when the dBa is fully contextual. For pure dBas, one obtains an isomorphism with the algebra of clopen object oriented semiconcepts of the CTSCR. Representation of finite dBas and Boolean algebras are also addressed in the process. Abstraction of properties of this CTSCR leads to the definition of Stone contexts. Stone contexts and CTSCR- homeomorphisms are seen to form a category, denoted Scxt. Furthermore, correspondences are observed between dBa isomorphisms and CTSCR-homeomorphisms. This motivates a study of categorical duality of dBas, constituting the second part of the article. Pure dBas and fully contextual dBas along with dBa isomorphisms form categories, denoted PDBA and FCDBA respectively. It is established that PDBA is equivalent to FCDBA, while FCDBA and PDBA are dually equivalent to Scxt., Comment: 40 pages, 2 figures

Published
2021

4. Paraconsistent Logics: A Survey Focussing on the Rough Set Approach

Author

Saha, Bidhan, Banerjee, Mohua, Dutta, Soma, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Campagner, Andrea, editor, Urs Lenz, Oliver, editor, Xia, Shuyin, editor, Ślęzak, Dominik, editor, Wąs, Jarosław, editor, and Yao, JingTao, editor

Published
2023
Full Text
View/download PDF

6. Contrapositionally Complemented Pseudo-Boolean Algebras and Intuitionistic Logic with Minimal Negation

Author

More, Anuj Kumar and Banerjee, Mohua

Subjects
Mathematics - Logic, 03B60 (Primary), 06D20, 03B20, 03G10 (Secondary), F.4.1
Abstract

The article is a study of two algebraic structures, the `contrapositionally complemented pseudo-Boolean algebra' (ccpBa) and `contrapositionally $\vee$ complemented pseudo-Boolean algebra' (c$\vee$cpBa). The algebras have recently been obtained from a topos-theoretic study of categories of rough sets. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. We study properties of these algebras, give examples, and compare them with relevant existing algebras. `Intuitionistic Logic with Minimal Negation (ILM)' corresponding to ccpBas and its extension ILM-${\vee}$ for c$\vee$cpBas, are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce's logic. With a focus on properties of the two negations, two kinds of relational semantics for ILM and ILM-${\vee}$ are obtained, and an inter-translation between the two semantics is provided. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn's logical framework for the purpose, two logics $K_{im}$ and $K_{im-{\vee}}$ are presented, where the language does not include implication. $K_{im}$-algebras are reducts of ccpBas. The negations in the algebras are shown to occupy distinct positions in an enhanced form of Dunn's Kite of negations. Relational semantics for $K_{im}$ and $K_{im-{\vee}}$ are given, based on Dunn's compatibility frames. Finally, relationships are established between the different algebraic and relational semantics for the logics defined in the work., Comment: 36 pages

Published
2020

10. Zdzisław Pawlak and Our Journey with Rough Sets

Author

Banerjee, Mohua, Chakraborty, Mihir K., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Peters, James F., editor, Skowron, Andrzej, editor, Bhaumik, Rabi Nanda, editor, and Ramanna, Sheela, editor

Published
2022
Full Text
View/download PDF

12. Rough Sets and the Algebra of Conditional Logic

Author

Panicker, Gayatri, Banerjee, Mohua, Hutchison, David, Editorial Board Member, Kanade, Takeo, Editorial Board Member, Kittler, Josef, Editorial Board Member, Kleinberg, Jon M., Editorial Board Member, Mattern, Friedemann, Editorial Board Member, Mitchell, John C., Editorial Board Member, Naor, Moni, Editorial Board Member, Pandu Rangan, C., Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Terzopoulos, Demetri, Editorial Board Member, Tygar, Doug, Editorial Board Member, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Mihálydeák, Tamás, editor, Min, Fan, editor, Wang, Guoyin, editor, Banerjee, Mohua, editor, Düntsch, Ivo, editor, Suraj, Zbigniew, editor, and Ciucci, Davide, editor

