A Multivalued Conditional Logic with Probabilistic
Interpretation for Causal Decision Theory

Franois Lepage
Dpartement de philosophie
Universit de Montral
JianYun Nie
Dept. d'informatique et R. O.
Universit de Montral

Causal decision theory has been developed to deal with rational decision making in the case
where making a decision may be seen as an indication that some outcome will obtain. It has
been suggested that counterfactual conditionals should be used in such a decision situation. The
crucial problem posed is that of calculating the probability of a counterfactual conditional. The
only technique available until now is imaging which, however, only applies to a restricted
structure of possible worlds. In order to make the causal decision theory applicable to the
general case, in this paper, we extend the imaging technique to the general structure. This
results in a logic in which counterfactual conditionals are multivalued. We further provide a
probabilistic interpretation to this logic.

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