We investigate the generalization of causal models to the case of indeterministic causal laws that was suggested in Halpern (2000). We give an overview of what differences in modeling are enforced by this more general perspective, give a complete axiomatization for unnested counterfactuals in indeterministic causal models and compare it with Halpern’s deterministic version.
     We then generalize the framework to (causal) team semantics, so that it can also represent uncertainty. In this context, we see the failure of some typical laws for causal reasoning, and we present a rather different complete axiomatization of right-nested counterfactuals.
    Time permitting, we will explore the axiomatic characterizations of various subclasses of models.

Constructive and intuitionistic versions of conditional logics have recently been investigated by Weiss, Ciardelli and Liu, and Olkhovikov, with the goal of providing a constructive account of conditional reasoning. Differently from the classical case, in this framework the would and might conditional operators are no longer interdefinable. The systems considered in the literature arise by placing Chellas’ conditional logic CK – defined via selection function semantics – within the constructive and intuitionistic paradigm used for intuitionistic modal logics. This yields two systems: a would-only constructive version of CK, and an intuitionistic variant of CK featuring both might and would conditionals. Building on existing proof systems for CK and intuitionistic modal logics, we present new label-free proof systems for both logics. Guided by proof-theoretic insights, we then define CCK, a conservative extension of constructive CK with a might operator. We introduce a corresponding class of models and give an axiomatization for CCK, and we extend these results to several extensions of CCK.
    This talk is based on joint work with Tiziano Dalmonte, published in the proceedings of TABLEAUX 2025. A preprint is available at: https://arxiv.org/abs/2507.02767

Dimensions for team-based logics have been studied in the first-order setting [Hella, Luosto & Väänänen 2024], and can similarly be applied to the propositional setting. One use of dimensions is to prove inexpressibility results for reduction formulas based on the arity and number of occurrences of, for instance, a dependence atom. Furthermore, we identify natural ways to calculate the dimensions for certain types of properties, such as convex ones. Other examples are the (quasi) downward and (quasi) upward closed properties which have dual dimension results. This leads us to define and study logics that are expressively complete for the dual properties, building on results for propositional dependence logic [Yang & Väänänen 2016] and propositional inclusion logic [Yang 2022].

In truthmaker semantics, we understand propositions in terms of their truthmakers. The resulting model of propositions is more fine-grained than the standard possible-worlds model, but it is unclear how much more fine-grained. The aim of this talk is to get a handle on this question. For this, we take an algebraic approach to truthmaker propositions, where we abstract away from their internal truthmaker structure and study them in terms of the relations they bear to each other. The idea is that if we can determine the propositional (in)equalities that hold in the algebra of exact truthmaker propositions, this allows us to determine the grain of the semantics.
    The central technical question is thus: What is the algebra of truthmaker propositions? It turns out that this question is rather difficult to answer. The source of these difficulties is the behavior of negation in truthmaker semantics, which allows for two propositions to have the same truthmakers, while their negations have different truthmakers. To address these difficulties, we draw on methods from Abstract Algebraic Logic. We take as a starting point the logic of exact entailment (truthmaker preservation from premises to conclusion, studied by Fine and Jago 2019, Knudstorp 2023, and Korbmacher 2023) and consider notions of equivalence in this logic to be our guide to propositional equality.
    This approach allows us to characterize the class of algebras of truthmaker propositions in terms of an algebraic construction in terms of bisemilattices with one distributive law (Romanowska 1980). This construction allows us to prove that the algebras of truthmaker propositions form a quasi-variety, meaning that it can be defined in terms of implications of propositional equalities. It remains an open question whether the algebras form a variety, meaning that they can be defined in terms of propositional equalities alone.

We discuss the notion of semantic pollution in the context of bilateral proof systems. Semantic pollution is most commonly thought to occur in labeled proof systems, which internalize Kripke semantics in the syntax of the proof system (by formulas xRy, x:A).
    A measure that detects this type of semantic pollution checks whether the formulas from the proof system relate to the semantics in a different way than the object language. In particular, it checks whether syntax from the proof system is able to violate invariance results under (object-language) model equivalences.
    Bilateral formal systems take a notion of denial as primitive next to the usual notion of assertion. This results in an enrichment of the language of a proof system, and provides a suitable case study for semantic pollution, which has been unexplored in these systems so far. Contradictory logics seem to have an especially high likelihood to show semantic pollution when their proof systems are bilateral – we will discuss some results for paraconsistent Nelson’s logic N4, and contradictory Abelian logic A.

The languages of logics based on team semantics typically only allow atomic negation or restricted negation. In this talk, we demonstrate that including full (intutionistic) negation does not complicate the axiomatization of propositional team logics with the downward closure property. We also review known expressive completeness results for these logics, highlighting how relevant complemented properties are expressed in propositional dependence logic without directly using negation. Building on these insights, we prove a new result: propositional logic extended with both dependence and inclusion atoms is expressively complete.