Fausto Barbero

Fausto Barbero, Jonni Virtema

Causal multiteam semantics is a framework where probabilistic dependencies arising from data and causation between variables can be formalized together and studied logically. We discover complete characterizations of expressivity for several logics that can express probabilistic statements, conditioning and interventionist counterfactuals. The results characterize the languages in terms of families of linear inequalities and closure conditions that define the corresponding classes of causal multiteams; we find that the strict tensor disjunction, an operator typical of team semantics but absent from the literature on causation, is needed to capture the full class of all linear inequalities. The characterizations yield a strict hierarchy of expressive power and some undefinability results.

Fausto Barbero, Marianna Girlando, Valentin Müller et al.

Team semantics is a general framework where formulas are not interpreted with respect to a single point of evaluation, but with respect to sets of such points. Team semantics is used in dependence logic, to reason about dependencies between variables, and in inquisitive logic, to formalize the meaning of questions. We provide sound and complete labelled sequent calculi for four logics based on team semantics: basic inquisitive logic, propositional intuitionistic dependence logic, and their respective extensions with tensor disjunction. For technical reasons, we restrict ourselves to languages with finitely many propositional atoms. The rules of weakening, contraction and cut are shown to be admissible in each of our calculi. In the last part of the paper, we present terminating proof search procedures for variants of our proof systems, in which labels have a simplified structure.

Fausto Barbero, Katrin Schulz, Fernando R. Velázquez-Quesada et al.

This paper makes a first step towards a logic of learning from experiments. For this, we investigate formal frameworks for modeling the interaction of causal and (qualitative) epistemic reasoning. Crucial for our approach is the idea that the notion of an intervention can be used as a formal expression of a (real or hypothetical) experiment. In a first step we extend the well-known causal models with a simple Hintikka-style representation of the epistemic state of an agent. In the resulting setting, one can talk not only about the knowledge of an agent about the values of variables and how interventions affect them, but also about knowledge update. The resulting logic can model reasoning about thought experiments. However, it is unable to account for learning from experiments, which is clearly brought out by the fact that it validates the no learning principle for interventions. Therefore, in a second step, we implement a more complex notion of knowledge that allows an agent to observe (measure) certain variables when an experiment is carried out. This extended system does allow for learning from experiments. For all the proposed logical systems, we provide a sound and complete axiomatization.

Fausto Barbero, Katrin Schulz, Sonja Smets et al.

This paper proposes a formal framework for modeling the interaction of causal and (qualitative) epistemic reasoning. To this purpose, we extend the notion of a causal model with a representation of the epistemic state of an agent. On the side of the object language, we add operators to express knowledge and the act of observing new information. We provide a sound and complete axiomatization of the logic, and discuss the relation of this framework to causal team semantics.