Published
2019
Full Text
View/download PDF

15. Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras

Author

Howlader, Prosenjit, Banerjee, Mohua, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Bello, Rafael, editor, Miao, Duoqian, editor, Falcon, Rafael, editor, Nakata, Michinori, editor, Rosete, Alejandro, editor, and Ciucci, Davide, editor

Published
2020
Full Text
View/download PDF

16. Kleene Algebras and Logic: Boolean and Rough Set Representations, 3-valued, Rough and Perp Semantics

Author

Kumar, Arun and Banerjee, Mohua

Subjects
Mathematics - Logic
Abstract

A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with the Kleene property (called the `Kleene negation') always arises from the set theoretic complement. The corresponding propositional logic is then studied through a 3-valued and rough set semantics. It is also established that Kleene negation can be considered as a modal operator, and enables giving a perp semantics to the logic. One concludes with the observation that all the semantics for this logic are equivalent.

Published
2015

19. Transformation Semigroups for Rough Sets

Author

More, Anuj Kumar, Banerjee, Mohua, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Nguyen, Hung Son, editor, Ha, Quang-Thuy, editor, Li, Tianrui, editor, and Przybyła-Kasperek, Małgorzata, editor

Published
2018
Full Text
View/download PDF

20. Algebras from Semiconcepts in Rough Set Theory

Author

Howlader, Prosenjit, Banerjee, Mohua, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Nguyen, Hung Son, editor, Ha, Quang-Thuy, editor, Li, Tianrui, editor, and Przybyła-Kasperek, Małgorzata, editor

Published
2018
Full Text
View/download PDF

24. A Semantic Analysis of Stone and Dual Stone Negations with Regularity

Author

Kumar, Arun, Banerjee, Mohua, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Ghosh, Sujata, editor, and Prasad, Sanjiva, editor

Published
2017
Full Text
View/download PDF

25. New Algebras and Logic from a Category of Rough Sets

Author

More, Anuj Kumar, Banerjee, Mohua, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Polkowski, Lech, editor, Yao, Yiyu, editor, Artiemjew, Piotr, editor, Ciucci, Davide, editor, Liu, Dun, editor, Ślęzak, Dominik, editor, and Zielosko, Beata, editor

Published
2017
Full Text
View/download PDF

30. Labelled Calculi for the Logics of Rough Concepts

Author

van der Berg, Ineke, De Domenico, Andrea, Greco, Giuseppe, Manoorkar, Krishna B., Palmigiano, Alessandra, Panettiere, Mattia, Banerjee, Mohua, Sreejith, A.V., Ethics, Governance and Society, Banerjee, Mohua, and Sreejith, A.V.

Subjects
Non-distributive modal logic, Rough formal contexts, Labelled calculi, Proof calculi
Abstract

We introduce sound and complete labelled sequent calculi for the basic normal non-distributive modal logic and some of its axiomatic extensions, where the labels are atomic formulas of the first order language of enriched formal contexts, i.e., relational structures based on formal contexts which provide complete semantics for these logics. We also extend these calculi to provide a proof system for the logic of rough formal contexts.

Published
2023

31. Labelled Calculi for Lattice-Based Modal Logics

Author

van der Berg, Ineke, De Domenico, Andrea, Greco, Giuseppe, Manoorkar, Krishna B., Palmigiano, Alessandra, Panettiere, Mattia, Banerjee, Mohua, Sreejith, A.V., Banerjee, Mohua, Sreejith, A.V., and Ethics, Governance and Society

Subjects
Algorithmic correspondence theory, Non-distributive modal logic, Algorithmic proof theory, Labelled calculi
Abstract

We introduce labelled sequent calculi for the basic normal non-distri-butive modal logic and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of the algebras in the variety corresponding to the logic. Modular proofs are presented that these calculi are all sound, complete and conservative w.r.t, and enjoy cut elimination and the subformula property. The introduction of these calculi showcases a general methodology for introducing labelled calculi for the class of LE-logics and their analytic axiomatic extensions in a principled and uniform way.

