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Expressivity Landscape for Logics with Probabilistic Interventionist Counterfactuals

Authors Fausto Barbero , Jonni Virtema

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ACM Subject Classification
  • Computing methodologies → Probabilistic reasoning
  • Mathematics of computing → Causal networks
Keywords
  • Interventionist counterfactuals
  • Multiteam semantics
  • Causation
  • Probability logic
  • Linear inequalities
  • Expressive power

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Abstract

Causal multiteam semantics is a framework where probabilistic dependencies arising from data and causation between variables can be together formalized 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 equations and closure conditions that define the corresponding classes of causal multiteams. The characterizations yield a strict hierarchy of expressive power. Finally, we present some undefinability results based on the characterizations.

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Fausto Barbero and Jonni Virtema. Expressivity Landscape for Logics with Probabilistic Interventionist Counterfactuals. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CSL.2024.15

Author Details

Fausto Barbero
  • University of Helsinki, Finland
Jonni Virtema
  • University of Sheffield, UK

Funding

  • Barbero, Fausto: DFG grant VI 1045-1/1; Academy of Finland grants 316460 and 349803
  • Virtema, Jonni: DFG grant VI 1045-1/1; Academy of Finland grant 345634

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