Abstract
It has been common to formalize counterfactuals (or subjunctive conditionals) in natural language in terms of a certain binary sentential connective, as in Stalnaker [12] and D. Lewis [8]. This paper suggests that another formalization by means of unary multi-modal operators is natural and appropriate for some counterfactuals. To see this naturalness and appropriateness, we observe an instance of transitive inference constituted of three counterfactuals in natural language, and formalize it by using expressive power of multi-modal logic, in particular Hennessy-Milner logic(HML) and Dynamic logic (DL). As a result, the instance of transitive inference turns out to be justified by the multi-modalized version of the most fundamental and familiar rules of modal logic, that is, the necessitation rule (NAct) and the axiom (KAct).
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