Expanding Causal Modelling Semantics

(Philosophy of Science, )

ausal Models allow us to represent the structure of a system of variables and draw inferences about causal connections among variables in the system. Pearl (2000) and Galles&Pearl (1998) have shown how to construct a semantics for counterfactuals based on causal models, call it CMS. According to CMS, a counterfactual A > B is true at a causal model M, iff it is true at M_A_ where M_A_ is the model obtained by the intervention do(A) on M, where do(A) on a model M is manipulation on the structure of M that makes A true at M. However, CMS fails to assign a truth value to counterfactuals with disjunctive antecedents of the form (A or B) > D , since do(A or B) is not well defined.

A solution to the limited expressive power of CMS is provided by Briggs (2012). Briggs' main innovation to CMS lies in the application of Kit Fine's truthmaker semantics in order to define disjunctive interventions of the form do(A or B).

According to CMS, we can also calculate the probability of a counterfactual A > B at a model M as the probability of B obtaining in the submodel generated by the intervention do(A) on M . But again, in standard CMS, counterfactuals with disjunctive antecedents fail to have a probability. I propose that in order to calculate the probability of such counterfactuals, we should assign a likelihood to the submodels generated by a disjunctive intervention as defined by Briggs. The intuition is that we can employ Lewis_ idea of similarity among possible worlds and equip causal models with a similarity order as well; having this order, we can measure the likelihood of causal models according to their similarity: the more similar to M a model is, the more likely it is.

Eva et al. (2019) have introduced some procedures to measure the similarity distance among causal models. I propose that the likelihood of the submodels of a model M should intuitively be inversely proportional to the similarity distance from M (in the sense of Eva et al.): the more distant from M a model is, the less likely it is. So, the probability of a counterfactual (A or B) > B at M can be calculated as the sum of the probabilities that B gets assigned at each submodel of M generated by do(A or B) weighted by the likelihood of that submodel.

In conclusion, by combining Briggs_ semantics with the work of Eva et al., we can expand CMS to account for the probability of counterfactuals with disjunctive antecedents.

Briggs, R., (2012), ``Interventionist Counterfactuals'',Philosophical Studies, 160(1):139--166.

Eva, B., Stern, R., Hartmann, S., (2019), ``The Similarity of Causal Structure'', Philosophy of Science, 86(5):821-835.

Galles, D., Pearl, J. (1998), ``An Axiomatic Characterization of Causal Counterfactuals'', Foundations of Science, 3(1), 151--182.

Pearl, J., (2000),Causality: Models, Reasoning and Inferences, Cambridge University Press.

Chair: Andelija Milic

Time: 16:00-16:30, 09 September 2021 (Thursday)

Location: SR 1.006

Remark: (Online Talk)

Giuliano Rosella

(University of Turin, Italia)

I am a Ph.D. student in Philosophy at the University of Turin, in the context of FINO (Northwestern Italian Philosophy Consortium).

My research interests focus on Logic, Philosophical Logic and Theories of Causality.

Prior to my Ph.D., I completed a Master's Degree in Logic at the Institutite of Logic, Language and Computation (ILLC) of the University of Amsterdam and a Bachelor's Degree in Philosophy at the University of Trento as a pupil of Collegio Bernardo Clesio. During my undergraduate studies, I spent a research period at the Faculty of Humanities of the University of Amsterdam.

I am currently a Visiting Ph.D. student at Hamburg University in the Relevance - Emmy Noether Group.

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