THREE QUESTIONS TO
THREE QUESTIONS TO
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- When and how did you hear about paraconsistent logic and start your work?
It was sometime around 2004, after completing my masters, I started working as a project assistant in a project in Jadavpur University, Kolkata. The title of the project was ‘Inconsistency Tolerant Systems’. This was the time when I started getting acquainted with the terms like dialetheism, true-contradiction, paraconsistency etc. Around the same time I started pursuing my PhD under the supervision of Prof. Mihir K. Chakraborty (retired professor University of Calcutta). As a part of my PhD research I was exploring a notion of graded consequence and an equivalent notion of graded inconsistency. The main idea was to explore the possibilities of restoring the classical consequence-inconsistency relationship in a context where both consequence and inconsistency are many-valued notions, and thus it allows an inconsistent premise to be explosive to a degree that is not necessarily 1. During the same time in our weekly study group, called Calcutta Logic Circle, Dr. Sanjukta Basu (Rabindra Bharati University, Kolkata) was presenting a series of lectures on inconsistency tolerant systems. This in some sense brought me into the field. Slowly I started taking interest into different Paraconsistent logics and their perspectives of violating classical law of explosion.
It was sometime around 2004, after completing my masters, I started working as a project assistant in a project in Jadavpur University, Kolkata. The title of the project was ‘Inconsistency Tolerant Systems’. This was the time when I started getting acquainted with the terms like dialetheism, true-contradiction, paraconsistency etc. Around the same time I started pursuing my PhD under the supervision of Prof. Mihir K. Chakraborty (retired professor University of Calcutta). As a part of my PhD research I was exploring a notion of graded consequence and an equivalent notion of graded inconsistency. The main idea was to explore the possibilities of restoring the classical consequence-inconsistency relationship in a context where both consequence and inconsistency are many-valued notions, and thus it allows an inconsistent premise to be explosive to a degree that is not necessarily 1. During the same time in our weekly study group, called Calcutta Logic Circle, Dr. Sanjukta Basu (Rabindra Bharati University, Kolkata) was presenting a series of lectures on inconsistency tolerant systems. This in some sense brought me into the field. Slowly I started taking interest into different Paraconsistent logics and their perspectives of violating classical law of explosion.
Born September 5, 1977, Kolkata, India.
Born September 5, 1977, Kolkata, India.
2. How did you further develop your work on paraconsistent logic ?
2. How did you further develop your work on paraconsistent logic ?
As mentioned before, in the beginning of my PhD studies I was interested to look for suitable axiomatizations for the graded notions of consequence and inconsistency so that, as like the classical context, consequence and inconsistency remain inter-definable. From the basic principle of paraconsistent logics, it is evident that the classical sense of one to one correspondence between consequence and inconsistency does not hold. So, somehow we (with Prof. Chakraborty) got interested to explore whether in the context of paraconsistent logics there can be some suitable sets of axioms that characterize a nonexplosive consequence and a respective notion of inconsistency so that one of the notions can be defined in terms of the other. It turned out that in the context of paraconsistent logics, we need to relativize the notion of inconsistency with respect to a formula. That means, a set of formulae can be inconsistent with respect to a particular formula if both the formula and its negation follow from the set. Following the idea, two sets of axioms were developed for a non-explosive consequence and a relativized notion of inconsistency in the negation-fragment of a propositional language.
As mentioned before, in the beginning of my PhD studies I was interested to look for suitable axiomatizations for the graded notions of consequence and inconsistency so that, as like the classical context, consequence and inconsistency remain inter-definable. From the basic principle of paraconsistent logics, it is evident that the classical sense of one to one correspondence between consequence and inconsistency does not hold. So, somehow we (with Prof. Chakraborty) got interested to explore whether in the context of paraconsistent logics there can be some suitable sets of axioms that characterize a nonexplosive consequence and a respective notion of inconsistency so that one of the notions can be defined in terms of the other. It turned out that in the context of paraconsistent logics, we need to relativize the notion of inconsistency with respect to a formula. That means, a set of formulae can be inconsistent with respect to a particular formula if both the formula and its negation follow from the set. Following the idea, two sets of axioms were developed for a non-explosive consequence and a relativized notion of inconsistency in the negation-fragment of a propositional language.
