THREE QUESTIONS TO
THREE QUESTIONS TO
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- When and how did you hear about paraconsistent logic and start your work?
I first heard about paraconsistency during my MA studies in Poland. Prof. Andrzej Wiśniewski brought with him the ideas promoted by the Flemish school of paraconsistency led by Prof. Diderik Batens. This is how I learnt about inconsistency-tolerant logics and adaptive logics in particular: I was intrigued (and did not understand much). Prof. Tomasz Skura directed my interest towards an alternative approach to logic where instead of proving, we disprove, or reject, formulas. As it turned out, I was able to combine paraconsistency and refutation in my work.
I first heard about paraconsistency during my MA studies in Poland. Prof. Andrzej Wiśniewski brought with him the ideas promoted by the Flemish school of paraconsistency led by Prof. Diderik Batens. This is how I learnt about inconsistency-tolerant logics and adaptive logics in particular: I was intrigued (and did not understand much). Prof. Tomasz Skura directed my interest towards an alternative approach to logic where instead of proving, we disprove, or reject, formulas. As it turned out, I was able to combine paraconsistency and refutation in my work.
Born December 11, 1980, Lublin, Poland.
Born December 11, 1980, Lublin, Poland.
2. How did you further develop your work on paraconsistent logic ?
2. How did you further develop your work on paraconsistent logic ?
I applied methods from refutation calculus, developed by my MA supervisor Professor Tomasz Skura, to the case of maximal paraconsistent logics. At first I focused on certain well-known systems and showed their maximality using the refutation-related methods to then work on 3-valued logics in general ("A Generalisation of a Refutation-related Method in Paraconsistent Logics", Logic and Logical Philosophy). I extended my results from the 3-valued case to n-valued paraconsistent systems ("n-valued Maximal Paraconsistent Matrices", Journal of Applied Non-classical Logics), which is an ongoing project.
I applied methods from refutation calculus, developed by my MA supervisor Professor Tomasz Skura, to the case of maximal paraconsistent logics. At first I focused on certain well-known systems and showed their maximality using the refutation-related methods to then work on 3-valued logics in general ("A Generalisation of a Refutation-related Method in Paraconsistent Logics", Logic and Logical Philosophy). I extended my results from the 3-valued case to n-valued paraconsistent systems ("n-valued Maximal Paraconsistent Matrices", Journal of Applied Non-classical Logics), which is an ongoing project.
Adam Trybus and Alan Turing
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 ?
Despite paraconsistent systems being an established research field for quite a while now, I think there are still some foundational challenges that are not answered and perhaps will remain so. I mean here such basic notions as the nature of contradiction or the formulation of the principle of non-contradiction. I looked into this in my most recent research stemming from my work on Ladd-Franklin on one hand and Łukasiewicz on the other ("What is the Principle of (Non-)Contradiction Precisely? A Struggle at the Dawn of Formal Logic", Logic and Logical Philosophy). I am also interested in the status of contradiction from the neuro-psychological point of view. Finally, I am involved in testing how the AI systems cope with contradictions.
Despite paraconsistent systems being an established research field for quite a while now, I think there are still some foundational challenges that are not answered and perhaps will remain so. I mean here such basic notions as the nature of contradiction or the formulation of the principle of non-contradiction. I looked into this in my most recent research stemming from my work on Ladd-Franklin on one hand and Łukasiewicz on the other ("What is the Principle of (Non-)Contradiction Precisely? A Struggle at the Dawn of Formal Logic", Logic and Logical Philosophy). I am also interested in the status of contradiction from the neuro-psychological point of view. Finally, I am involved in testing how the AI systems cope with contradictions.
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