Soma Dutta - Academia.edu (original) (raw)

Papers by Soma Dutta

Logic in Asia: Studia Logica Library, 2019

Logic in Asia: Studia Logica Library This book series promotes the advance of scientific research... more Logic in Asia: Studia Logica Library This book series promotes the advance of scientific research within the field of logic in Asian countries. It strengthens the collaboration between researchers based in Asia with researchers across the international scientific community and offers a platform for presenting the results of their collaborations. One of the most prominent features of contemporary logic is its interdisciplinary character, combining mathematics, philosophy, modern computer science, and even the cognitive and social sciences. The aim of this book series is to provide a forum for current logic research, reflecting this trend in the field's development. The series accepts books on any topic concerning logic in the broadest sense, i.e., books on contemporary formal logic, its applications and its relations to other disciplines. It accepts monographs and thematically coherent volumes addressing important developments in logic and presenting significant contributions to logical research. In addition, research works on the history of logical ideas, especially on the traditions in China and India, are welcome contributions. The scope of the book series includes but is not limited to the following: • Monographs written by researchers in Asian countries. • Proceedings of conferences held in Asia, or edited by Asian researchers. • Anthologies edited by researchers in Asia. • Research works by scholars from other regions of the world, which fit the goal of "Logic in Asia".

Lecture Notes in Computer Science, 2016

In this paper, the meaning of a vague concept α is assumed to be rendered through two (mutually e... more In this paper, the meaning of a vague concept α is assumed to be rendered through two (mutually exclusive) finite sets of prototypes and counterexamples. In the remaining set of situations the concept is assumed to be applied only partially. A logical model for this setting can be fit into the three-valued Łukasiewicz's logic Ł 3 set up by considering, besides the usual notion of logical consequence |= (based on the truth preservation), the logical consequence |= ≤ based on the preservation of all truth-degrees as well. Moreover, we go one step further by considering a relaxed notion of consequence to some degree a ∈ [0, 1], by allowing the prototypes (counterexamples) of the premise (conclusion) be a-similar to the prototypes (counterexamples) of the conclusion (premise). We present a semantical characterization as well as an axiomatization.

Thriving Rough Sets, 2017

In this chapter we propose a departure from classical notion of information systems. We propose t... more In this chapter we propose a departure from classical notion of information systems. We propose to bring in the background of agent's interaction with physical reality in arriving at a specific information system. The proposals for generalizing the notion of information systems are made from two aspects. In the first aspect, we talk about incorporating relational structures over the value sets from where objects assumes values with respect to a set of attributes. In the second aspect, we introduce interaction with physical reality within the formal definition of information systems, and call them as interactive information systems.

Rough Sets, 2018

This paper proposes an interpretation of characterizing required condition and desired condition ... more This paper proposes an interpretation of characterizing required condition and desired condition of an user, that is a bipolar query, from the perspective of rough set semantics with an additional feature of learning the user's need through dialogue.

Rough sets, introduced by Zdzisaw Pawlak [1], play a crucial role in the development of Granular ... more Rough sets, introduced by Zdzisaw Pawlak [1], play a crucial role in the development of Granular Computing (GrC) [2–4]. The extension of GrC to Interactive Granular Computing (IGrC) (initiated by Skowron and co-workers [5–7]5), requires generalization of the basic concepts of rough sets and GrC. For instance, it is needed to shift from granules to complex granules (including both physical and abstract parts), information (decision) systems to interactive information (decision) systems as well as methods of inducing hierarchical structures of information (decision) systems to methods of inducing hierarchical structures of interactive information (decision) systems. IGrC takes into account the granularity of information as used by humans in problem solving, as well as interactions with (and within) the real physical world. The computations in this IGrC model are realized on the interactive complex granules and that must be based on the consequences of the interactions occurring in the...

In the paper, we discuss an extension of exploration systems introduced by Andrzej Ehrenfeucht an... more In the paper, we discuss an extension of exploration systems introduced by Andrzej Ehrenfeucht and Grzegorz Rozenberg. The extension is defined by adding an interpretation of nodes and edges in zoom structure of exploration system. The interpretation is based on the concepts, namely local logic and logic infomorphism, from the notion of information flow by Jon Barwise and Jerry Seligman. This extension makes it possible, in particular, to give a natural interpretation of reaction systems in exploration systems as tools for controlling attention in reasoning about the perceived situation in the physical world.

This short paper is an attempt to clarify the role of Interactive Granular Computing (IGrC) as a ... more This short paper is an attempt to clarify the role of Interactive Granular Computing (IGrC) as a computation model which respects that a real cognition about a real physical complex phenomenon and making decisions based on that cannot be formalized only being in the language of mathematics. In this regard, the paper focuses on presenting a real life example of computation where in order to move forward, without stumbling over the obstacles, a blind person needs to explore and learn the surrounding environment through interactions with the environment. The paper simply describes different components and features of IGrC model in the light of the concerned example and explains how this computing model has the potential to handle the grounding problem by bridging a connection between the abstract mathematical modeling and the real physical semantics.

