Adam Trybus

News

Current work themes: LLMs and paraconsistent logic; Russell and Euclid; Leon Chwistek's PhD Thesis; Liberal Arts Mathematics in Poland; reasoning in LLMs.
Presenting “Making Bielik LLM Reason (Better): A Field Report”, Polish Conference on AI, Kraków (20–24 April 2026). [abs] [pdf]
A forthcoming book on the history of Studia Logica entitled Studia Logica: A History of the Journal, expected publication date: August 2026.
A forthcoming book on Jan Łukasiewicz's work on the principle of contradiction entitled Around the translation of Jan Łukasiewicz's "On the Principle of Contradiction in Aristotle".

About

Adam Trybus, PhD

Having a diverse educational background, I am interested in many aspects of reasoning and logic: its history, philosophy, formal development, computational analysis, applications, implementations and industrial uses. My research interests include spatial reasoning, formalisation of geometry, mathematical logic, artificial intelligence, knowledge representation and reasoning and non-classical logics. My recent interests gravitate towards a mixture of mathematics, computer science, modern AI and formal systems. I am very much interested in neurosciences and cognitive science. I care a lot about critical thinking as I believe it is a very important contributing factor to the development of society. I also dabble in philosophy of science.

I am an assistant professor at the Institute of Philosophy, Jagiellonian University (since 2022). I previously worked at the Institute of Philosophy, the University of Zielona Góra (2014–2022). Before that I was a translator for a while and before that I did my Ph.D. in Computer Science, University of Manchester (2011) on spatial logics with convexity and M.A. in Philosophy on refutation and maximal paraconsistent systems at the University of Zielona Góra (2006) in Poland. I also did a B.A. in political science on Mikhail Bakunin, the Russian anarchist.

I was the Principal Investigator in the project Philosophical and Formal Analysis of Qualitative Spatial Logics funded by Polish National Science Centre, June 2018 – September 2022

I taught courses on the history of British Philosophy, programming in Al (including Prolog), philosophical logic, formal logic, Knowledge Representation and Reasoning, Natural Language Processing etc. I have a dedicated YouTube channel where I record educational materials on logic, reasoning, open source and computer literacy in the age of AI. I have an extensive experience in teaching various other courses both in English and in Polish, including argumentation and informal reasoning, critical thinking, introduction to computer science (covering various open-source tools, such as LaTeX) and creativity. I am a fan of Linux, LaTeX and all things open-source.

I am an instructor on Coursera: Critical Thinking: A Brain-Based Guide for the ChatGPT Era specialisation with Barb Oakley and Terry Sejnowski. I am involved in the development of Bielik, one of the Polish Large Language Models. I also maintain a Github profile which is a testing ground at most.

Professional Involvement

Book Reviews Editor at Studia Logica
British Logic Colloquium
Polish Philosophical Association
Bertrand Russell Society
Commission for History and Philosophy of Computing
Society for Exact Philosophy
Polish Association for Logic and Philosophy of Science
Reviewer for AMS Mathematical Reviews

Co-organiser/organiser of:

Refutation Symposium 2018, Poznań, Poland
CLoCk 2023 and CLoCk 2024, Kraków, Poland
The 2025 Chwistek Lecture, Kraków, Poland

Publications

Preprints, unpublished or unrefereed work

Translation into Polish of Russell, B., The Teaching of Euclid, The Mathematical Gazette, Vol. 2, No. 33, 1902, pp. 165–167. [original] [pdf (Polish translation)]
2026 — Trybus, A., Bartnicki, B., Kinas, R., Making Bielik LLM Reason (Better): A Field Report, arXiv:2603.10640. [abs] [pdf]
2026 — Trybus, A., Rożko, K., Skura, T., A Non-Binary Method for Finding Interpolants: Theory and Practice, arXiv:2603.15876. [abs] [pdf]
2026 — Trybus, A., Three-Dimensional Affine Spatial Logics, arXiv:2603.16308. [abs] [pdf]
Translation into Polish of Oakley, B., Rogowsky, B., Sejnowski, T. J., Uncommon Sense Teaching as Naucz się nauczania. Praktyczne wykorzystanie osiągnięć neurobiologii, Sensus, 2023. [link]

Polish edition of Uncommon Sense Teaching

Books/Book Chapters

2025 — Trybus, A., Logika i analiza rozumowań w dobie sztucznej inteligencji, in: 130 lat Szkoły Lwowsko–Warszawskiej, Academicon.