Later, in 2005 , I got an opportunity to present this idea in an informal meeting with Prof. Graham Priest and Prof. Chakaraborty in Kolkata. Prof. Priest was during that time visiting Kolkata for an international conference on logic and applications, organized in the memory of Late Professor Bimal Krishna Matilal. As a beginner researcher, I still remember the encouragement and appreciation of Prof. Graham Priest for proceeding with the work further. Later, I found a similar idea like relativized inconsistency in one of the papers on logics of formal inconsistency.
Later, in 2005 , I got an opportunity to present this idea in an informal meeting with Prof. Graham Priest and Prof. Chakaraborty in Kolkata. Prof. Priest was during that time visiting Kolkata for an international conference on logic and applications, organized in the memory of Late Professor Bimal Krishna Matilal. As a beginner researcher, I still remember the encouragement and appreciation of Prof. Graham Priest for proceeding with the work further. Later, I found a similar idea like relativized inconsistency in one of the papers on logics of formal inconsistency.
Fortunately, I also had an opportunity to share the idea in detail with Joao Marcos during his visits in India. Our first paper was published in Logica Universalis in 2011. Then we extended the study over all fragments of a propositional language including standard logical connectives such as negation, disjunction, conjunction, and implication. We came up with a tree diagram where each branch represents a (potential) paraconsistent system with an equivalent notion of relativized inconsistency. It was observed that many existing paraconsistent systems can be placed under the left branch of the tree diagram. I had an opportunity to present this work in front of Prof. Shahid Rahman, who was invited in a seminar in Kolkata. This extended version of the work was published in the book viz., New Directions in Paraconsistent Logics, published by Springer. This book was an outcome of the 5th World Congress on Paraconsistency (WCP5) which held in Indian Statistical Institute Kolkata in 2014. With the initiative of Prof. Jean-Jves Beziau, in the same conference I got an opportunity to present an invited talk on Consequence-Inconsistency interrelation: Paraconsistent Logics, and I was also invited to serve as one of the editors of the book published after the conference. One more related paper was published with Sourav Tarafdar in the Handbook of Logical Thoughts in India published by springer in 2022.
Fortunately, I also had an opportunity to share the idea in detail with Joao Marcos during his visits in India. Our first paper was published in Logica Universalis in 2011. Then we extended the study over all fragments of a propositional language including standard logical connectives such as negation, disjunction, conjunction, and implication. We came up with a tree diagram where each branch represents a (potential) paraconsistent system with an equivalent notion of relativized inconsistency. It was observed that many existing paraconsistent systems can be placed under the left branch of the tree diagram. I had an opportunity to present this work in front of Prof. Shahid Rahman, who was invited in a seminar in Kolkata. This extended version of the work was published in the book viz., New Directions in Paraconsistent Logics, published by Springer. This book was an outcome of the 5th World Congress on Paraconsistency (WCP5) which held in Indian Statistical Institute Kolkata in 2014. With the initiative of Prof. Jean-Jves Beziau, in the same conference I got an opportunity to present an invited talk on Consequence-Inconsistency interrelation: Paraconsistent Logics, and I was also invited to serve as one of the editors of the book published after the conference. One more related paper was published with Sourav Tarafdar in the Handbook of Logical Thoughts in India published by springer in 2022.
Presently, I am, jointly with Prof. Mohua Banerjee (Indian Institute of Technology, Kanpur) co-supervising a PhD student (Bidhan Saha) who has developed our work further, and introduced a series of new three-valued paraconsistent logics for which the notions of consequence and inconsistency are inter-definable.