Fundamenta Informaticae, 2018

Natural Computing, 2018

Introduction of rough sets by Professor Zdzisław Pawlak has completed 35 years. The theory has al... more Introduction of rough sets by Professor Zdzisław Pawlak has completed 35 years. The theory has already attracted the attention of many researchers and practitioners, who have contributed essentially to its development, from all over the world. The methods, developed based on rough set theory alone or in combination with other approaches, found applications in many areas. In this article, we outline some selected past and present research directions of rough sets. In particular, we emphasize the importance of searching strategies for relevant approximation spaces as the basic tools in achieving computational building blocks (granules or patterns) required for approximation of complex vague concepts. We also discuss new challenges related to problem solving by intelligent systems (IS) or complex adaptive systems (CAS). The concern is to control problems using interactive granular computing, an extension of the rough set approach, for effective realization of computations realized in IS or CAS. These challenges are important for the development of natural computing too. Keywords Rough set Á Granular computing Á (Approximate) Boolean reasoning Á Interaction Á Adaptive judgment Á Complex adaptive system Á Natural computing 1 Introduction The rough set approach was proposed by Pawlak (1982, 1991) as a tool for dealing with imperfect knowledge, in particular with vague concepts. Rough set theory has gained interest of many researchers and practitioners from all over the world. The rough set approach is of fundamental importance in artificial intelligence and cognitive sciences, especially in machine learning, data mining and knowledge discovery, pattern recognition, decision support systems, expert systems, intelligent systems, multiagent systems, (complex) adaptive systems, autonomous systems, cognitive systems, conflict analysis, risk management systems. Many methods based on rough sets have wide applications in many real life projects, e.g., acoustics, bioinformatics, business and finance, chemistry, computer engineering and electrical engineering (including data compression, control, digital image processing, digital signal processing, parallel and distributed computer systems, power systems, sensor fusion, fractal engineering), decision analysis and systems, economics, environmental studies, digital image processing, informatics, medicine, molecular biology, musicology, neurology, robotics, social science, software engineering, spatial visualization, Web engineering, and Web mining. Rough sets have established relationships with many other approaches such as fuzzy set theory, granular computing, evidence theory, formal concept analysis, (approximate) Boolean reasoning, multicriteria decision analysis, statistical methods, decision theory, matroids. Despite the overlap with many other theories, rough set theory may be considered as an independent discipline on its own right. There are reports on many hybrid methods & Andrzej Skowron

Granular Computing, 2016

Decision support in solving problems related to complex systems requires relevant computation mod... more Decision support in solving problems related to complex systems requires relevant computation models for the agents as well as methods for reasoning on properties of computations performed by agents. Agents are performing computations on complex objects [e.g., (behavioral) patterns, classifiers, clusters, structural objects, sets of rules, aggregation operations, (approximate) reasoning schemes]. In Granular Computing (GrC), all such constructed and/or induced objects are called granules. To model interactive computations performed by agents, crucial for the complex systems, we extend the existing GrC approach to Interactive Granular Computing (IGrC) approach by introducing complex granules (c-granules or granules, for short). Many advanced tasks, concerning complex systems, may be classified as control tasks performed by agents aiming at achieving the high-quality computational trajectories relative to the considered quality measures defined over the trajectories. Here, new challen...

Soft Computing, 2014

Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Ber... more Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Berlin Heidelberg. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Lecture Notes in Computer Science, 2015

This paper is a preliminary step towards proposing a scheme for synthesis of a concept out of a s... more This paper is a preliminary step towards proposing a scheme for synthesis of a concept out of a set of concepts focusing on the following aspects. The first is that the semantics of a set of simple (or independent) concepts would be understood in terms of its prototypes and counterexamples, where these instances of positive and negative cases may vary with the change of the context, i.e., a set of situations which works as a precursor of an information system. Secondly, based on the classification of a concept in terms of the situations where it strictly applies and where not, a degree of application of the concept to some new situation/world would be determined. This layer of reasoning is named as logic of prototypes and counterexamples. In the next layer the method of concept synthesis would be designed as a graded concept based on the already developed degree based approach for logic of prototypes and counterexamples.

All in-text references underlined in blue are linked to publications on ResearchGate, letting you... more All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.

Handbook of Logical Thought in India, 2020

Fundamenta Informaticae, 2014

ABSTRACT Fuzzy Logic a la Pavelka has been reintroduced here in terms of consequence relation ins... more ABSTRACT Fuzzy Logic a la Pavelka has been reintroduced here in terms of consequence relation instead of consequence operator. Metalogical notions like, consistency and inconsistency are pro- posed as graded notions. The relationship between consequence relation and inconsistency, both fuzzy here, is studied. Another metalogical notion viz., equivalence of two sets of formulae that originates from Tarski is defined and investigated in this context when the premise is a fuzzy set.

Lecture Notes in Computer Science, 2011

This paper is aimed to study the algebraic background of some proof theoretic rules in a set up w... more This paper is aimed to study the algebraic background of some proof theoretic rules in a set up where distinct levels of logic activity have been maintained carefully. In this regard, Introduction, Elimination rules for ¬, and ⊃ have been considered as specific cases whose necessary and sufficient conditions from the perspective of graded consequence will reveal a new analysis.

Lecture Notes in Computer Science, 2009

In this paper we shall investigate some properties of graded consequence relation. These properti... more In this paper we shall investigate some properties of graded consequence relation. These properties are in some sense counterparts of proof theoretic assertions in the classical, intuitionistic or other logics. Theory of graded consequence was introduced by Chakraborty [1,2] in 1986 as a ...

gimac.uma.es

In this paper axioms of parainconsistency as well as those of paraconsistent consequence have bee... more In this paper axioms of parainconsistency as well as those of paraconsistent consequence have been introduced and their equivalence established.

Logica Universalis, 2011

Does there exist any equivalence between the notions of inconsistency and consequence in paracons... more Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation (¬) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During this study two points have come out. The first one is that the notion of inconsistency of paraconsistent logics turns out to be a formuladependent notion and the second one is that the characterization (i.e. equivalence) appears to be pertinent to a class of paraconsistent logics which have double negation property.

Fuzzy Sets and Systems, 2010

In this paper some basic aspects of the theory of graded consequence are reconsidered, based on m... more In this paper some basic aspects of the theory of graded consequence are reconsidered, based on many results that appeared since the inception of graded consequences in 1986. Relationships of the notion of graded consequence with the notions of consequence in many-valued ...