ESSLLI2025
Introduction to Logical Argumentation
(Foundational Course)
week 1
Introduction to Logical Argumentation
(Foundational Course)
week 1
This is the course page for the ESSLLI 2025 course "Introduction to Logical Argumentation" by van Berkel and Strasser.
Course abstract:
This course shows how logical argumentation provides a natural model of defeasible reasoning. Most of our every day reasoning is defeasible. When we draw conclusions in light of incomplete and inconsistent information, the possibility to retract some of these conclusions on acquiring more information makes this reasoning defeasible. Nonmonotonic logics model such reasoning. Over the past decades, logical argumentation proved to be a highly unifying framework for such logics. In this course, we explain some of the core methods of logical argumentation in which arguments are premise-conclusions pairs are generated by an underlying logic (such as a proof calculus). We discuss how conflicts between arguments are tracked by means of various types of argumentative attacks. This gives rise to a so-called argumentation framework from which arguments can be selected following the rationale of an argumentation semantics, as defined by Dung in his seminal work on abstract argumentation. We furthermore apply this method to defeasible reasoning with normative codes that generate obligations for agents and to their doxastic interpretation for generating agent beliefs. Furthermore, we discuss important meta-theoretic desiderata for argumentative models of defeasible reasoning. In the last session, we discuss how AI explainability methods can be harnessed to explain defeasible reasoning in logical argumentation.
Lecture 1: Argumentation Theory and Basics of Abstract Argumentation
Summary: In this first lecture, we briefly go through some history and philosophy of argumentation, defeasible reasoning, and why it is different from classical logical reasoning. We then introduce you to the basics of Abstract Argumentation, a computational approach to nonmonotonic reasoning using arguments, counter-arguments, and attack relations between those arguments. We also discuss different semantics for assessing which arguments in such a framework are collectively justifiable/defensible.
Slides can be downloaded here: part 1 and part 2.
Exercises are found in the slides "part 2"
Additional reading material:
Toulmin, S.E.: The Uses of Argument. Cambridge University Press, Cambridge (1958) (seminar work for argumentation theory; excerpt) (read link)
Pollock, J.L.: Defeasible reasoning. Cogn. Sci. 11(4), 481–518 (1987) (on defeasible reasoning) (download link)
Mercier, H., Sperber, D.: Why do humans reason? Arguments for an argumentative theory. Behav. Brain Sci. 34(2), 57–74 (2011) (link between human reasoning and argumentation) (download link)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. 77, 321–358 (1995) (seminal paper introducing abstract argumentation) (download link)
Baroni, P., Caminada, M., Giacomin, M.: An introduction to argumentation semantics. Knowl. Eng. Rev. 26(4), 365–410 (2011) (introduction to argumentation semantics) (download link)
Lecture 2: Logical argumentation & rationality postulates.
Summary: In this lecture we go deeper into the question of how arguments can be generated by a logic, what the structural components of such arguments are and how the structure of those arguments can give rise to various formal definitions of attack and defeat between arguments. In particular, we discuss logical argumentation as a proof-theoretic approach to deriving arguments. Once we have access to the internal structure of those arguments we can look at desirable properties collectively justifiable arguments should satisfy. For instance, collectively justifiable arguments must be consistent.
Slides can be downloaded here.
Additional exercises can be found in the slides.
Additional reading material:
Arieli, O., Straser, C.: Sequent-based logical argumentation. Argument Comput. 6(1), 73–99 (2015) (seminal work on sequent-based logical argumentation) (download link)
Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. Artif. Intell. 171(5–6), 286–310 (2007) (rationality postulates) (download link)
Arieli, O., Borg, A., Heyninck, J., Straser, C.: Logic-based approaches to formal argumentation. In: Gabbay, D., Giacomin, M., Simari, G.R., Thimm, M. (eds.) Handbook of Formal Argumentation, vol. 2, pp. 1793–1898. College Publications (2021) (overview paper of different approaches to logical argumentation) (download link)
Lecture 3: Meta-theory & Properties of Nonmonotonic Consequence Relations
Summary: On Day 3, we broaden our perspective to situate formal argumentation within the wider landscape of Nonmonotonic Logic (NML). The session provides a systematic introduction to the formal modeling of defeasible reasoning—a type of reasoning where conclusions are drawn provisionally and may be retracted in light of new information. We will explore central syntactic and semantic methodologies for NML. The main goal is to reveal the deep connections between these seemingly disparate formalisms. We will demonstrate through a series of translations that formal argumentation can serve as a unifying perspective for navigating and understanding the multifaceted world of defeasible reasoning.
