### Keynote speeches

**Jiji Zhang (Hong Kong Baptist University)**

Title: Intervention and Causal Conditionals in Causal Markov Categories

Abstract: We build on a category-theoretic treatment of causality that associates a free Markov category with a directed acyclic graph (DAG) that formalizes the syntax for causal reasoning with the DAG. This framework enables us to define and study important concepts in causal reasoning from an abstract and ''purely causal'' point of view, such as causal independence/separation, causal conditionals, and disintegration of intervention effects. Our results regarding these concepts abstract away from the details of the commonly adopted causal models such as (recursive) structural equation models or causal Bayesian networks. They are therefore more widely applicable and in a way conceptually clearer. Our results are also intimately related to Judea Pearl's celebrated do-calculus, and yield a syntactical version of the causal core of the do-calculus. In addition, we construct a functor between such DAG-induced Markov categories, which we argue provides a natural and general setup for studying transformations between DAG-based causal models, including interventions as a special case.

**Wen-Fang Wang (Shandong University)**

Title: On Garfield and Priest's Interpretation of the Use of the Catuskoti in MMK

Abstract: According to Garfield and Priest's interpretation, the positive use of the catuskoti by Nāgārjuna in MMK shows that he endorses, at least from the conventional perspective, a four-valued semantics similar to that of Belnap’s FDE, while the negative use of the catuskoti by Nāgārjuna in MMK indicates that, when the ineffable ultimate reality is also considered, what he really has in mind is a plurivalent five-valued semantics. Though their interpretation is interesting and of heuristic value, this talk argues that their interpretation suffers from a number of problems: the problem of an adequate logic, the problem of the collapse of kotis, the problem of literature and historical support, and the problem of a suitable explanation. This talk also discusses but rejects both Cotnoir's and Westerhoff's interpretations of the use of the catuskoti in MMK, though it also argues that some insights from them, as well as several insights from Garfield and Priest, should be preserved. The final part of the paper combines these insights together and describes the right interpretation of Nāgārjuna's use of the catuskoti in MMK with the right semantics and the right logic of MMK. In short, this talk argues that Nāgārjuna's "rebuttal" of all four kotis in a catuskoti should be understood not as an external negation, but as a mere denial or a mere rejection of these kotis. If time allowed, the speaker will also talk a bit more on an interesting topic: how to "say" things unsayable.

**Wesley Holliday (UC Berkeley)**

Title: Logical Perspectives on Voting

Abstract: In this talk, based on joint work with Eric Pacuit, I will survey some aspects of social choice and voting theory from the perspective of logicians. Topics will include: formal logics for social-choice theoretic reasoning (Holliday and Pacuit 2020); the application of logical tools, such as SAT solving and interactive theorem proving, to voting theory (Holliday et al. 2021a); generalizing impossibility theorems via preservation results inspired by model theory (Holliday et al. 2021b); and finally, the design of voting methods guided by logical ideas, such as coherence (Holliday and Pacuit 2020a, 2020b) and recursion (Holliday and Pacuit 2021).

**Sara Negri (University of Helsinki)**

Title: Bridges between classical and constructive reasoning for infinitary logic

Abstract: A survey will be presented on the bridges between classical and constructive reasoning in infinitary logic. At the level of provability we show how the method of conversion of axioms into rules gives a natural approach to Glivenko sequent classes for geometric theories. The latter encompass axiomatizations used, among other venues, for the modelling of social and epistemic notions (Negri 2021, Fellin et al. 2021). At the structural level, we show that enriching the syntax of sequents with labels for neighbourhood semantics gives an intuitionistic calculus that shares all the properties of its classical counterpart (Tesi et al. 2021).

**Ulrike Hahn (Birkbeck College London)**

Title: Norms for Real World Argumentation: Successes, Challenges and Developments

Abstract: The talk provides an overview of the development of a normative Bayesian framework for the evaluation of argument strength. It details success of this framework in explicating a variety of well-known argument schemes, and illustrates the power of the framework to elucidate argumentation. It also details directions along which such an account might be broadened to capture ever larger fragments of everyday argument.

**Olivier Roy (University of Bayreuth)**

Title: Deliberation, Coherent Aggregation, and Path Dependence

Abstract: In this talk, I will report on recent results obtained in collaboration with Soroush Rafiee Rad (UvA, Amsterdam), Maher Abou Zeid (Bayreuth), and Sebastian Braun (Bayreuth), regarding some positive and negative effects of group deliberation. In the first part, we will look at what has been called the meta-agreement hypothesis. The hypothesis states that deliberation can help avoid intransitive or cyclic group preferences by fostering the creation of meta-agreements, which should ensure single-peaked preferences. Our results provide a qualified support for the meta-agreement hypothesis. More precisely, the results point towards conditions under which deliberation does help avoiding intransitive or cyclic group preferences, either in terms of how open-minded the participants are or the number of alternatives they can choose from. The second part will look at one form of path dependence in deliberation, the so-called anchoring effect, that is when the first speakers carry substantially more weight than the others in the final result of deliberation. Our results show not only that anchoring frequently occurs. and does so in a way that is correlated with the creation of single-peaked profiles. but that it has the strongest effect on the outcome of deliberation, in comparison with other factors like expertise or the popularity of opinions. I will conclude by reflecting on balancing such positive and negative effects to arrive at a more nuanced view of what deliberation can and cannot achieve.

**Katrin Schulz (University of Amsterdam)**

Title: Attention instead of Intervention: Exploring alternatives to the interventionist approach to counterfactuals

Abstract: Traditionally, we are used to understanding counterfactual sentences in terms of the similarity approach of Lewis and Stalker. But in the last 20 years a new paradigm was set by Pearl’s interventionist approach. In this talk we will look at one central challenge to the interventionist approach and related proposals: backtracking. Backtracking refers to the fact that sometimes counterfactuals that reason from effect to cause are acceptable. In this talk I will discuss different proposals for how an interventionist approach can deal with backtracking. We will zoom in on one particular alternative: replacing intervention with attention. The idea here is that counterfactual queries are answered with respect to a submodel of the causal network that the agents are interested in. If that submodel contains the causal history of the antecedent, then backtracking can occur. Otherwise, no backtracking is possible. We will look at the viability of this approach in the face of some experimental data.