Kagaku tetsugaku
Online ISSN : 1883-6461
Print ISSN : 0289-3428
ISSN-L : 0289-3428
Formalization of Counterfactual Inference by Dynamic Logic
Yuichiro Hosokawa
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2012 Volume 45 Issue 1 Pages 17-33


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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© 2012 The Philosophy of Science Society, Japan
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