Journal Articles/Conference Proceedings

2025 — Trybus, A., Współczesna sztuczna inteligencja a dziedzictwo Szkoły Lwowsko–Warszawskiej, Przegląd Filozoficzny. Note that Przegląd Filozoficzny does not display certain issues on their website.
2025 — Trybus, A., What Is the Principle of (Non-)Contradiction, Precisely? The Struggle at the Dawn of Formal Logic, Logic and Logical Philosophy, Vol. 34, No. 4, pp. 581–602. [doi] [link]
2023 — Trybus, A., On the Principle of Contradiction in Aristotle: Łukasiewicz's Opus Primum and Ultimum, Przegląd Filozoficzny, No. 2. Note that Przegląd Filozoficzny does not display certain issues on their website.
2022 — Trybus, A., Three-Dimensional Affine Spatial Logics, Logica Universalis 16(4): 603–620. [link]
2022 — Trybus, A., Linsky, B., Two Poles Worlds Apart: Chwistek, Ingarden, and the Split Between Phenomenology and Analytic Philosophy, Journal for the History of Analytical Philosophy.
2021 — Trybus, A., Russell and the Foundations of Qualitative Spatial Reasoning: The First Steps, Interdisciplinary Science Reviews 46(4): 591–608. [doi]
2020 — Trybus, A., Linsky, B., On Jan Łukasiewicz's "The Principle of Contradiction and Symbolic Logic", History and Philosophy of Logic 41(2): 183–190.
2019 — Trybus, A., Two of a Kind: Setting the Record Straight on Russell's Exchange with Ladd-Franklin on Solipsism, Russell: The Journal of Bertrand Russell Studies 39(2): 101–120.
2019 — Trybus, A., n-valued Maximal Paraconsistent Matrices, Journal of Applied Non-Classical Logics 29(2): 171–183. [doi]
2018 — Trybus, A., A Generalisation of a Refutation-related Method in Paraconsistent Logics, Logic and Logical Philosophy.
2016 — Trybus, A., Rational Region-Based Affine Logic of the Real Plane, ACM Transactions on Computational Logic 17(3). [doi]
2010 — Trybus, A., An Axiom System for a Spatial Logic with Convexity, ECAI 2010, pp. 701–706.

