  Counterfactual reasoning -- envisioning hypothetical scenarios, or possible
worlds, where some circumstances are different from what (f)actually occurred
(counter-to-fact) -- is ubiquitous in human cognition. Conventionally,
counterfactually-altered circumstances have been treated as "small miracles"
that locally violate the laws of nature while sharing the same initial
conditions. In Pearl's structural causal model (SCM) framework this is made
mathematically rigorous via interventions that modify the causal laws while the
values of exogenous variables are shared. In recent years, however, this purely
interventionist account of counterfactuals has increasingly come under scrutiny
from both philosophers and psychologists. Instead, they suggest a backtracking
account of counterfactuals, according to which the causal laws remain unchanged
in the counterfactual world; differences to the factual world are instead
"backtracked" to altered initial conditions (exogenous variables). In the
present work, we explore and formalise this alternative mode of counterfactual
reasoning within the SCM framework. Despite ample evidence that humans
backtrack, the present work constitutes, to the best of our knowledge, the
first general account and algorithmisation of backtracking counterfactuals. We
discuss our backtracking semantics in the context of related literature and
draw connections to recent developments in explainable artificial intelligence
(XAI).