Published
2023

33. Possibilistic vs. Relational Semantics for Logics of Incomplete Information

Author

Banerjee, Mohua, Dubois, Didier, Godo, Lluis, Junqueira Barbosa, Simone Diniz, editor, Chen, Phoebe, editor, Cuzzocrea, Alfredo, editor, Du, Xiaoyong, editor, Filipe, Joaquim, editor, Kara, Orhun, editor, Kotenko, Igor, editor, Sivalingam, Krishna M., editor, Ślęzak, Dominik, editor, Washio, Takashi, editor, Yang, Xiaokang, editor, Laurent, Anne, editor, Strauss, Olivier, editor, Bouchon-Meunier, Bernadette, editor, and Yager, Ronald R., editor

Published
2014
Full Text
View/download PDF

38. Definable and Rough Sets in Covering-Based Approximation Spaces

Author

Kumar, Arun, Banerjee, Mohua, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Li, Tianrui, editor, Nguyen, Hung Son, editor, Wang, Guoyin, editor, Grzymala-Busse, Jerzy, editor, Janicki, Ryszard, editor, Hassanien, Aboul Ella, editor, and Yu, Hong, editor

Published
2012
Full Text
View/download PDF

39. Information Systems and Rough Set Approximations: An Algebraic Approach

Author

Khan, Md. Aquil, Banerjee, Mohua, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Kuznetsov, Sergei O., editor, Mandal, Deba P., editor, Kundu, Malay K., editor, and Pal, Sankar K., editor

Published
2011
Full Text
View/download PDF

40. A Study of Multiple-Source Approximation Systems

Author

Khan, Md. Aquil, Banerjee, Mohua, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Peters, James F., editor, Skowron, Andrzej, editor, Słowiński, Roman, editor, Lingras, Pawan, editor, Miao, Duoqian, editor, and Tsumoto, Shusaku, editor

Published
2010
Full Text
View/download PDF

41. Communicative Approximations as Rough Sets

Author

Banerjee, Mohua, Pathak, Abhinav, Krishna, Gopal, Mukerjee, Amitabha, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Szczuka, Marcin, editor, Kryszkiewicz, Marzena, editor, Ramanna, Sheela, editor, Jensen, Richard, editor, and Hu, Qinghua, editor

Published
2010
Full Text
View/download PDF

42. A Preference-Based Multiple-Source Rough Set Model

Author

Khan, Md. Aquil, Banerjee, Mohua, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Szczuka, Marcin, editor, Kryszkiewicz, Marzena, editor, Ramanna, Sheela, editor, Jensen, Richard, editor, and Hu, Qinghua, editor

Published
2010
Full Text
View/download PDF

45. An Algebraic Semantics for the Logic of Multiple-Source Approximation Systems

Author

Khan, Md. Aquil, Banerjee, Mohua, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Sakai, Hiroshi, editor, Chakraborty, Mihir Kumar, editor, Hassanien, Aboul Ella, editor, Ślęzak, Dominik, editor, and Zhu, William, editor

Published
2009
Full Text
View/download PDF

46. A Logic for Complete Information Systems

Author

Khan, Md. Aquil, Banerjee, Mohua, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Sossai, Claudio, editor, and Chemello, Gaetano, editor

Published
2009
Full Text
View/download PDF

47. A Simple Modal Logic for Reasoning about Revealed Beliefs

Author

Banerjee, Mohua, Dubois, Didier, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Sossai, Claudio, editor, and Chemello, Gaetano, editor

Published
2009
Full Text
View/download PDF

48. Some Rough Consequence Logics and their Interrelations

Author

Bunder, Martin W., Banerjee, Mohua, Chakraborty, Mihir K., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Peters, James F., editor, and Skowron, Andrzej, editor

Published
2008
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results