Academic translations

Noble D., Illusions of the modern synthesis, Biosemiotics, 14(1), p. 5–24. [doi] Translated as: Iluzje nowoczesnej syntezy [in:] O pochodzeniu. Ujęcie naukowe, vol. 3, 2025, p. 207–243.
Kelly, A., The Destruction of Idols: Alexander Herzen and Francis Bacon, Translated (together with J. Uglik) as: Zniszczenie idoli: Aleksander Hercen i Franciszek Bacon [1980], Przegląd Filozoficzny – Nowa Seria, R. 29 (2020), Nr 1 (113), pp. 135–167. [doi]
Łukasiewicz J., Zasada sprzeczności a logika symboliczna. Translated as: The Principle of Contradiction and Symbolic Logic, Łukasiewicz J., Trybus A., Linsky B., History and Philosophy of Logic, Vol. 41, issue 2, 154–182, 2020.
Chwistek L., Tragedia werbalnej metafizyki (Z powodu książki Dra Ingardena: Das literarische Kunstwerk), Kwartalnik Filozoficzny, Vol. X, 1932, 46–76. Translated as: Chwistek L., The Tragedy of Verbal Metaphysics, Journal for the History of Analytical Philosophy.
Chwistek L., Zasada sprzeczności w świetle nowszych badań Bertranda Russella, Rozprawy Akademii Umiejętności Wydział Historyczno-Filozoficzny, Serya II, Tom XXX, Kraków 1912, 270–334. Translated as: Chwistek L., The Law of Contradiction in the Light of Recent Investigations of Bertrand Russell translated by Rose Rand (partially corrected and translated by Adam Trybus, edited by Bernard Linsky), to appear in A. Brożek, J. Woleński (eds), The Significance of the Lvov-Warsaw School in European Culture.
Chwistek L., Zasady czystej teorii typów [in:] Pasenkiewicz K. (ed.), Pisma filozoficzne i logiczne, vol. 2, Warsaw, PWN 1963, p. 256–286. Translated as: Leon Chwistek, The Principles of the Pure Type Theory (1922) translated by Adam Trybus with an introductory note by Bernard Linsky, History and Philosophy of Logic, Volume 33, Issue 4, 2012, p. 329–352.
Noble D., Genes and Causation, Philosophical Transactions of the Royal Society A 2008, vol. 366, p. 3001–3015. Translated as: Geny a przyczynowość, Filozoficzne Aspekty Genezy 2011, p. 191–217.
Fitelson B. et al., How Not to Detect Design — A Critical Notice: William A. Dembski, The Design Inference, Philosophy of Science, vol. 66, Sept. 1999, p. 472–488. Translated as: Jak nie należy wykrywać projektu, Filozoficzne Aspekty Genezy 2007/2008, p. 53–80.

Conference Talks (representative selection)

Trybus A., Bartnicki B. (presenter), Kinas R., “Making Bielik LLM Reason (Better): A Field Report”

