Journal of Philosophical Logic 44 (3):237-258 (2015)

Authors
Jonathan Payne
University of Sheffield (PhD)
Abstract
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.
Keywords Modal logic  Backtracking  Natural deduction
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DOI 10.1007/s10992-014-9316-8
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Bad Company Tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.
Plural Quantification and Modality.Gabriel Uzquiano - 2011 - Proceedings of the Aristotelian Society 111 (2pt2):219-250.
Mereology and Modality.Gabriel Uzquiano - 2014 - In Shieva Kleinschmidt (ed.), Mereology and Location. Oxford University Press. pp. 33-56.

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