Slides can be downloaded here.
Additional exercises can be found on the slides
Additional reading material:
Straßer, C.: Nonmonotonic Logic. Elements Series. Cambridge University Press. (202x). Forthcoming. (download link)
Straßer, C.: Non-monotonic Logic, The Stanford Encyclopedia of Philosophy. (reading link)
Arieli, O., Borg, A., Heyninck, J., Straser, C.: Logic-based approaches to formal argumentation. In: Gabbay, D., Giacomin, M., Simari, G.R., Thimm, M. (eds.) Handbook of Formal Argumentation, vol. 2, pp. 1793–1898. College Publications (2021) (overview paper of different approaches to logical argumentation) (download link)
Lecture 4: Normative Reasoning and Norm Conflicts in Logical Argumentation
Summary: In this session we look at logical argumentation from a specific application context: normative reasoning. Normative reasoning is conflict sensitive and defeasible in nature. For this reason, logical argumentation is particularly suitable for formal reasoning with norms. We refine the theory addressed in the first three parts by looking at specific requirements of normative reasoning. We introduce a calculus for generating arguments based on norms concluding what an agent "ought to do" and what under what contexts norms become "inapplicable". We will also look at different types of conflicts that may arise between norms and how argumentation frameworks provide more nuances notions of an agent's duties.
Slides can be downloaded here.
Exercises can be found on the slides.
Additional reading material:
Hilpinen, R., McNamara, P.: Deontic logic: A historical survey and introduction. In: Gabbay, D., Horty, J.F., Parent, X., van der Meyden, R., van der Torre, L. (eds.) Handbook of Deontic Logic and Normative Systems, vol. 1, pp. 3–136. College Publications (2013) (introduction to the history of deontic logic) (download link)
Also on permissions in normative reasoning.
van Berkel, K., Straßer, C.: Reasoning with and about norms in logical argumentation. In: Toni, F., Polberg, S., Booth, R., Caminada, M., Kido, H. (eds.) Frontiers in Artificial Intelligence and Applications: Computational Models of Argument, Proceedings (COMMA22), vol. 353, pp. 332–343. IOS Press (2022). (initial paper on the DAC formalism) (download link)
van Berkel, K., & Straßer, C. Reasoning With and About Normative Conflicts. 17 DEON, 21. (on conflict-types in normative reasoning and argumentation) (download link)
Parent, X., & van der Torre, L. (2018). Introduction to deontic logic and normative systems. College Publications, London, United Kingdom. (textbook introduction to deontic logic and input/output logic) (download link)
Lecture 5: Explainability and Logical Argumentation
Summary: In this final session, we dive into various eXplainable AI (XAI) methods developed for logical argumentation. We discuss how argumentation frameworks provide additional clarification of why certain conclusions are justifiable, both from an internal and an external, that is, dynamic perspective. This last part is in line the two tiers of explanation in philosophy. We furthermore introduce you to argumentation dialogues/games, that can be used to construct explanations of an argument/conclusion's acceptability.
Slides can be downloaded here.
Exercises in the slides.
Additional reading material:
Borg, A., Bex, F.: A basic framework for explanations in argumentation. IEEE Intell. Syst. 25–35 (2021). (explanation for logical argumentation) (download link)
Fan, X., Toni, F.: On computing explanations in argumentation. In: Bonet, B., Koenig, S. (eds.) Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (AAAI 2015), pp. 1496–1502 (2015) (explanation for abstract argumentation) (download link)
Cyras, K., Rago, A., Albini, E., Baroni, P., Toni, F.: Argumentative XAI: a survey (2021). (survey paper on argumentative XAI) (download link)
Seselja, D., Straßer, C.: Abstract argumentation and explanation applied to scientific debates. Synthese 190(12), 2195–2217 (2013) (explanation and argumentation with philosophical foundations) (download link)
van Berkel, K., Straßer, C.: Towards deontic explanations through dialogue. In: Proceeding of the 2nd International Workshop on Argumentation for eXplainable AI (ArgXAI 2024), pp. 29–40. CEUR-WS Workshop Proceedings (2024) (explanations through dialogues for normative reasoning) (download link)
Handbooks:
Many comprehensive handbooks are now available introducing one through individual chapters to specific subfields of research in formal argumentation and deontic logic and normative systems.
Handbook in formal argumentation vol 1, 2, and 3. (download links)
Handbook in deontic logic and normative systems, vol 1, and 2. (download links)