Thinking About Causation: A Causal Language with Epistemic Operators

Abstract

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 [16,17,26,11] 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.

Characterizing counterfactuals and dependencies over causal and generalized causal teams

“…A system of functions F over σ is a function that assigns to each variable V in a domain En(F ) ⊆ Dom a set PA F V ⊆ Dom \ {V} of parents of V, and a function F V : Ran(PA F V ) → Ran(V). 5 Variables in the set En(F ) are called endogenous variables of F , and variables in Ex(F ) = Dom \ En(F ) are called exogenous variables of F .…”

“…We remark that Recur is actually a scheme of rules (one rule for each 1 < k ∈ N. Its formulation strongly depends on the finitude of the signature, but it could be in principle replaced by a more elementary rule that does not have this requirement. 15 Furthermore, the role of in the formulation of Recur could be taken instead by the relation of direct cause, as shown in [5]. Rule I is a rule of conjunction conditionalization, from which the Composition rule of [12] is derivable, as we show in the next proposition.…”

Changing Minds ― Epistemic Interventions in Causal Reasoning

“…Such a counterfactual dependence test, however, is insensitive to the agent's epistemic states: it would render the doctor a cause of the health problems, irrespective of whether or not the doctor knew about the unknown side effects of the drug. While some proposals have been made on how to integrate mental states into formal frameworks of causation (Barbero, Schulz, Smets, Velázquez-Quesada, & Xie, 2020;Halpern & Hitchcock, 2015;Quillien & German, 2021) and responsibility or blame (Chockler & Halpern, 2004;Gerstenberg, Halpern, & Tenenbaum, 2015), the general framework in its current form does not quite capture the influence of epistemic states discussed earlier (Hilton et al, 2016) -the perceived causal difference between a causal agent who is ignorant vs. knowledgeable. In this paper, we argue for counterfactual theories to extend their focus for mental states.…”