Natural Deduction for Modal Logic with a Backtracking Operator

Journal of Philosophical Logic 44 (3):237-258 (2015)
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Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. I prove soundness and completeness theorems with respect to Hodes’ semantics, as well as semantics with fewer restrictions on the accessibility relation.
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Mereology and Modality.Uzquiano, Gabriel
Bad Company Tamed.Linnebo, Øystein

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