Abstract
A formal theory of causal reasoning is presented that encompasses both Pearl’s approach to causality and several key formalisms of nonmonotonic reasoning in Artificial Intelligence. This theory will be derived from a single rationality principle of causal acceptance for propositions. However, this principle will also set the theory of causal reasoning apart from common representational approaches to reasoning formalisms.
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Notes
This will also mean that our theory should not be viewed as an ‘explication’ of our commonsense understanding of causation (if there is such a thing today).
Some of these philosophical studies, however, also curiously reinforced these connections by viewing, for instance, inference or explanation as a proper replacement (or disambiguation) for the philosophically problematic notion of causation.
Thus, causal relata are propositions in our theory, in contrast to some other approaches that take such relata to be events, properties, or even variables.
We assume that the labels of associated propositions are self-explanatory.
Cf. (Prawitz, 2019) for a similar point.
In order to simplify the notation, causal rules \(a{{\,\mathrm{\Rightarrow }\,}}A\) are used in what follows both as formal objects of our theory and as statements in the meta-language (saying that a causes A).
For instance, A can directly cause B, though there are no intermediate causes between A and B. In this case, B will belong to \({{\,\mathrm{\mathcal {C}}\,}}(A)\), though not to \({{\,\mathrm{\mathcal {C}}\,}}({{\,\mathrm{\mathcal {C}}\,}}(A))\).
See, e.g., (Denecker et al., 2015) for an abstract theory of justifications in nonmonotonic reasoning.
In clear contrast both with modern proof-theoretic and inferentialist approaches in which the reducibility of the logical language to its atomic (pre-logical) basis is commonly viewed as an important desideratum.
Pearl has also called it a causal model, but this would conflict with our terminology.
This description presupposes a token interpretation of structural equations as expressing relations among their instantiations, as opposed to a type-level interpretation according to which a structural equation expresses a direct causal relation among variables themselves.
Note also that this refutation does not always change the acceptance status of the effect E, since E can also have other causes.
Just as it happened once in geometry.
It is essentially this idea that lies at the basis of one of the first formalisms of nonmonotonic reasoning in AI, namely circumscription of McCarthy (1980).
See (Denecker et al., 2015).
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I would like to thank the anonymous reviewers for their instructive comments, requests, and suggestions. They contributed a lot to the final form of this paper.
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