Presently, I am, jointly with Prof. Mohua Banerjee (Indian Institute of Technology, Kanpur) co-supervising a PhD student (Bidhan Saha) who has developed our work further, and introduced a series of new three-valued paraconsistent logics for which the notions of consequence and inconsistency are inter-definable.
3. How do you see the evolution and further challenges for paraconsistent logic ?
3. How do you see the evolution and further challenges for paraconsistent logic ?
Among different approaches to non-classical logics, I feel approaches emerged to deal with different aspects of inconsistency are of special importance. Keeping aside different aspects of inconsistency tolerant systems, even if we focus on the basic principle of paraconsistent logics, that is the law of non-explosion, there are plenty of approaches to avoid explosion in a logical framework. All these existing approaches such as, non-truth functional approach, relevance approach, discussive logics, adaptive logics, logics of formal inconsistency, paraconsistentization approach etc, have emerged to address some intuitive aspects of reasoning that is missing in the classical scenario. So, they are built on strong philosophical and technical ground. Already the researchers made a huge development regarding building a parallel set-up for mathematics that can have a base on paraconsistent set theory. So, slowly the grip of paraconsistency is getting stronger and stronger.
Among different approaches to non-classical logics, I feel approaches emerged to deal with different aspects of inconsistency are of special importance. Keeping aside different aspects of inconsistency tolerant systems, even if we focus on the basic principle of paraconsistent logics, that is the law of non-explosion, there are plenty of approaches to avoid explosion in a logical framework. All these existing approaches such as, non-truth functional approach, relevance approach, discussive logics, adaptive logics, logics of formal inconsistency, paraconsistentization approach etc, have emerged to address some intuitive aspects of reasoning that is missing in the classical scenario. So, they are built on strong philosophical and technical ground. Already the researchers made a huge development regarding building a parallel set-up for mathematics that can have a base on paraconsistent set theory. So, slowly the grip of paraconsistency is getting stronger and stronger.
I am presently involved, both from the context of teaching and research, in exploring tools and strategies related to data mining and machine learning. In data mining, two challenging tasks are to select a sufficiently small part of the data and design an appropriate decision valuation so that it can describe a huge data table in an effective way and there is not much information loss. In data we often talk about inconsistent data. In a simplified way we can say that we have instances which can be described by the same (propositional) formula but they are attributed with different decision labels. That is, one can say that there are both (if A then B) as well as (if A then not-B). However, we want to design a decision valuation which is not trivial – that is, a decision valuation which still maintains a sound (inductive) reasoning strategy to describe the nature of the data. This form of inconsistency is not exactly the same as the standard notion of negation inconsistency usually found in deductive reasoning. Now, machine learning being a very prevalent area of research in the present age, I feel one of the challenges could be to find a more general approach to dealing with inconsistency which can characterize not only inconsistency and non-triviality in the context of deductive reasoning, but also in the context of data mining.
I am presently involved, both from the context of teaching and research, in exploring tools and strategies related to data mining and machine learning. In data mining, two challenging tasks are to select a sufficiently small part of the data and design an appropriate decision valuation so that it can describe a huge data table in an effective way and there is not much information loss. In data we often talk about inconsistent data. In a simplified way we can say that we have instances which can be described by the same (propositional) formula but they are attributed with different decision labels. That is, one can say that there are both (if A then B) as well as (if A then not-B). However, we want to design a decision valuation which is not trivial – that is, a decision valuation which still maintains a sound (inductive) reasoning strategy to describe the nature of the data. This form of inconsistency is not exactly the same as the standard notion of negation inconsistency usually found in deductive reasoning. Now, machine learning being a very prevalent area of research in the present age, I feel one of the challenges could be to find a more general approach to dealing with inconsistency which can characterize not only inconsistency and non-triviality in the context of deductive reasoning, but also in the context of data mining.
Soma Dutta, Mihir Chakraborty and João Marcos
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