abs

pdf

Trybus A., Panel Discussion on Logic as Polish Speciality, International Logic Day, 2026, Warsaw.
Trybus A. (2025), “Can Hybrid LLMs Become the Next Frontier in Theorem Provers?”, Rule-based Automated Provers for Geometry, 3–5 June 2025, Kraków, Poland.
Trybus A. (2025), “Formal Logic and Machine Learning: Strange Bedfellows?”, First Polish Congress of Logic, Toruń, Poland.
Trybus A. (2025), “Czy czat może być racjonalny? Systemy LLM a logika.”, Nowe Horyzonty Kognitywistyki 2025, UKEN, Kraków, Poland.
Trybus A. (2025), “Exploring the Feedback Loop Between Large Language Models and Formal Reasoning: Research and Didactics”, Special Interest Group on Machine Learning, Institute of Mathematics, Jagiellonian University, Kraków, Poland.
Malinowski J., Trybus A., History of Studia Logica, 27th Conference Applications of Logic in Philosophy and in the Foundations of Mathematics, 2024, Institute of Philosophy, Institute of Mathematics, The University of Opole and the University of Wrocław, Poland.
Malinowski J., Trybus A., Trends in Logic Conferences - A History, 27th Conference Applications of Logic in Philosophy and in the Foundations of Mathematics, 2024, Institute of Philosophy, Institute of Mathematics, The University of Opole and the University of Wrocław, Poland.
Trybus A., “On the Principle of Contradiction in Aristotle”: Łukasiewicz's opus primum and ultimum, Jan Lukasiewicz. Between Lwow, Warsaw and Dublin, International Symposium, 2023, Warsaw.
Trybus A., Christine Ladd-Franklin and the principle of (non-)contradiction, Sixth World Congress of Paraconsistency, 2022, Toruń, Poland.
Trybus A., Chwistek's “On Axioms” as a Foundational Text in the History of Polish Logic, 25th Conference Applications of Logic in Philosophy and in the Foundations of Mathematics, 2022, Institute of Philosophy, Institute of Mathematics, The University of Opole and the University of Wrocław, Poland.
Trybus A., Coordinatising Affine Spatial Logics, Logic4Peace, University of Amsterdam, 2022.
Trybus A., Affine Spatial Logic: Three Dimensions and Beyond, LOGICA 2021, Hejnice, Czech Republic, 2021.
Trybus A., Philosophical Foundations of Qualitative Spatial Reasoning: A Case for Bertrand Russell, HaPoC, Bergamo, Italy, 2019.
Trybus A., Can Russell be relevant to a contemporary computer scientist?, Histoire de la philosophie analytique, Clermont-Ferrand, France, 2019.
Trybus A., Russell on Qualitative Geometry, Logic Reading Group, University of Alberta, Canada, 2019.
Trybus A., Maximal Paraconsistent Logics: How Far Can We Get?, Logic Reading Group, University of Alberta, Canada, 2019.
Trybus A., Russell and Philosophical Motivations of Contemporary Spatial Logics, The Bertrand Russell Research Centre, 2019.
Trybus A., Paraconsistency meets refutation: a case of maximality, 6th World Congress on Universal Logic, Vichy, France, 2018.
Trybus A., The Development of Affine Spatial Logic, 21st Conference Applications of Logic in Philosophy and in the Foundations of Mathematics 2016, Institute of Philosophy, Institute of Mathematics, The University of Opole, Poland.
Trybus A., An Axiom System for a Spatial Logic with Convexity, ECAI 2010, Lisbon, Portugal.
Trybus A., Spatial Logics. An Introduction, Entia et Nomina 2010, Institute of Philosophy, The University of Gdańsk, Poland.
Trybus A., Affine Spatial Logics, Logical Workshop 2010, Institute of Philosophy, Institute of Mathematics, The University of Warsaw, Poland.
Trybus A., Expressiveness, Computational Complexity and Model Theory of a Spatial Logic with Convexity, Poster Session, MAGIC Conference 2009, School of Mathematics, The University of Manchester.
Trybus A., On Some Open Problems in Mereotopology, Fourth MATHLOGAPS Training Workshop 2008, School of Mathematics, The University of Manchester.
Trybus A., Mereotopological Theories of Space, 13th Conference Applications of Logic in Philosophy and in the Foundations of Mathematics 2008, Institute of Philosophy, Institute of Mathematics, The University of Wrocław, Poland.
Trybus A., Ad Nauseam or the Troubles with Science. An Introduction to the Theory of Intelligent Design, Philosophers’ Rally 2007, Institute of Philosophy, The University of Groningen, The Netherlands.
Trybus A., Historical and Philosophical Background of Paraconsistency, Italian-Polish Workshop 2006, Institute of Philosophy, The University of Zielona Góra, Poland.
Trybus A., Refutation Calculus in Paraconsistent Logic, Philosophers’ Rally 2006, Institute of Philosophy, The University of Opole, Poland.
Trybus A., Adaptive Logics, Philosophers’ Rally 2004, Institute of Philosophy, Marie Curie-Skłodowska University, Lublin, Poland.

Teaching

Current Course materials

I currently work at Jagiellonian University focusing on the following courses: Introduction to Logic (tutor, for philosophy students). Information Technology (tutor, for philosophy and cognitive science), Introduction to Logic and Set Theory (lecturer and tutor, for philosophy and cognitive science), Artificial Intelligence: Theory and Practice (lecturer, for philosophy and cognitive science) Critical Thinking in The Age of AI (lecturer, university-wide course taught online in English).

When I worked at the University of Zielona Góra, I was both a tutor (supervising exercise classes) and a lecturer (giving lectures) at the following courses (2015–2022): Introduction to Logic (in Polish), Introduction to British Philosophy, Introduction to American Philosophy, Introduction to Philosophy (including ERASMUS students), Philosophical Logic (in Polish), Argumentation and Reasoning (in Polish), Rhetorics (in Polish), Philosophy of AI (in Polish), Creativity (in Polish), Introduction to Open-source Tools (in Polish).

During my PhD studies I was a Lab Demonstrator, Teaching Assistant, and Grader at the School of Computer Science, The University of Manchester (2007–2011) for various courses: Knowledge Representation and Reasoning, Artificial Intelligence Programming, Introduction to Linux, Symbolic AI, Logic and Applications.